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EX-MERIDIAN 

ALTITUDE,  AZIMUTH  AND  STAR-FINDING 

TABLES 

WITH  DIAGRAMS  FOR  FINDING  THE  LATITUDE 
AND  FACILITATING  PLOTTING  LINES  OF  POSI- 
TION AND  GIVING  NEW  AND  PRACTICAL  METHODS 
FOR   IDENTIFYING    STARS    IN    CLOUDY  WEATHER 

LATITUDES  0°-65°;  DECLINATIONS  0°-71°  NORTH  AND  SOUTH 


BY 
LIEUTENANT-COMMANDER 

ARMISTEAD    RUST 

U.  S.  NAVY 


FIRST  EDITION- 
FIRST  THOUSAND 


NEW   YORK 

JOHN    WILEY    &    SONS 

London:  CHAPMAN  &  HALL,  Limited 

1908 


BENEHA. 


Copyright,  1908, 

BV      ^ 

ARMISTEAD  RUST 


1/^^^" 


Stanhope  iprcss 

F.    H.   CILSON     COMPANY 
BOSTON.      U.S    A 


<,^«< 


PREFACE 


In  these  Tables  I  have  followed  the  arrangement  of  ordinary  Azimuth 
Tables  as  that  most  convenient  to  Navigators,  the  plan  adopted  by  Lieu- 
tenant J.  F,  R.  Bateman,  Royal  Navy,  and  Captain  James  Bairnson  in 
their  excellent  works.  Other,  arrangements  might  have  made  the  book 
smaller,  but  at  the  same  time  not  so  convenient. 

As  this  is  not  a  text-book,  I  have  not  taken  up  spfice  with  rules  for  the 
conversion  of  time,  finding  hour  angles,  and  for  plotting  lines" of  position 
by  the  usual  methods  familiar  to  Navigators,  which  may  be  found  in  any 
work  on  navigation.  Attention,  however,  is  called  to  the  use  of  Ex- 
Meridian  Tables  in  connection  with  Commandant  Marcq  Saint-Hilaire's 
method,  the  "New  Navigation."  In  this  method  the  "Reduction  to  the 
Meridian"  is  added  to  the  meridian. zenith  distance  to  obtain  the  calculated 
zenith  distance.  For  a  full  explanation  the  reader  is  referred  to  "  Naviga- 
tion and  Nautical  Astronomy,"  by  Staff-Commander  W.  R.  Martin,  Royal 
Navy;  "Navigation  and  Compass  Correction,"  by  Commander  W.  C.  P. 
Muir,  U.  S.  Navy,  and  "  Explanation  of  the  Method  of  the  New  Naviga- 
tion," by  Naval  Instructor  J.  R.  Walker,  Royal  Navy. 

Every  care  has  been  taken  to  guard  against  errors,  .and  the  tabulated 
"First  Reductions"  have  been  compared,  as  far  as  practicable,  wtth  the 
results  given  in  Bairnson 's  Tables  and  othev  works. 

The  methods  for  the  identification  of  stars  here  given  are  very  simple 
and  will  at  times  be  found  most  useful. 

In  the  accompanying  plates  I  have  introduced  a  number  of  new  dia- 
grams which  I  believe  will  be  found  upon  trial  more  convenient  than  the 
corresponding  tables,  which  in  some  cases  have  been  also  inserted.  In 
using  the  plates  no  interpolation  is  necessary. 

A  few  examples  have  been  worked  to  illustrate  the  use  of  the  various 
tables  and  diagrams. 

In  the  preparation  of  this  book  and  plates  I  have  to  acknowledge  the 
assistance  received  from  the  following  works: 

Chauvenet's  "Astronomy;"  Chauvenet's  "Trigonometry." 

Rice  and  Johnson's  "Differential  Calculus." 

Bairnson 's  "Ex-Meridian  Tables." 

"Short  Method  Ex-Meridian  Tables,"  by  Lieutenant  J.  F.  R.  Bateman, 
R.N. 

"Notes  on  Navigation,"  by  Commander  P.  F.  Harrington,  U.  S.  Navy. 


Cofl&n's  "  Navigation. 


ui 


190830 


iv  PREFACE 

Bowditch's  "American  Practical  Navigator." 

"Azimuth  Tables,"  —  Hydrographic  Office. 

"Ex-Meridian  Tables,"  by  Brent,  Walter,  and  Williams. 

Chambers'  "Mathematical  Tables." 

"The  Practice  of  Navigation, "  by  Lieutenant  Henry  Raper,  Royal  Navy. 

"Navigation  and  Nautical  Astronomy,"  by  Staff-Commander  W.  R. 
Martin,  R.N. 

"A  Companion  to  the  Epitome  of  Navigation,"  by  Captain  H.  S.  Black- 
burne. 

"Navigation  and  Nautical  Astronomy,"  by  J.  Gill,  F.R.A.S. 

"Ex-Meridian  Tables  for  Sun  or  Star,"  by  Captain  A.  J.  MacHattie. 

"Navigation  and  Compass  Correction,"  by  Commander  W.  C.  P.  Muir, 
U.  S.  Navy. 

Lee ky 's  "  General  Utility  Tables. ' ' 

"Nautical  Tables  for  Ex-Meridian  Observations,"  by  Bossen  and  Mars. 

"Solving  the  Ex-Meridian  Problem  on  Kinematic  Principles,"  by  H.  B. 
Goodwin,  Royal  Navy. 

This  last  book  was  received  as  these  Tables  were  going  to  press,  and  I 
find  that  Table  V  is  practically  the  same  as  the  table  given  by  Mr.  Good- 
win.    His  rules  for  finding  the  "First  Reduction"  are: 

"(1)  With  latitude,  declination,  and  half  hour  angle,  take  from  the 
Azimuth  Tables  of  Burdwood,  Davis,  or  Goodwin  the  approximate 
Azimuth. 

"(2)  With  the  Azimuth  so  obtained,  and  latitude,  take  out  'rate  of 
change  '  from  the  Table. 

"  (3)  Multiplying  this  rate  by  the  number  of  minutes  of  time  in  the 
whole  hour  angle  we  have  the  'Reduction.'  " 

It  may  be  shown  from  formulas  (22)  and  (23)  that  Ci     =  h  Ct^  hence, 

2 

A,/i  =  C/  X  I  =  i  C/  X  f  =  C/  X  t,  that  is,  rule  (3)    gives  the  same 

2 

value  for  the  "First  Reduction"  as  that  given  in  the  text. 

Mr.  Goodwin's  pamphlet  will  be  found  a  most  useful  addition  to  the 
library  of  every  Navigator. 

For  the  Table  giving  the  values  of  "B"  used  in  the  identification  of 
stars,  I  am  indebted  to  Professor  H.  L.  Rice,  U.  S.  Navy,  and  also  for 
the  formula  by  which  Table  VII  was  computed,  and  to  Commanders 
W.  C.  P.  Muir  and  T.  C.  Fenton,  U.  S.  Navy,  for  reviewing  the  text. 

Armistead  Rust, 

Washington,  D.  C,  July  25,  1908.  Lieul.-Commander,  U.  S.  Navy. 


CONTENTS. 


PAGE 

Explanation  of  the  Tables vii 

Explanation  of  the  Plates ix 

Use  of  the  Tables x 

Use  of  the  Plates xiii 

Table         I.  —  Logarithms  of  Numbers  from  0  to  999 xi,  xxvii 

Table       II.  —  For  Correcting  the   Observed  Altitudes  of  the  Sun  and 

Stars xi,  xxix 

Table      III.  —  Correction  for  Height  of  Eye  of  Observer xxx 

Table      IV.  —  Correction  for  the  Sun's  Semi-Diameter xxx 

Table  V.  —  Altitude-Azimuth  Table,  and  the  Error  in  the  First 
Reduction  Due  to  an  Error  of  One  Minute  in  the  Hour 
Angle viii,  xii,  xxxi 

Table      VI.  —  Error   in  the  First  Reduction  Due  to  an  Error  in  the 

Latitude  Used  in  Computation viii,  xii,  xxxviii 

Table     VII.  —  Error  in  the  Latitude  Due  to  an  Error  in  the  Latitude 

Used  in  the  Computation viii,  xiii,  xxxix 

Table  VIII.  —  For  Converting  Arc  to  Time  and  Time  to  Arc xl 

Table      IX.  —  Hour  Angles  and  Altitudes  at  Prime  Vertical  Transit.  .  .xxi,  xiii 

Plate         I.  —  Diagram  for  the  Second  Reduction  to  the  Meridian  . . . .  ix,  xiii 

Plate       II.  —  Altitude- Azimuth  Diagram ix,  xiii 

Plate      III.  —  Time-Azimuth  Diagram ix,  xv 

Plates  IV  and  V.  —  Error  in  the  Latitude  Due  to  an  Error  of  One  Min- 
ute OF  Time  in  the  Hour  Angle,  or  Longitude.,  .ix,  xvii 

Plate      VI.  —  Star-Finding  Diagram ix,  xviii,  xix,  xx 

Azimuth,  How  to  Find xii 

Change  of  Altitude  in  One  Minute,  How  to  Compute,  Formula  (22) xii 

Equation  of  Equal  Altitudes xv,  xvii 

First  Reduction,  To  Compute,  Formulas  (6)  and  (23) vii,  xii 

First  Reduction,  Tables  for 1-393 


VI  C0-\  TENTS 

PAGE 

Hour  Angle  and  Latitude,  To  Find,  when  the  Time  is  not  Known,  For- 
mula (25) xiv 

Lines  of  Position,  How  to  Plot xvii 

Longitude  from  Ex-Meridian  Observations,  Formulas  (4)  and  (25).  .  .xiv,  xxiv 

Stars,  Identification  of,  in  Cloudy  Weather xviii,  xix,  xx 

Stars,  To  Identify  with  the  Aid  of,  a  Great  Circle  Sailing  Chart xxi 

Second  Reduction  to  the  Meridian viii,  xiii 

N.  B. — The  plates  will  be  found  at  the  end  of  the  volume.  WTiile  it  is  not  advisable 
to  remove  the  plates  from  the  book  for  fear  of  losing  them,  it  will  be  found  convenient 
in  practice  and  tend  to  preserve  the  plates  to  have  an  extra  set  pasted  on  heavy  card- 
board for  every-'day  use. 

Additional  sets  of  plates  may  be  obtained  for  $1.00  per  set. 


Explanation  of  the  Tables, 

In  the  astronomical  triangle  PMZ,  P  is  the  elevated  pole,  M  the  position  of 
the  observed  body,  Z  the  zenith  of  the  observer,  L  his  latitude,  d  the  declination 
and  h  the  altitude  of  the  observed  body;  90°  —  /i  =  the  zenith 
distance  of  this  body.  Let  ho  =  the  meridian  altitude  of  M, 
then  90°  —  ho  =  meridian  zenith  distance  of  M. 

The  reduction  to  the  meridian  is  that  arc  which  applied  to  the 
true  altitude  of  an  observed  body  will  give  the  meridian  altitude 
of  that  body  at  the  place  of  observation. 

Delambre's  formula  for  the  reduction  to  the  meridian  is: 


(1)  Reduction  to  the  meridian  (in  seconds  of  arc)  = 

cos  L  cos  d  \'  ^  2  sin^  §  t  cot  (L  T  d) 

> 

sin  1" 


cos  L  cos  d     2  sin-  h  t 


sin  {L  +  d)       sin 


■ht  _  I  cos  L  cos  d  Y    : 
\"       \sin(L4"f/)/ 


Fig.  1. 


where  t  is  in  seconds  of  time. 

The  positive  sign  for  the  first  term  corresponds  to  an  observation  near  the  upper 
transit  and  the  negative  sign  to  an  observation  near  the  lower  transit,  when  the 

hour  angle  is  reckoned  from  the  lower  branch  of  the  meridian.     The  upper  sign 

^^ 
in  the  expression   (L  +  cf)   for  the  zenith  distance  corresponds  to  a  case  when 
the  latitude  and  the  declination  are  the  same  name,  and  the  lower  sign  when  they 
are  of  contrary  names,  or  for  lower  transit. 

The  first  term  of  (1)  is  the  first  reduction  tn  thp  mprirHar.  onri  fV,o  £,««^^^  +«-«^ 


ERRATA. 

Page  vii,  line  18,  insert  comma  after  "upper  transit,"  and  in  line  19  omit  comma 
after  "lower  transit." 

Page  X,  line  6  from  bottom,  insert  semicolon  after  "observed  body." 
Page  xii,  last  line,  "  latitude  "  should  be  "  altitude." 
Page  xxiv,  line  2,  "  Eriadni "  should  be  "  Eridani." 


xvaper  s  lormuia  lor  tne  second  reduction  to  the  meridian  is 
(7)  Sin  (second  reduction)  =  K  sin^  A  «/i  tan  ho  =  0, 
where  iv  is  a  constant  and  log  K  =  9.6990;  hence, 

vii 


PAGE 

Hour  Angle  and  Latitudk,  To  Find,  when  the  Time  is  not  Known,  For- 
mula (25) xiv 

Lines  of  Position,  How  to  Plot xvii 

Longitude  from  Ex-Meridian  Observations,  Formulas  (4)  and  (25).  ..xiv,  xxiv 

Stars,  Identific.\tion  of,  in  Cloudy  Weather xviii,  xix,  xx 

Stars,  To  Identify  with  the  Aid  of,  a  Great  Circle  Sailing  Chart xxi 

Second  Reduction  to  the  Meridian viii,  xiii 

N.  B. — The  plates  will  be  found  at  the  end  of  the  volume.  While  it  is  not  advisable 
to  remove  the  plates  from  the  book  for  fear  of  losing  them,  it  will  be  found  convenient 
in  practice  and  tend  to  preserv^e  the  plates  to  have  an  extra  set  pasted  on  heavy  card- 
board for  everj'-day  use. 

Additional  sets  of  plates  may  be  obtained  for  $1.00  per  set. 


Explanation  of  the  Tables* 

In  the  astronomical  triangle  FMZ,  P  is  the  elevated  pole,  M  the  position  of 
the  observed  body,  Z  the  zenith  of  the  observer,  L  his  latitude,  d  the  declination 
and  h  the  altitude  of  the  observed  body;  90°  —  h  =  the  zenith 
distance  of  this  body.  Let  ho  =  the  meridian  altitude  of  M, 
then  90°  —  ho  =  meridian  zenith  distance  of  M. 

The  reduction  to  the  meridian  is  that  arc  which  applied  to  the 
true  altitude  of  an  observed  body  will  give  the  meridian  altitude 
of  that  body  at  the  place  of  observation. 

Delambre's  formula  for  the  reduction  to  the  meridian  is: 


(1)  Reduction  to  the  meridian  (in  seconds  of  arc)  = 
/  cos  L  cos  I 
\sin  (L  +  c 


cos  L  cos  d     2sin^J_i 


cos  L  cos  d  y    2  sin*  ^  t  cot  (L  +  d) 
)X  > 

I)  I  sin  1" 


Fig.  1. 


sin  {L  -\-  d)       sin  1" 

where  t  is  in  seconds  of  time. 

The  positive  sign  for  the  first  term  corresponds  to  an  observation  near  the  upper 
transit  and  the  negative  sign  to  an  observation  near  the  lower  transit,  when  the 

hour  angle  is  reckoned  from  the  lower  branch  of  the  meridian.     The  upper  sign 

'^ 
in  the  expression   (L  +  d)   for  the  zenith  distance  corresponds  to  a  case  when 
the  latitude  and  the  declination  are  the  same  name,  and  the  lower  sign  when  they 
are  of  contrary  names,  or  for  lower  transit. 

The  first  term  of  (1)  is  the  first  reduction  to  the  meridian  and  the  second  term 
the  second  reduction : 

(2)  Reduction  to  meridian  =  ±  first  reduction  —  second  reduction.     If  t  be 
expressed  in  minutes  of  time,  the  first  reduction  may  be  reduced  to  the  form 


(3)  First  reduction  =  ± 
Let  t  =  \  minute. 


r^  96349  cos  L  cos  d 
sin  (L  +  c?) 


Y.&. 


(4)  First  reduction  =  A  ./t  =  ±  1^96349  cos^L  cos  (^ 

sin  (L  +  d) 

=  change  in  altitude  in  one  minute  from  meridian  passage  in  seconds  of  arc; 
A  i/i  is  constant  for  any  given  latitude  and  declination.     Then  for  any  hour  angle  t 

(5)  First  reduction  =  ±  A  ,/i  x  i^  in  seconds  of  arc. 
Let  A  (/i  =  first  reduction  in  minutes  of  arc,  then 

A  i/i  X  V' 
''       60 

Raper's  formula  for  the  second  reduction  to  the  meridian  is 
(7)  Sin  (second  reduction)  =  K  sin^  A^/i  tan  ho=  0, 
where  K\s  a,  constant  and  log  K  =  9.6990;  hence, 

vii 


(6)  .\  h 


viii  EXPLANATION  OF  THE  TABLES 

(S)  Second  reduction  =  sin~'  0  and 

(9)  Reduction  to  the  meridian  =   ±  A,h  —  sin~'  0. 

The  values  of  a  (A  are  given  in  the  tables  opposite  the  respective  hour  angles, 
in  minutes  and  seconds,  and  Plate  I  gives  the  values  of  the  second  reduction 
corresponding  to  any  given  meridian  altitude  and  first  reduction. 

TABLE   V. 

Altitude-Azimuth  Table. 

From  this  table  the  true  azimuth  may  be  obtained  from  the  change  of  altitude 
in  one  minute. 

From  No.  285,  Chauvenet's  Trigonometry  (10th  edition),  we  have: 

(10)  A/i  =  cosZaL  +  cos  M  Ad  —  cosLsinZAf. 
Let  L  and  d  be  constant,  then 

(11)  Ah  =  —  cos  L  sin  Z  At.     U  At  =  one  minute  in  time,  we  have 

(12)  Ah  =  —  15  cos  L  sin  Z,  corresponding  to  the  hour  angle  <,  which  gives  the 
azimuth  Z. 

Denote  this  value  oi  Ah  by  Ct\  then 

(13)  Ct^  =  —  15  cos  L  sin  Z  =  the  change  in  altitude  in  one  minute  corre- 
sponding to  the  hour  angle  t,  which  is  also  the  error  in  the  altitude  or  the  first 
reduction  due  to  an  error  of  one  minute  in  the  hour  angle  at  the  hour  angle  t  corre- 
sponding to  the  azimuth  Z. 

Table  V  was  computed  from  formula  (13).     When  Z  =  90°; 
(13a)  CV   =  -  15  cos  L. 

TABLE  VL 

Error  int  the  First  Reduction  due  to  an  Error  in  the  Latitude  used  in 

THE  Computation. 

This  table  was  computed  from  the  formula 

(14)  Ah  =  aL  (1  —  cosZ)  derived  from  the  formula  for  Table  VIL 

TABLE  VIL 

Error  in  the  Latitude   due  to  an  Error  in  the  Latitude  used  in  the 

Computation. 

The  formula  deduced  by  Professor  H.  L.  Rice,  U.  S.  Navy,  is 

Z  (  Z) 

(15)  A Li  =  2 A Lo  sec  Z  sin^  -<l  +  aL, tan  h  cos^  —  >  , 

h  being  the  observed  altitude.  aLo  in  the  parenthesis  must  be  expressed  in 
radians.  For  the  practical  purposes  of  navigation  at  sea  we  may  neglect  the 
second  term  in  the  parenthesis,  and  we  have 

(16)  aLi  =  2  aL<,  sec  Z  sin^  —  ,  from  which  Table  VII  was  computed.     In  this 

formula  A  Le  =  the  difference  between  the  latitude  by  observation  and  the  latitude 
by  dead  reckoning. 

aL,  =  correction  to  be  applied  to  the  computed  latitude. 


EXPLANATION  OF  THE  PLATES  ix 

Explanation  of  the  Plates. 

PLATE  I. 

Diagram  for  the  Second  Reduction  to  the  Meridian. 

This  diagram  shows  the  value  of  the  second  reduction  computed  by  Raper's 
formula :  sin  (second  reduction)  =  K  sin'  (first  reduction)  X  tan  (meridian  altitude) , 
where  log  K  =  9.6990. 

PLATE   II. 

Altitude-Azimuth  Diagram. 

This  diagram  expresses  graphically  formula  (13),  (23)  and  Table  V,  and  may  be 
used  with  Prestel's  method  for  finding  the  approximate  latitude  near  the  prime 
vertical. 

PLATE   III. 

Time-Azimuth  Diagram. 

We  have  from  (11)  A/i  =  —  cos  L  sinZ  Af. 
Let  A/i  =  1'  of  arc,  then 

(17)  A<  =  —  4  sec  L  cosec  Z,  where  Aiis  the  number  of  seconds  of  time  neces- 
sary to  change  the  altitude  one  minute.     Plate  III  shows  formula  (17). 

PLATES  IV  AND  V. 

Error  in  the  Latitude  due  to  an  Error  of  One  Minute  of  Time  in  the  Hour 

Angle  or  Longitude. 

We  have  (11)  A  A  =  —  cos  L  sin  Z  /\t;  if  A  <  =  1  minute  in  time,  Ah=  —  15  cos  L 
sin  Z ;  but  A  L  =  sec  Z  A  h,  hence 

(18)  aL  =  —  15  cos  L  tan  Z.  Plates  IV  and  V  were  constructed  by  this 
formula. 

PLATE  VI. 

Stae-finding  Diagram. 

Represents  the  formulas 

(19)  Sin  Z  cos  h  =  sin  t  cos  d; 

(20)  Sin  Z  cos  L  =  sin  .1/  cos  d. 

To  find  the  Star's  Declination  from  the  Diagram. 

Enter  with  the  azimuth  on  the  margin;  the  intersection  of  the  horizontal  line 
through  this  point  with  the  curve  corresponding  to  the  true  altitude  fLxes  a  verti- 
cal line  the  intersection  of  which  with  the  horizontal  line  corresponding  to  the 
hour  angle  previously  found,  determines  the  curve  corresponding  to  the  declination 
of  the  body. 


USE  OF  THE  TABLES 


The  Use  of  the  Tables^ 

To  find  the  latitude  it  is  necessary  to  know 

1.  The  latitude  by  dead  reckoning  =  L. 

2.  The  declination  at  time  of  observation  =  d. 

3.  The  hour  angle  at  time  of  observation  =  t. 

4.  The  true  altitude  of  the  observed  body  =  h. 

The  reduction  to  the  meridian  is  that  arc  which  applied  to  the  true  altitude  of 
an  observed  body  will  give  the  meridian  altitude  of  that  body  at  the  place  of 
observation. 

Afh  =  the  first  reduction  to  the  meridian,  in  minutes,  for  the  hour  angle  of 
observation,  t. 

(2)    Reduction  to  meridian  =  ±  first  reduction  —  second  reduction. 
Reduction  to  meridian  =  ±  A  «/i  —  second  reduction. 

The  first  reduction,  Afh,  is  found  on  the  page  for  the  latitude  by  dead  reckon- 
ing (to  the  nearest  degree),  under  the  declination  of  the  body  (to  the  nearest 
degree),  and  opposite  the  hour  angle. 

If  the  exact  hour  angle  is  not  found  in  the  table,  correct  by  simple  interpolation 
for  the  odd  minutes  and  decimals. 

The  correction  thus  found  will  be  sufficiently  exact  for  practical  purposes, 
except  when  the  meridian  zenith  distance  is  small  or  the  hour  angle  large;  then 
the  hour  angle  must  be  corrected  by  Table  V,  or  it  may  be  readily  computed  by 
formula : 

(6)     A  J^  =   ±  —^^. 

Formula  (6)  may  be  used  to  find  the  first  reduction  when  the  hour  angle  of  the 
body  exceeds  the  tabular  hour  angle. 

Aj/i  =  the  change  in  altitude  in  one  minute  from  meridian  passage  with  its 
logarithm,  is  given  for  this  purpose ;  then 

(21)    Log  A, A  =  2  log  i  +  log  A,;i  +  8.22185  (colog  60). 

When  very  exact  results  are  desired  the  corrections  for  the  minutes  of  declina- 
tion and  latitude  may  be  made  with  the  aid  of  Table  VL 

In  each  column  of  declination  is  given  the  "limit"  of  the  hour  angle  for  which 
the  value  of  the  second  reduction  is  less  than  one  minute,  about  45  seconds.  The 
second  reduction,  however,  may  be  readily  found  from  Plate  I  by  entering  with 
the  meridian  altitude  at  the  bottom  and  the  first  reduction  on  the  curves.  The 
meridian  altitude  is  given  in  each  column  of  declination  for  this  purpose. 

When  the  altitude  was  observed  near  the  upper  transit,  add  the  reduction  to 
the  meridian  to  the  true  altitude  of  the  observed  body  when  near  the  lower  transit, 
subtract  the  reduction  (first  and  second  combined)  from  the  true  altitude;  the 
result  is  the  meridian  altitude  of  the  body  at  the  place  of  observation,  and  if  the 
sun  was  observed,  the  latitude  found  must  be  corrected  for  the  run  to  noon  in 
order  to  find  the  latitude  at  noon. 


USE  OF  THE  TABLES  xi 

TABLE  I. 

Logarithms  of  Numbers  from  0  to  999. 

This  table  may  be  used  to  find  the  logarithm  of  a  number  of  five  figures  or  to 
find  to  five  places  the  number  corresponding  to  any  given  logarithm  by  using  the 
proportional  parts. 

To  find  the  logarithm  of  a  number  of  five  figures. 

Rule.  To  the  logarithm  of  the  first  three  figures  add  the  product  of  the  last 
two  figures  multiplied  by  the  proportional  part  found  opposite  the  first  three 
figures  after  pointing  off  seven  places  from  the  right. 

ExAMPL^ :  —  Find  the  logarithm  of  35.674. 

35.6         log    1.55145  .00122 

.00090  .U 

35.674     log   1.55235  488 

854 
.0009028 

Rule.   To  find  to  five  places  the  number  corresponding  to  a  given  logarithm. 

Find  the  logarithm  next  less  than  the  given  logarithm  and  take  out  the 
corresponding  number  for  the  first  three  figures.  Subtract  this  logarithm  from 
the  given  logarithm  and  divide  the  remainder  by  the  proportional  part  opposite 
the  first  three  figures,  to  two  places,  and  annex  the  quotient  to  the  right  of  the 
three  figures  already  found ;  point  off  from  the  left  the  whole  number  determined 
by  the  characteristic. 

Example:  —  Find  the  number  corresponding  to  log  3.79643. 

6250.0  log   3.79588  f5  =     73     . 

6257.8  log   3 . 79643  (given) 

Diff.  55  Required  number  =  6257.8 

TABLES  II,  III,  IV. 

For  correcting  the  observed  altitudes  of  the  sun  and  stars.  First  apply  the 
index  correction,  then  the  corrections  from  the  tables. 

TABLE  V. 

Altitude-Azimuth  Table  and  the  Error  in  the  First  Reduction  due   to 
AN  Error  of  One  ^Minute  in  the  Hour  Angle. 

To  find  the  azimuth. 

It  is  necessary  to  know  the  change  of  altitude  in  one  minute  corresponding  to  the 
hour  angle  of  observation.     Now  we  have 

A  h  y.  t^ . 

(6)    Afh  =  ±:  — ^—— —  in  minutes  of  arc,  t  being  in  minutes  of  time. 
60 

Differentiating,  A  ^h  being  constant, 

d(A,h)=±^^^  dt. 


xii  USE  OF  THE  TABLES 

If  (It  =  1  minute  of  time,  then  d  (A,/i)  =  ±  — ^— —  =  the  change   in  altitude  in 

one  minute  or  rate  of  change  per  minute  corresponding  to  the  hour  angle  t  and 
the  azimuth  Z. 

Denote  this  by  Ct\    Then 

(22)  C.'  =  ±  ^j^  ; 

hence  to  find  the  change  of  altitude  in  one  minute,  multiply  the  change  of 
altitude  in  one  minute  from  meridian  passage  ( A  ^h)  for  the  given  latitude  and 
declination  by  the  hour  angle  in  minutes  and  decimals  and  divide  by  30.     With 
this  number,  C«',  enter  Table  V  or  Plate  II  with  the  latitude  for  the  azimuth. 
The  first  reduction  may  also  be  found  thus: 

(6)  A,;i  =  ±  AA^'  =  ±  AA^  X  4  ;  hence  from  (22) 

bO  60  z 

(23)  Ath=  ±C«'X  I  . 

Therefore,  find  the  change  in  altitude  in  one  minute  corresponding  to  the 
whole  hour  angle  of  the  body  and  multiply  this  by  one-half  of  the  hour  angle  of 
the  body. 

If  the  declination  is  used  instead  of  the  latitude,  the  position  angle,  AI,  will 
be  found  in  place  of  the  azimuth  in  Table  V  and  Plate  II. 

Table  V  also  shows  the  error  in  the  first  reduction  or  the  altitude  due  to  an 
error  of  one  minute  in  the  hour  angle,  and  may  therefore  be  used,  when  the 
azimuth  is  known,  for  correcting  the  first  reduction  for  the  odd  minutes  and 
decimals  of  hour  angle.  That  is,  when  the  azimuth  has  been  found  from  the 
Azimuth  Tables,  enter  Table  V  with  the  azimuth  and  latitude,  multiply  the 
value  of  C«'  thus  found  by  the  minutes  of  hour  angle,  and  apply  the  result  to 
the  first  reduction  corresponding  to  the  tabular  hour  angle.  When  formula  (22) 
is  used  to  find  the  azimuth  this  value  of  Ct'  should  be  used  for  correcting  Ath  for 
the  odd  minutes  of  hour  angle. 


TABLE  VI. 

Error  in  the  First  Reduction  due  to  an  Error  in  the  Latitude 
USED  IN  the  Computation. 

This  table  is  used  to  correct  the  first  reduction  for  the  difference  between  the 
latitude  by  dead  reckoning  and  the  tabular  latitude  for  which  the  first  reduction 
was  taken  out,  but  is  onlj'  needed  when  great  accuracy  is  required. 

The  way  to  apply  the  correction  to  the  first  reduction,  A,h,  may  be  easily 
determined  by  looking  on  the  page  for  the  next  degree  of  latitude  in  the  same 
declination  column  to  see  whether  the  first  reduction  increases  or  decreases  with 
an  increase  of  latitude,  and  in  the  same  manner  determine  the  sign  for  the  cor- 
rection for  minutes  of  declination  which  mav  be  found  from  this  table  as  there 
directed.  All  corrections  should  be  made  to  Ath  before  this  is  applied  to  the 
latitude.    - 


USE  OF  THE  PLATP:S  xiii 

TABLE   MI. 

Error  in  the  Latitude  due  to  an  Error  in  the  Latitude  used  in  the 

Computation. 

Enter  with  the  azimuth  and  the  difference  between  the  latitude  used  and  the 
latitude  by  observation.  The  correction  found  must  be  so  applied  to  the  latitude 
by  observation  as  to  bring  this  latitude  numerically  between  the  true  latitude  and 
the  latitude  bv  dead  reckoning  used;  thus,  D.R.  —  Obs.  —  True,  or  True  —  Obs. 
-  D.R.;  that'is: 

1.  ^Vhen  the  latitude  by  D.R.  is  greater  than  that  by  observation,  subtract 

the  correction  from  the  latter. 

2.  When  the  latitude  by  D.R.  is  less  than  that  by  observation,  add  the 

correction  to  the  latter. 


Use  of  the  Plates. 

PLATE  I. 

Diagram  for  the  Second  Reduction  to  the  Meridian. 

Enter  with  the  meridian  altitude  corresponding  to  -the  given  latitude  and 
declination  at  the  bottom  of  the  diagram.  The  intersection  of  the  vertical  line 
at  this  point  with  the  curve  corresponding  to  the  first  reduction  gives  the  second 
reduction  on  the  margin. 

PLATE  II. 
Altitude-Azimuth  Diagram. 

This  diagram  corresponds  to  Table  V,  but  it  is  not  on  a  sufficiently  large  scale 
for  interpolating  for  the  odd  minutes  of  hour  angle,  except  the  enlarged  portion, 
which  includes  azimuths  up  to  14°. 

To  find  the  azimuth,  first  find  CV  (see  formula  (22),  Table  V)  and  enter  with 
Ct  and  the  latitude.  If  the  declination  is  used  instead  of  the  latitude,  the  position 
angle,  M,  will  be  found  in  place  of  the  azimuth. 

From  formula  (13)  we  have 

(24)    Sin  Z  =  -  —  sec  L.     The  value  of  r«'  may  be  computed  from  formula 
lo 

(22)  as  long  as  the  hour  angle  does  not  exceed  the  "limit"  given  in  the  tables; 
that  is,  the  second  reduction  must  be  practically  zero.  Plate  II  expresses  formula 
(24). 

The  value  of  C«"  may  be  found  in  practice  by  dividing  the  difference  between 
two  altitudes  by  the  number  of  minutes  in  the  elapsed  time;  and  correcting  the 
.quotient  for  the  run  of  the  ship  in  the  interval.     See  remarks  under  (25). 

The  azimuth  obtained  from  this  diagram,  being  negative,  must  be  reckoned  from 
the  depressed  pole,  or  its  supplement  from  the  elevated  pole. 


xiv  USE  OF  THE  PLATES 

From  an  inspection  of  the  Azimuth  Tables  these  rules  will  be  seen  to  hold  good, 
the  azimuth  being  always  less  than  90°. 

1.  Mark  the  azimuth  east  or  west  like  the  hour  angle. 

2.  When  the  latitude  is  0°  give  the  azimuth  the  same  name  as  the  declination. 

3.  When  the  latitude  and  the  declination  are  of  the  same  name  and  the 

latitude  is  less  than  the  declination,  the  azimuth  has  the  same  name. 

4.  When  the  latitude  and  declination  are  of  the  same  name  and  the  declina- 

tion less  than  the  latitude,  the  azimuth  is  of  the  contrary  name,  for  the 
limit  of  the  diagram,  that  is,  until  the  body  reaches  the  prime  vertical, 
after  which  it  is  of  the  same  name. 

5.  WTien  the  latitude  and  declination  are  of  contrary  names  the  azimuth 

has  the  same  name  as  the  declination. 

When  the  body  is  so  near  the  prime  vertical  as  to  cause  any  doubt,  refer  to 
Table  IX,  "Altitudes  on  the  Prime  Vertical";  when  the  altitude  is  greater  than 
the  tabular  altitude,  the  azimuth  is  of  the  contrary  name ;  when  less,  of  the  same 
name.  Plate  II  was  designed  for  use  with  "Ex-Meridian  Altitudes"  and  should 
be  used  with  great  care  when  the  body  is  near  the  prime  vertical,  as  here  a  small 
error  in  Ct  will  cause  a  large  error  in  the  azimuth.* 

To  find  the  Hour  Angle  of  an  Observed  Body  and  the  Latitude  when  the  Time  is 

not  known. 

Formula  (22)  C,'  =  ±  ^A~^ ,  from  which 


(25)  t  =  ± 


30 

Ct'  X  30 
A^h 


from  which  t  may  be  found  in  minutes  when  it  does  not  exceed  the  limits  given, 
that  is,  when  the  second  reduction  is  practically  zero,  and  when  the  conditions  are 
good  the  longitude  may  be  found  with  considerable  accuracy. 

By  dividing  the  difference  of  altitudes  by  the  interval  we  obtain  the  change  in 
altitude  in  one  minute,  due  to  combined  motion  of  ship  and  body,  which  corrected 
for  run  gives  CW 

Unless  the  ship  be  steering  a  course  at  right  angles  to  the  direction  of  the  body, 
the  change  in  altitude  in  one  minute  must  be  corrected  for  the  run  of  the  ship; 
that  is,  if  D  minutes  is  the  speed  of  the  ship  per  hour,  then  D  seconds  is  the  speed 
per  minute  and  the  correction  =  D"  cos  (course  —  azimuth).  Enter  the  Traverse 
Tables  with  D"  as  a  distance  and  (C  —  Z)  as  a  course,  then  the  correction  is  found 
in  the  latitude  column,  to  be  subtracted  from  the  observed  change  of  altitude  per 
minute  when  the  ship  is  moving  towards  the  body,  and  to  be  added  when  mo\nng 
away  from  the  body;  in  other  words,  when  (C '-  Z)  is  less  than  90°,  subtract; 
when  (C  -  Z)  is  greater  than  90°,  enter  with  the  supplement  of  (C  -  Z)  and 

*  To  compute  Ct'  on,  or  very  near,  the  prime  vertical:  Multiply  the  natural  cosine  of  the 
Latitude  by  15.     See  (13a). 


USE  OF  THE  PLATES  xv 

add  the  correction.     The  above  rules  apply  when  the  body  is  rising ;  when  falling, 
add  when  approaching  and  subtract  when  separating. 

To  make  this  method  of  any  value  the  following  must  be  observed : 

1.  The   altitudes  must  be   observed   with  the   greatest   accuracy,   with  an 

interval  of  not  less  than  five  minutes  between  them. 

2.  The  hour  angle  must  be  within  the  "limit"  so  that  the  second  reduction 

may  be  regarded  as  zero. 

3.  The  correction  for  run  must  be  accurately  known  and  correctly  applied. 

4.  The  watch  time  corresponding  to  the  hour  angle  t  is  the  mean  of  the  watch 

times  of  the  two  observations. 

The  declination  of  the  body  is  supposed  to  be  constant  in  the  interval  between 
the  sights,  which  is  practically  true  for  the  sun  and  planets;  but  when  the  moon  is 
used  a  correction  must  be  made  for  the  change  in  declination,  and  this  applies  also 
when  Plates  II  and  III  are  used  for  finding  the  azimuth  of  the  moon. 

Ordinarily  the  value  of  A  ^h  to  be  used  in  formula  (24)  may  be  found  from  those 
given  in  the  tables  by  interpolating  for  minutes  of  latitude  and  declination.  Where 
greater  accuracy  is  required  the  value  of  A  Ji  should  be  found  from  formula  (4) , 
as,  for  instance,  when  (25)  is  used  for  finding  the  longitude. 

PLATE  III. 

TiME-AziMUTH    DiAGHAM. 

This  is  sometimes  more  convenient  than  Plate  II  for  finding  the  azimuth  and 
position  angle.  Near  the  prime  vertical  it  is  necessary  for  the  time  to  change  the 
altitude  one  minute  to  be  very  accurately  known.  Rules  1,  2,  3,  4  and  5  and 
remarks  under  Plate  II,  apply  to  Plate  III. 

Equation  df  Equal  Altitudes. 

Mr.  G.  W.  Littlehales,  Hydrographic  Engineer,  U.  S.  Hydrographic  Office,  has 
derived  the  following  formula  for  this  equation  in  which  it  is  necessary  to  know 
the  value  of  the  position  angle : 

(26)  t.dt  =  -  -I- seed  cot  M  dd. 
15 

In  (26)  t  =  \  the  elapsed  time  between  the  a.m.  and  p.m.  altitudes. 

Quoting  from  Mr.  Littlehales'  article  in  No.  128  of  the  U.  S.  Naval  Institute: 
"This  ecjuation,  besides  being  much  easier  to  compute,  is  rid  of  the  ambiguities 
of  sign  which  attach  to  each  of  the  two  terms  that  compose  the  right-hand  member 
of  the  usual  form  of  the  equation.  It  will  be  observed  that  in  this  form  the  correc- 
tion does  not  change  sign  unless  the  position-angle  changes  from  a  value  less  than 
90°  to  a  value  greater  than  90° ;  and  that  when  the  position-angle  has  a  value  of 
90°,  the  'equation'  vanishes.  We  may,  therefore,  lay  down  the  simple  rule  that, 
for' values  of  the  position-angle  less  than  90°,  the  correction  should  be  added 
when  the  polar  distance  is  increasing  and  subtracted  when  the  polar  distance  is 


XVI 


USE  OF  THE  PLATES 


decreasing;  and,  for  values  of  the  position-angle  greater  than  90°,  the  reverse  is 
the  case. " 

On  Plates  II  and  III,  if  the  declination  be  used  instead  of  the  latitude,  then  the 
position  angle  or  its  supplement  will  be  found  in  place  of  the  azimuth,  and  the 
same  rule  applies  to  the  azimuth  tables,  where  by  interchanging  the  latitude  and 
the  declination  the  position  angle  is  found  in  place  of  the  azimuth. 

The  position  angle  may  also  be  found  from  Plate  VI.  When  the  hour  angle  is 
small  it  is  better  to  use  Plate  III,  as  it  is  seen  that  with  the  aid  of  the  vertical 
lines  for  interpolating  the  exact  value  of  the  position  angle  may  be  easily  deter- 
mined. 

Ex.\MPLE  1.  —  Niquero,  Cuba,  February  5,  1908,  lat.  20°  02'  30"  N.,  long.  77° 
35'  20"  VV.,  observed  the  following  altitudes  0  for  chronometer  error.  C  —  W  = 
5U 22m 478  A.M.;  C  -W  =  5^22^4:5"  p.m. 


A.M.  Watch  Times. 

A.M.  Altitudes. 

P.M.  Watch  Times. 

P.M.  Altitudes. 

h.  m.      s. 

h.  m.       s. 

8  55  36.5 

63°  00' 

3  04  33.3 

64°    00' 

55  55.5 

10 

04  59.6 

50 

56  28.5 

20 

05  25.7 

40 

56  55 

30 

05  53.6 

30 

57  19.5 

40 

06  18 

20 

57  48 

50 

06  44 

10 

58  14.3 

64°  00 

07  09.3 

63°  00 

The  altitude  here  changes  30'  in  156  seconds,  or  1'  in  5.2  seconds,  or  in  one  minute 
the  altitude  changes  11.54'  and  we  find  M  =  53°. 


We  find  middle  chronometer  time  = 


5  24  09 
Eq.  E.A.  -  07.2° 


Eq.  t 

Long. 
Chro. 


5  24  01.8 
-   14  07 
5  09  54.8 
5  10  20  West. 
0  00  25.2 
slow  G.M.T. 


Dec.  =  16°  11'  14"  S. 

Eq.  time       14    07 

Corrected  for  local 

apparent  noon.     Eq.  time 

to  be  subtracted  from  mean  time. 

,  H.D.  for  Dec,  +  44.83". 


Elapsed  time  =  6  08  56 
<  =  3  04  28 
=  3.0744  hrs. 


t  =  3.0744 log  0.4878 

15 colog  8.8239 

The  same  result  was    d  =  16°  11'  14" sec  0.0176 

obtained  by  the  or-  M  =  53° cot  9.8771 

dinary  method.  dd  =  +  44.83" log  1.6516 

<.d<  =  7.21  sec log  0.8580 

Hence  Eq.  E.A.  =  -  7.21  sec. 


As  the  log  cot  M  is  the  same  as  the  log  cot  (180°  -  M)  it  is  immaterial  which  is 
used  in  the  computation,  but  we  must  know  whether  M  is  greater  or  less  than  90*' 


USE  OF  THE   PLATES 


xvn 


to  determine  the  sign  of  the   correction  t.dl,  which  is  easily  determined  from 
Fig.  2  or  getting  the  approximate  value  from  the  Azimuth  Tables. 

Fig.  2  is  the  celestial  sphere  projected  on  the  plane  of  the  horizon.  P,  ele- 
vated pole;  Z,  zenith  of  the  observer;  IFQE,  equator;  and  WZE,  the  prime 
vertical. 

1.  Let  L   and  d  have   the   same  name 

and  d>  L;  then  the  value  of  M 
varies  from  0°  where  the  body 
crosses  the  lower  branch  of  the 
meridian  to  180°  where  it  crosses 
the  upper  branch,  being  90°  when 
the  diurnal  circle  is  tangent  to 
the  vertical  circle  at  its  maximum 
elongation. 

2.  Let   L  and   d  have   the   same  name 

and   L  >  d.      In    this    case    M' 

varies   from    its   maximum  when 

in   the    horizon   to   0°    when    on  Fig.  2. 

the   meridian. 

3.  Let  L  and  d  be  of  contrary  names,  then  M"  is  always  less  than  90°  while 

the  body  is  above  the  horizon. 


PLATES   IV  AND  V. 

Error  in  the  Latitude  due  to  an  Error  of  One  Minute  of  Time  in  the 
Hour  Angle  or  Longitude. 

Plate  V  is  a  continuation  of  Plate   IV.     These  plates  afford   a  convenient 
fj  means    of    plotting    lines  of    posi- 

60°  tion    without    the    aid    of    parallel 

rulers  or  protractors  of  any  kind, 
and  are  therefore  a  great  conven- 
ience on  board  ship.  After  finding 
the  ship's  position  for  a  given 
longitude,  assume  an  error  of  one 
minute    of    time    or   15'  of  arc   in 

15"         s[^ the     longitude,    with    the    latitude 

.P-jOs     ^^K  and    azimuth    of     the    body    find 

the  correction  from  Plate  '  IV  or 
V,  which  lay  off  on  the  new  merid- 
ian so  as  to  make  the  line  of 
position  thus  established  come  at 
right  angles  to  the  line  of  azimuth 
passing  through  the  body. 

Example  2.  —  Let  S  be  the  posi- 
tion  of    the    ship    in   lat.   37°  N., 
long.  60°  W.,  the  sun  bearing  S.  30° 
Fig.  3.  EI.,  plot  the  line  of  position. 

In  the  figure  NS  is  the  meridian. 
The  line  runs  N.  60°  E.,  or  S.  60°  W.  Lay  off  PS  =  15'  of  longitude  on  the 
parallel  37°.     From  Plate  V,  aL  =  6.9',  take  on  the  meridian  through  P,  PR  = 


37" 


xvm 


USE   OF  THE   PLATES 


aL  =  6.9',  then  RS  is  the  required  line  of  position,  which  is  easily  proved  thus: 

PR 
tan  Z  =  — ,  where  p  =  the  departure  corresponding  to  PS  =  15'  longitude  in 

P 
latitude  37°  =  11.98',  and  we  find  Z  =  S.  29°  57'  E. 

If  the  chart  used  is  on  a  large  scale,  make  PS  =  5'  of  longitude,  then 
aL  =  2.3'.  If  a  small  scale  chart  is  used,  make  PS  =  30'  and  multiply  aL 
taken  from  the  plate  by  2. 

PLATE  VI. 

Star-finding  Diagram. 

To  be  used  in  connection  with  the  Azimuth  Tables  and  Plate  II  for  the  identifi- 
cation of  stars  in  cloudy  weather. 


P-'-' 


JE 


\ 


Fig.  4. 

In  Fig.  4,  P  is  the  elevated  pole,  A  the  zenith  of  the  observer,  and  S  the  posi- 
tion of  the  star. 

Given  AP  =  90°  -  L,  AS  =  90°  -  h,  and  Z  =  the  azimuth;  to  find  t  =  the 
hour  angle  and  d  =  the  declination. 

Reduce  the  observed  altitude  and  azimuth  to  true  and  find  the  local  sidereal 
time  at  ship. 

Shift  the  pole  of  the  triangle  PAS  from  P  to  ^ ;  then  renaming  the  parts 

as  shown  in  Fig.  5,  we  find  the  hour  angle 
\  thus : 

Enter  the    Azimuth    Tables   in   the   lati- 
tude of   the   ship  with  the  azimuth  as  an 
hour  angle   and   the    altitude    as  a   deplina- 
\  tion ;   the  corresponding  azimuth  is  the  hour 

angle  of  the  star ;  then 

(27)  Cos  d  =  sin  Z  cos  h  cosec  t. 
Plate  VI  shows  the  relation  expressed  in 

formula  (27)  or 

(28)  Sin  t  cos  d  =  sin  Z  cos  h, 
from  which  the  declination  is  found  after  find- 
ing the  hour  angle  from  the  Azimuth  Tables,  the  azimuth  having  been  observed 
or  found  from  the  azimuth  diagram. 

To  find  the  star's  declination  from  the  diagram. 

Enter  with  the  azimuth  on  the  margin ;  the  intersection  of  the  horizontal  line 
through  this  point  with  the  curve  corresponding  to  the  true  altitude  fixes  a  ver- 
tical line  the  intersection  of  which  with  the  horizontal  line  corresponding  to  the 
hour  angle  previously  found,  determines  the  curve  corresponding  to  the  declina- 
tion of  the  body. 


Fig.  5. 


USE  OF  THE   PLATES 


XIX 


This  diagram  also  shows  the  relation 

(29)  Sin  Z  cos  L  =  sin  M  cos  d,  from  which  the  position  angle  M  of  a  given 
body  may  be  found  thus : 

Enter  with  the  azimuth  on  the  margin;  the  intersection  of  the  horizontal  line 
through  this  point  with  the  curve  corresponding  to  the  latitude  fixes  a  vertical 
line  the  intersection  of  which  witli  the  curve  corresponding  to  the  given  decli- 
nation, determines  the  horizontal  line  corresponding  to  the  position  angle  of  the 
body. 

Supplementary  azimuths,  hour  angles,  and  position  angles  are  given  on  the 
riglit-hand  margin. 

Ordinarily  the  azimuth  may  be  observed  with  sufficient  accuracy  for  the 
purpose  of  identification,  but  it  is  not  always  convenient  to  take  the  bearings, 
and  conditions  may  be  such  as  to  make  them  inaccurate.  In  such  cases  take 
several  altitudes,  noting  the  time,  and  find  Cj',  the  change  in  altitude  in  one 
minute,  and  then  find  the  azimuth  from  Plate  II.  To  be  exact  Ct  should  be  cor- 
rected for  the  run  of  the  ship,  but  in  identifying  stars  this  correction  may,  as  a 
rule,  be  neglected. 

It  is  always  best  to  take  a  compass  bearing  as  a  check,  even  though  a  rough 
one,  as  this,  with  the  altitude  and  latitude,  will  enable  the  observer  to  decide 
whether  the  latitude  and  declination  are  of  the  same  or  contrary  names.  This  is 
necessary  in  order  to  find  the  hour  angle  from  the  azimuth  tables. 

There  will  be  no  difficulty  in  determining  the  names  of  the  declination  except 
when  the  star  is  near  the  equator.  After  finding  the  declination  it  is  well  to 
verify  the  name  by  entering  the  Azimuth  Tables  with  the  hour  angle  and  this 
declination  to' see  whether  the  azimuth  so  found  agrees  with  that  used. 

In  all  cases  the  name  of  the  declination  may  be  readily  found  from  the  follow- 
ing table  for  which  the  writer  is  indebted  to  Professor  H.  L.  Rice,  U.  S.  Navy. 


VALUES   OF 

B. 

For  Azimuths  North  toward  West  or  North  toward  East 

Altitudes 

Altitudes 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

o 

o 

o 

0 

0 

0 

o 

0 

o 

o 

o 

o 

10 

16.0 

16.0 

15.9 

15.7 

15.4 

14.9 

14.1 

12.5 

8.9 

0.0 

10 

20 

14.0 

13.9 

13.8 

13.4 

12.9 

12.1 

10.8 

8.6 

5.1 

0.0 

20 

30 

12.0 

11.9 

11.7 

11.3 

10.6 

9.6 

8.2 

6.1 

3.3 

0.0 

30 

40 

10.0 

9.9 

9.6 

9.2 

8.5 

7.5 

6.2 

4.4 

2.3 

0.0 

40 

50 

8.0 

7.9 

7.7 

7.2 

6.5 

5.7 

4.6 

3.2 

1.7 

0.0 

50 

60 

6.0 

5.9 

5.7 

5.3 

4.8 

4.1 

3.2 

2.2 

1.1 

0.0 

60 

70 

4.0 

3.9 

3.8 

3.5 

3.1 

2.6 

2.1 

1.4 

0.7 

0.0 

70 

80 

2.0 

2.0 

1.9 

1.7 

1.5 

1.3 

1.0 

0.7 

0.4 

0.0 

80 

90 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

90 

Altitudes 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Altitudes 

F 

or  Azir 

nuths  i 

South  toward  West  or  South 

towar 

d  East 

Express  the  latitude  in  degrees  and  tenths  as  B  in  the  table. 
Mark  north  latitude  +  and  south  latitude  — . 
When  the  azimuth  is  found  at  the  top  of  the  Table  B  is  + . 
When  the  azimuth  is  found  at  the  bottom  of  the  Table  B  is 

The  declination  has  the  sign  of  5  4 —  . 


XX  USE  OF  THE   PLATES 

Example  3.  —  At  sea,  February  26,  1901,  6.30  p.m.,  L.M.T.,  weather  overcast 
and  cloudy,  observ'cd  the  altitude  of  an  unknown  star  of  about  the  second 
magnitude,  through  a  break  in  the  clouds,  29°  30'  (true),  bearing  X.  74°  W. 
(true).  Lat.  by  dead  reckoning  35°  N.,  long.  60°  W.  What  is  the  name  of  the 
star? 

74°  =  4  hrs,.  56  min.  Entering  the  Azimuth  Tables  (H.O.  No. 

h  m  s  120)    in  lat.    35°,    latitude   and   dec- 

L.M.T 6  30  00  lination  same  name,  with  4  hrs.   56 

R.A.M.S 22  22  33  min.  as  an  hour  angle  and  for  29°  30' 

Cor.  G.M.T 1  43  dec,    we    find    the    azimuth    72°  24' 

L.S.T 4  54  16  =4  hrs.  49  min.  36  sec.  the  required 

Star  H.A.  '.'.'.'.'.     4  49  36  hour  angle.                                  ^    ,     , 

a^„„  r>  \                        7^ — TTi — 77;  Then    from   Plate   VI   we  find   the 

^^""^  ^-^ 0  04  40  declination  =  28°  30'  N. 

R.A.  of  star  =  0  hrs.  04  min.  40  sec. 

Dec.  of  star  =  28°  30'  X.  In  the  X'^autical  Almanac  these  correspond  to 
a  Andromedae,  R.A.  0  hrs.  03  min.  19  sec. 

Dec.  28°  33'  N. 

Example  4.  —  At  sea,  February  6,  1903,  lat.  15°  53'  S.,  long.  38°  12'  W., 
observed  the  following  altitudes  of  a  star  bearing  about  W.N.W.  Cloudy  weather 
with  heavy  sea  and  too  much  motion  on  the  ship  to  obtain  a  bearing  by  compass. 
What  star  was  observed? 

Obs.  altitudes      Watch  times 

.    °  '  h     m  8  C  -  TF  =  3  hrs.  8  min.  13  sec. 

20  18  5     05  07  Chro.  fast  G.M.T.  0  hrs.  20  min.  9  sec. 

19  58  06  38 

19  39  08  00  Correction  for  I.e.,  dip  and  refraction,  -  7' 00*. 

In  2  min.  53  sec.  change  in  altitude  =  39' and  C,'  =  13.52',  and  from  Plate  II, 
Z  =  X.  69°  35'  W.  or  S.  110°  25'  W. 

To  find  the  hour  angle,  enter  H.O.  X*o.  71  (Azimuth  Tables),  latitude  16°,  dec- 
lination 20°,  contrary  name  (the  corrected  mean  altitude  being  19°  51'  20")- 
We  find  that  the  hour  angle  110°  25'  =  7  hrs.  21  min.  40  sec.  is  not  given,  so  we 
enter  with  the  supplement  of  this  hour  angle  4  hrs.  38  min.  40  sec,  and  the 
supplement  of  the  corresponding  azimuth,  115°  30'  or  64°  30',  is  the  hour  angle 
required. 

h    m    s 

w.t.  (mean) 5  06  35  f  =  64°  30'  =  4  hrs.  18  min. 

C.  -  W 3  08  13 

Chro 8  14  48  Entering    Plate    VI    with    azimuth 

Chro.  Cor -  20  09  =S.  110°25'W. 

G.M.T 19  54  39  Altitude  =  19°  51'  20";    hour   angle 

R.A.M.S 20  57  50.4  64°    30';     we    find    declination  = 

Cor.  G.M.T 03  16.2  12°    30'  N.      Check    the   declina- 

G.S.T 16  55  45.6  ^i^^  ^""^^   hour  angle  by  entering 

Long 2  32  48  (W)     the  Azimuth  Tables  and  we   find 

T  g  rp  14  22  'i?  6 —     ^^^  azimuth  agrees  with  that  used 

Star's  H.A.  ;   ".;::::  4  is  OO'  Intheproblem. 

Star's  R.A 10  04  57.6 


USE  OF  THE   PLATES  xxi 

Example  5.  —At  sea,  August  10,  1904,  about  5.30  a.m.,  lat.  ITS?'  N.,  long. 
81°  09'  W.  Correction  for  dip,  refraction  and  I.C.  -  9'  00".  Observed  the 
following  altitudes  of  a  bright  star  bearing  about  E.S.E. 

„..,..  „.       ....    ,  When  the  watch  showed  5  hrs.   35 

Watch  times      Obs.  altitudes  •        ..>  4.1,    r^  a  t^  ou        to 

.  o      ,     „  min.  43sec.  theG.b.T.  was  8  hrs.  12 

c  nA  oc  00  oc  nr>  Diin.  17  SBC.     As  the  ship  was  roll- 

26  "j"!  24  07  '^0  *"^  heavily   no  accurate   bearing 

r,r  Ao  oc  r\A  nn  could    be   taken.    What   was   the 

35  43  26  04  00  ^^^^  ^ 

It  is  evident  from  the  approximate  bearing  and  the  altitude  that  the  star  is 
in  south  declination.  When  d  =  0,  meridian  altitude  =  90°  —  L  =  79°  23'  in 
this  case,  evidently  too  great  an  altitude  for  this  star  to  reach. 

From  the  difference  of  altitudes  divided  by  the  number  of  minutes  in  the 
interval  we  find  Ct'   =  13.3',  and  from  Plate  II  we  find  Z  =  S.  65°  E. 

h  m  s 

G.S.T.  of  obs 8  12  17 

Long,  west 5  24  36 

L.S.T 2  47  41 

Star's  H.A 3  52  16  (East) 

Star's  R.A 6  39  57 

To  find  the  hour  angle  in  this  case  we  must  enter  the  Azimuth  Tables  with 
the  supplement  of  the  azimuth  found  from  Plate  II  =  115°  =  7  hrs.  40  min.  as 
an  hour  angle,  and  in  the  26  column  we  find  58°  04'  =  3  hrs.  52  min.  16  sec.  for 
the  hour  angle  of  the  star. 

From  Plate  VI,  with  Z  =  S.  65°  E.,  altitude  =  25°  55',  and  hour  angle  = 
58°  04',  we  find  declination  =  16°  30'  S. 

Star's  R.A.  6  hrs.  40  min.  7  sec,  Star's  Dee.  16°  30'  S. 

These  correspond  to  a  Canis  ^lajoris  (Sirius), 

R.A.  6  hrs.  40  min.,  55  sec,  Dec.  16°  35'  S. 

^Vhen  the  star  is  on  or  very  near  the  meridian  so  that  its  hour  angle  is  prac- 
tically 0,  the  star's  right  ascension  is  equal  to  the  local  sidereal  time,  and  its 
declination  may  be  readily  found  by  looking  in  the  Ex-Meridian  Tables  in  the 
latitude  b}^  dead  reckoning  for  the  meridian  altitude  of  the  star,  and  in  the  same 
column  at  the  top  will  be  found  the  declination.  If  the  azimuth  is  so  great  that 
the  hour  angle  must  be  taken  into  account  in  computing  the  right  ascension, 
then  proceed  as  in  Examples  3,  4,  and  5.  Or  having  found  the  hour  angle 
from  the  azimuth  and  altitude,  we  may  take  out  the  approximate  correction 
from  the  Ex-Meridian  Tables,  which  added  to  the  observed  altitude  for  upper 
passage,  or  subtracted  for  lower,  will  give  the  meridian  altitude,  from  which 
the  declination  may  be  found  as  when  the  star  is  on  the  meridian.* 

To  Identify  a  Star  with  the  Aid  of  a  Great  Circle  Sailing  Chart.  - 

As  azimuth  tables  for  the  higher  declinations  are  not  always  available  the 
following  method  is  given. 

If  we  use  the  Great  Circle  chart  of  the  North  Atlantic  Ocean : 
On  the  meridian  of  Greenwich,  or  any  convenient  meridian,  mark  the  point 
5  in  a  latitude  equal  to  h,  the  true  altitude  of  the  star.     Mark  A,  the  position 
of  the  ship  in  latitude,  L,  and  in  longitude  from  S  equal  to  the  true  azimuth 

*  T^Tien  the  star  is  near  the  prime  vertical,  find  the  Latitude  in  Table  IX,  and  look  for 
the  altitude  in  the  same  line.  The  declination  will  be  found  at  the  head  of  the  column,  and 
the  hour  angle  under  this  declination  and  in  the  same  line  as  the  altitude. 


OF  THE 

UNIVERSlTT 

■.jf 


XXll 


USE  OF  THE   PLATES 


of  the  star,  Z.  Find  the  Great  Circle  course  and  distance  between  A  and  5  by 
the  method  of  the  chart.  The  course  is  the  hour  angle  of  S,  and  the  distance 
is  the  complement  of  the  declination. 

Local  sidereal  time  =  R.A.  of  star  ±  H.A.  of 
star;  hence  apply  the  hour  angle  of  the  star  to 
the  L.S.T.  at  ship,  subtracting  when  west  and 
adding  when  east,  and  the  result  is  the  right  ascen- 
sion of  the  star,  d  =  90°  -  AS,  and  the  star  may  be 
found  in  the  Nautical  Almanac. 

It  is  evident  from  Fig.  G  that  the  azimuth  of  the 
star  from  A  is  the  Great  Circle  course  from  A  to  & 
in  latitude  =  d\  hence  the  well-known  rule  for 
finding  the  Great  Circle  course  from  the  Azimuth 
Tables: 

"With  the  difference  of  longitude  as   an  hour 
angle  enter  the  latitude  of  departure  and  the  Great 
Circle  course  will  be  found  in  place  of  the  azimuth 
Pjq  g_  in  the  declination  column  corresponding  to  the  lati- 

tude of  destination." 
When   the   latitude   and   the   declination  are  of   contrary  names,  proceed   as 
directed  on  the  chart  for  finding  the  course  and  distance  between  two  places  on 
opposite  sides  of  the  equator. 
The  following  examples  illustrate  the  use  of  the  tables  and  plates. 
Example  6.  —  At  sea,  June  30,  1904,  lat.  37°  33'  S.,  long.  24°  00'  E.  by  D.R., 
Local  Ap.  Time  0  hrs.  23  min.,  observed  altitude  sun's  lower  limb  29°  10',  height  of 
eye  28.5  feet,  declination  23°  11'  48"  N.     Find  the  latitude  and  plot  the  line  of 
position. 

From  page  223,  column  23,  we  have  A  ,4^  =  +  16'  02"    Aji  =  1 .  66" 
Correction  Table  V  for  1  min.  H.A.     .    .        -    1'  15"      „     _  1.66  X  23 
Correction  Table  VI      -        15"      ^*  30 


- 15;^ 

A«/i  =14'  32" 


1.27' 


Obs.  Alt.  Sun's  1.1.  .  .  29°  10'  00" 
Cor.  Table  II  ...  .  +  9  05 
True  Alt.  Sun's  c.   .    .  29°     19'     05" 

A*A       +14      32 

Mer.  Alt 29°     33'     37" 

90 

Mer.  Z.  Dist 60°     26' 

Declination 23       11 

Latitude 37°     14' 

Cor.  Table  VII     ... 

True  Lat 37°     14'     28"  S 


When  Z  and  M  are  so  small  the  cor- 
rections from  Tables  VI  and  VII 
may  be  omitted  without  any  ap- 
preciable error. 


23"  S 
48   N 
35"  S 
-7 


From  Plate  II, 
Z  =  6°  30' 
iW  =  6°  00' 

From  an  inspection  of  the  tables 
we  see  that  an  increase  in  both 
latitude  and  declination  causes 
a  decrease  in  A</i,  and  as  Z  and 
M  are  practically  equal  we  may 
enter  Table  VI  with  45'  and  6° 
and  take  out  both  corrections  at 
once  —  15". 

Lat.  bv  D.R 37°  33'     00" 

Lat.  by  calc 37     14      35 

Diff 18'     25" 

Cor.  Table  VII  ...  7" 

To  be  subtracted  to  make  good  the 
relation  D.R.  —  Calc.  —  True. 


Enter  Plate  IV  with  Z  =  6°  30'  and  L  =  37°  15';  we  find  the  error  in  latitude 
due  to  15'  error  in  longitude  =  1.33';  so  as  the  sun  is  in  the  N.W.  quadrant  the 


USE  OF  THE  PLATES 


XXlll 


line  runs  from  N.E.  to  S.W.  quadrant.     Lay  off  L5'  long,  to  W'd  and  1.33'  to  the 
S'd  and  join  the  latter  point  with  the  assumed  position  of  the  ship,  Fig.  7. 

Example  7,  —  March  20,  1907,  about  8.15  p.m., 
lat.  50°  14'  N.,  long.  1°  39'  W.  by  D.R.,  the  observed 
altitude  of  Castor  was  70°  01'  02"  bearing  to  the 
S'd  and  W'd,  chronometer  time  of  observation  8  hrs. 
49  min.  17  sec.,  chronometer  fast  of  G.M.T.  0  hrs. 
16  min.  7  sec.  Find  the  latitude  and  plot  the  line 
of  position. 


Castor,  Right  Ascension  7  hrs.  28  min.  40  sec. 
Declination  32°  05'  36"  North. 


Fig.  7. 


h  in       s 

Chro.  Time  Obs 8  49  17 

Chro.  Fast 16  07 

G.M.T.  Obs 8  33  10 

R.A.M.S 23  47  28 

Cor.  for  G.M.T 1  24 

G.S.T 8  22  02 

Long 6  36  W. 

L.S.T 8  15  26 

Star's  R.A 7  28  40 

Star's  H.A 0  46  46 


Obs.  Alt.    .    .    . 

.    .   70° 

01' 

02" 

Cor.  Table  II    . 

-5 

44 

69° 

55' 

18" 

Red.  to  Mer  .    . 

.    .     1 

56 

48 

Mer.  Alt.    .    .    . 

.    .  71° 
90 

52' 

06" 

M.Z.D 

.    .   18° 

07' 

54"  N 

Dec 

.    .  32 

05 

36  N 

Latitude    .    .    . 

.    .  50° 

13' 

30"  N 

On  page  299  we  find  that  for  t  =  46.76  min.,  A«/i  is  not  tabulated,  as  46.  min. 
exceeds  the  limiting  hour  angle  where  the  second  reduction  may  be  neglected. 
From  formula  (21),  Ath=  126.1'. 


WehaveAj/i  =      3.46" 
t  =    46.76 
60 
A(/i    =  126.1 


log  0.53908 
2  log  3.33974 
colog  8.22185 

log  2 .  10067 


Ath  =  +  126.1' 
2dRed.  =  -      7.1 


+  119.0' 

-      2.2 


Table  VI  

Total  Red.  =  +  116.8' 


On  page  299  in  column  32°  we  find  meridian  altitude  =  72°,  and  from  Plate  I 
second  reduction  =  7.1'. 

17         1     .oo^     r'l      ^  i^X  ^       3.46"  X  46.76       .  ^g, 
Formula  {22)     C«'=       ^^       =  ■ ^ ==  5.78'. 


From  Plate  II,  Z  =  S.  37°  W.;ilf  =  27°. 

Table  VI,  cor.  for  14'  lat.  =  -  2.82';  Table  VI,  cor.  for  5.6  dec.  =  +  .6'. 

Total  correction  for  minutes  of  lat.  and  dec.  =   —  2.22'. 

With  azimuth  37°  enter  Plate  IV,  and  we  find  error  in  latitude  for  15'  longitude 
=  7.24'.  As  the  star  is  in  the  third  quadrant  the  line  must  run  through  the  second 
and  fourth  to  N'd  and  W'd,  and  S'd  and  E'd.  Lay  ofT  15'  longitude  to  the  west- 
ward of  the  position  and  7.24'  latitude  to  the  north.  The  line  through  this  point 
and  the  ship's  position  is  the  line  of  position  required. 


XXIV  USE  OF  THE  PLATES 

Example  <S.  —  August  6,  1907,  lat.  59°  00'  S.,  long.  175°  27'  E.,  during  evening 
twilight,  observed  altitude  a  Eriadni  (Achernar)  near  lower  transit  26°  52'  GO", 
watch  time  4  hrs.  31  min.  12  sec,  C  —  W  =  0  hrs.  18  min.  7  sec,  chronometer 
fast  G.M.T.  0  hrs.  12  min.  42  sec,  I.C.  +  1'  20",  height  of  eye  24  feet.  Find  the 
latitude. 

h  m      s 

Watch  time     ...  4  31   12  Achernar,  R.A.  1  hr.  34  min.  15.1  sec. 

C  -  W 0  18  07  Achernar,  Dec.  57°  42'  33"  S. 

Chro.  Time  ....  4  49  19  Polar  Dist.  32°  17'  27"  =  p. 

Chro.  Cor 12  42  Lat.  =  ho  +  p 

G.M.T 10  36  37  Aug.  5        Obs.  Alt.  26°  52'  00"    I.   C.    +  1'  20" 

R.A.M.S 8  51  32.9  Cor.      .  5   22  Tab.  II.  -  6    42 

Cor.  G.M.T.     .    .    .  2  43.3  True  Alt.  26°  46'  38"       Cor.  -  5'  22" 

G.S.T.  ..:...  1  30  53.2 

Long.  East  ....  11  41  48  A  «A  .    .      -  4    40 

L.S.T 13  12  41.2  Mer.  Alt.  =  ho  =  26°  41'  58" 

12  h.  +  Star's  R.A.  13  34  15.1  p  =  32     17    27 

Star's  H.A.  =  t  =  0  21  33.9  Latitude  58°  59'  25"  South. 

Page  357,  column  57,  A  Ji  =  0.61",  T,'  =  Jl  "         =  0.44'. 

From  Plate  II,  Z  =  S.  3^°  W.;  .1/  =  3^°.  -1/  is  so  small  that  the  correction  for 
42'  dec.  is  not  sensible. 

A^h    =4'   02" 
Cor.  Table  V  for  1.55  min.  =  +   38 

A^!    =  4'     40" 

The  star  being  near  the  lower  transit,  Aji  must  be  subtracted  from  the  true 
altitude. 

Example  9.  —  At  Niquero,  Cuba,  March  5,  1908,  approximate  position,  lat. 
20°  N.,  long.  77°  30'  W.,  observed  the  following  altitudes  of  the  sun's  lower  limb 
with  artificial  horizon: 

Watch  time  11  55  51.5  2  Altitude  126°  20'  30" 

12  05  25  127    03    30 

C  —  W  =  5  hrs.  4  min.  18  sec.     Chronometer  49.76  sec.  slow  G.M.T.     Find  the 
longitude  and  the  latitude. 

We  have,  formula  (25),        t  =  — — ; 

A  !«. 

Let  h'  =  lower  altitude  for  upper  transit. 
T'  =  corresponding  watch  time. 
h"  =  higher  altitude  for  upper  transit. 
T"  =  corresponding  watch  time. 

T'  +  T" 

• — ^ =  Tm=  middle  watch  time. 

T"  -"w  T'  =  I  =  interval  between  sights  in  minutes. 

h"  —  h'  =  difference  of  altitudes  in  minutes  of  arc  =  D. 

The  hour  angle  t,  found  by  the  above  formula  (25),  corresponds  to  T„,  and 

(71  =  ^  =  21.5'  X  60 

*        i  573.5 


USE  OF  THE  PLATES  xxv 

From  page  121  we  find  a  ,/i  =  4.19",  hence  t  =  ~z^ prj:  • 

h       m         s 

r„  =00     00     38.25       G.A.T 4     54     06.95 

C  -W  =5       04     18  L.A.T 11     43     53.4 

Chro.  Time 5      04     56.25       Long 5     10     13.55 

Long.  77°  33'  23"  West. 

The  true  longitude  is  77°  35'  07". 

Chro.  Cor +49.76  21.5  log  1.33244 

G.M.T 5     05     46.01  1800  log  3.25527 

Eq.  Time  (- M.T.)  .  11     39.06  573.5  colog  7.24147 

G.A.T 4     54     06.95  4.19  colog  9.37779 

t=  16.11  log  1.20697 

t  =  16  min.  06.6  sec.  (East)* 

To  find  the  latitude  corresponding  to  this  hour  angle  it  is  necessary  to  find  the 
altitude  corresponding  to  the  middle  watch  time. 

It  will  be  found  more  convenient,  however,  to  find  the  hour  angle  correspond- 
ing to  one  of  the  altitudes  by  applying  ^  i  to  the  hour  angle  t,  already  found. 

Let  t'  =  hour  angle  corresponding  to  h',  the  lower  altitude. 
t"  =  hour  angle  corresponding  to  h",  the  higher  altitude. 
Then  r  =  <  +  it, 

and     I"  =  t  -  I  i;  we  have  i  =  T"  -  T'  =  9  min.  33.5  sec. 

Ji  =  4  min.  46.7  sec,  and  t'  =  20.9  min. 
t"  =  11.33  min. 

2obs.  alt.          =126°     20'  30"  ^,      20.9X4.19      „  „„ 

I.C +   0  15  '^'   = ^0~  ^ 

2; 126°     20'  45" 

obs.  alt 63       10  23  Cor.  for  .9  min.  =  2.92  X  .9  =  +  2.63' 

Cor.  S.D.,  etc.  .              15  56  A.^h  =  27'     56" 

h' 63°     26'  19"  Cor.  =  +    2'     38" 

Aih +30  34  Ath  =  30'     34" 

ho' 63°     56'     53" 

90° 

M.Z.D 26°    03'      7"  North 

Dec 6      00      24   South 

Latitude    ...     20°    02'     43"  North 

2  obs.  alt.    .    .    .    127°     03'     30"  /  v  a  7.      11  qq  v  /i  in 

I.C +  0       15  c.^  =  ^^  =  lM3><Ali=i.58' 

2;  127°     03'  45"  "^ 

obs.  alt 63      31  53 

Cor.  S.D.,  etc.  .  15  56  1.58  X  0.7  =  1'  06"  =  cor.  to  Aij/i 

h" 63°     47'  49"  A12/1  =      10'  03" 

Ath +   8  57  Cor.        -  1     36 

ho" 63°     56'  46"  A^  =      8'  57" 

90° 

M.Z.D 26°    03'  14"  North  The  latitude  from  h"  is  20°  02'  50". 

Dec 6     00  24    South  Mean  latitude  20°  02'  46". 

Latitude    ...      20°    02'  50"  North  True  latitude  =  20°  02'  40"  North. 

*  If  Aih  be  computed  by  formula  (4),  using  the  true  latitude,  we  find  Aih  =  4'  .177"  and 
longitude  =  77°  34'  03.75",' only  1'  03.75"  less  than  the  true  longitude. 


A.M. 

Watch. 

Altitudes. 

(1) 

llli  47"!  08.5s 

79°  19'  30" 

(3) 

(2) 

57     58 

42   30 

(4) 

xxvi  USE  OF  THE  PLATES 

Example  10.  —  U.  S.  S.  Dubuque,  at  sea,  off  Cape  Hatteras,  June  23,  1908;  lat. 
33°  33'  N.,  long.  75°  26'  W.,  from  a.m.  time  sight,  observed  the  following  altitudes 
of  the  sun's  lower  limb  near  noon : 

P.M. 

Watch.  Altitudes. 

12h  05m  529       79°  38'  50" 
10      56.5  26  40 

C  -W  =  4  hrs.  55  min.  05  sec.  Chronometer  slow  G.M.T.  0  hrs.  11  min.  40  sec. 
Sun's  dechnation,  corrected,  23°  26'  20"  X.  A,/i  =8.57"  computed  by  formula 
(4);  height  of  eye  20  feet;  corrected  equation  of  time,  to  be  subtracted  from 
mean  time  =  1  min.  55  sec.  Course  North,  true;  speed,  10  knots.  Find  the 
Longitude  and  Latitude  at  noon. 

ANSWERS. 
From  A.M.  Observations.  From  P.M.  Observations. 

Long.  75°  21.5'  West.  Long.  75°  22'  West. 

Lat.  from  (1)  33°  31'  45"  N.  Lat.  from  (3)  33°  30'  57"  N. 

"     (2)  33°  32'  12"  N.  "         "      (4)  33°  32'  00"  N. 

As  the  ship  was  in  the  Gulf  Stream  during  the  interval  between  the  a.m.  time 
sight  and  noon,  the  difference  of  longitude  is  accounted  for  by  the  current. 

If  the  ship  change  her  longitude  in  the  interval  between  the  observations,  the 
hour  angle  should  be  corrected  for  this  difference  when  appreciable,  that  is,  a 
westerly  difference  of  longitude  should  be  added  to  an  easterly  hour  angle  and  be 
subtracted  from  a  westerly  hour  angle  and  an  easterly  difference  of  longitude 
should  be  added  to  a  westerly  hour  angle  and  be  subtracted  from  an  easterly 
one;  or  more  briefly,  when  both  are  east  or  both  are  west,  subtract;  when  one  is 
east  and  the  other  west,  add. 

When  the  azimuth  exceeds  three  or  four  degrees  the  line  of  position,  corre- 
sponding to  the  latitude  found,  should  always  be  dra\vn  when  very  exact  results 
are  required. 


TABLE  L 
Logarithms  of  Numbers  from  0  to  499* 


No. 

0 

1 

2 

3 

47712 

4 
60206 

5 

69897 

6 

77815 

7 
84510 

8 

9 

95424 

Prop. 
Part 

0 

0 

00000 

30103 

90309 

10 

00000 

00432 

00860 

01284 

01703 

02119 

02531 

02938 

03342 

03743 

415 

11 

04139 

04532 

04922 

05308 

05690 

06070 

06446 

06819 

07188 

07555 

379 

12 

07918 

08279 

08636 

08991 

09342 

09691 

10037 

10380 

10721 

11059 

344 

13 

11394 

11727 

12057 

12385 

12710 

13033 

13354 

13672 

13988 

14301 

323 

14 

14613 

14922 

15229 

15534 

15836 

16137 

16435 

16732 

17026 

17319 

298 

15 

17609 

17898 

18184 

18469 

18752 

19033 

19312 

19590 

19866 

20140 

281 

16 

20412 

20683 

20952 

21219 

21484 

21748 

22011 

22272 

22531 

22789 

264 

17 

23045 

23300 

23553 

23805 

24055 

24304 

24551 

24797 

25042 

25285 

249 

18 

25527 

25768 

26007 

26245 

26482 

26717 

26951 

27184 

27416 

27646 

234 

19 

27875 

28103 

28330 

28556 

28780 

29003 

29226 

29447 

29667 

29885 

222 

20 

30103 

30320 

30535 

30750 

30963 

31175 

31387 

31597 

31806 

32015 

212 

21 

32222 

32428 

32634 

32838 

33041 

33244 

33445 

33646 

33846 

34044 

202 

22 

34242 

34439 

34635 

34830 

35025 

35218 

35411 

35603 

35793 

35984 

193 

23 

36173 

36361 

36549 

36736 

36922 

37107 

37291 

37475 

37658 

37840 

185 

24 

38021 

38202 

38382 

38561 

38739 

38917 

39094 

39270 

39445 

39620 

177 

25 

39794 

39967 

40140 

40312 

40483 

40654 

40824 

40993 

41162 

41330 

170 

26 

41497 

41664 

41830 

41996 

42160 

42325 

42488 

42651 

42813 

42975 

164 

27 

43136 

43297 

43457 

43616 

43775 

43933 

44091 

44248 

44404 

44560 

158 

28 

44716 

44871 

45025 

45179 

45332 

45484 

45637 

45788 

45939 

46090 

153 

29 

46240 

46389 

46538 

46687 

46835 

46982 

47129 

47276 

47422 

47567 

148 

30 

47712 

47857 

48001 

48144 

48287 

48430 

48572 

48714 

48855 

48996 

143 

31 

49136 

49276 

49415 

49554 

49693 

49831 

49969 

50106 

50243 

50379 

138 

32 

50515 

50651 

50786 

50920 

51055 

51189 

51322 

51455 

51587 

51720 

134 

33 

51851 

51983 

52114 

52244 

52375 

52504 

52634 

52763 

52892 

53020 

130 

34 

53148 

53275 

53403 

53529 

53656 

53782 

53908 

54033 

54158 

54283 

126 

35 

54407 

54531 

54654 

54777 

54900 

55023 

55145 

55267 

55388 

55509 

122 

36 

55630 

55751 

55871 

55991 

56110 

56229 

56348 

56467 

56585 

56703 

119 

37 

56820 

56937 

57054 

57171 

57287 

57403 

57519 

57634 

57749 

57864 

116 

38 

57978 

58093 

58206 

58320 

58433 

58546 

58659 

58771 

58883 

58995 

113 

39 

59106 

59218 

59329 

59439 

59550 

59660 

59770 

59879 

59988 

60097 

110 

40 

60206 

60314 

60423 

60531 

60638 

60746 

60853 

60959 

61066 

61172 

107 

41 

61278 

61384 

61490 

61595 

61700 

61805 

61909 

62014 

62118 

62221 

104 

42 

62325 

62428 

62531 

62634 

62737 

62839 

62941 

63043 

63144 

63246 

102 

43 

63347 

63448 

63548 

63649 

63749 

63849 

63949 

64048 

64147 

64246 

99 

44 

64345 

64444 

64542 

64640 

64738 

64836 

64933 

65031 

65128 

65225 

98 

45 

65321 

65418 

65514 

65610 

65706 

65801 

65896 

65992 

66087 

66181 

96 

46 

66276 

66370 

66464 

66558 

66652 

66745 

66839 

66932 

67025 

67117 

95 

47 

67210 

67302 

67394 

67486 

67578 

67669 

67761 

67852 

67943 

68034 

92 

48 

68124 

68215 

68305 

68395 

68485 

68574 

68664 

68753 

68842 

68931 

90  • 

49 

69020 

69108 

69197 

69285 

69373 

69461 

69548 

69636 

69723 

69810 

88 

TABLE  I. 
Logfarithms  of  Numbers  from  500  to  999.  —  Continued. 


No. 

0 

1 

69984 

2 

3 

4 

5 

6 

70415 

7 
70501 

8 

70586 

9 

Prop. 
Part, 

50 

69897 

70070 

70157 

70243 

70329 

70672 

86 

51 

70757 

70842 

70927 

71012 

71096 

71181 

71265 

71349 

71433 

71517 

84 

52 

71600 

71684 

71767 

71850 

71933 

72016 

72099 

72181 

72263 

72346 

82 

63 

72428 

72509 

72521 

72673 

72754 

72835 

72916 

72997 

73078 

73159 

81 

54 

73239 

73320 

73400 

73480 

73560 

73640 

73719 

73799 

73878 

73957 

80 

55 

74036 

74115 

74194 

74273 

74351 

74429 

74507 

74586 

74663 

74741 

78 

56 

74819 

74896 

74974 

75051 

75128 

75205 

75282 

75358 

75435 

75511 

77 

57 

75587 

75664 

75740 

75815 

75891 

75967 

76042 

76118 

76193 

76268 

75 

58 

76343 

76418 

76492 

76567 

76641 

76716 

76790 

76864 

76938 

77012 

74 

59 

77085 

77159 

77232 

77305 

77379 

77452 

77525 

77597 

77670 

77743 

73 

60 

77815 

77887 

77960 

78032 

78104 

78176 

78247 

78319 

78390 

78462 

72 

61 

78533 

78604 

78675 

78746 

78817 

78888 

78958 

79029 

79099 

79169 

71 

62 

79239 

79309 

79379 

79449 

79518 

79588 

79657 

79727 

79796 

79865 

70 

63 

79934 

80003 

80072 

80140 

80209 

80277 

80346 

80414 

80482 

80550 

69 

64 

80618 

80686 

80754 

80821 

80889 

80956 

81023 

81090 

81158 

81224 

68 

65 

81291 

81358 

81425 

81491 

81558 

81624 

81690 

81757 

81823 

81889 

67 

66 

81954 

82020 

82086 

81151 

82217 

82282 

82347 

82413 

82478 

82543 

66 

67 

82607 

82672 

82737 

82802 

82866 

82930 

82995 

83059 

83123 

83187 

64 

68 

83251 

83315 

83378 

83442 

83506 

83569 

83632 

83696 

83759 

83822 

63 

69 

83885 

83948 

84011 

84073 

84136 

84198 

84261 

84323 

84386 

84448 

63 

70 

84510 

84572 

84634 

84696 

84757 

84819 

84880 

84942 

85003 

85065 

62 

71 

85126 

85187 

85248 

85309 

85370 

85431 

85491 

85552 

85612 

85673 

61 

72 

85733 

85794 

85854 

85914 

85974 

86034 

86094 

86153 

86213 

86273 

60 

73 

86332 

86392 

86451 

86510 

86570 

86629 

86688 

86747 

86806 

86864 

59 

74 

86923 

86982 

87040 

87099 

87157 

87216 

87274 

87332 

87300 

87448 

58 

75 

87506 

87564 

87622 

87680 

87737 

87795 

87852 

87910 

87967 

88024 

57 

76 

88081 

88138 

88196 

88252 

88309 

88366 

88423 

88480 

88536 

88593 

57 

77 

88649 

88705 

88762 

88818 

88874 

88930 

88986 

89042 

89098 

89154 

56 

78 

89209 

89265 

89321 

89376 

89432 

89487 

89542 

89597 

89653 

89708 

55 

79 

89763 

89818 

89873 

89927 

89982 

90037 

90091 

90146 

90200 

90255 

54 

80 

90309 

90363 

90417 

90472 

90526 

90580 

90634 

90687 

90741 

90795 

54 

81 

90849 

90902 

90956 

91009 

91062 

91116 

91169 

91222 

91275 

91328 

53 

82 

91381 

91434 

91487 

91540 

91593 

91645 

91698 

91751 

91803 

91855 

53 

83 

91908 

91960 

92012 

92065 

92117 

92169 

92221 

92273 

92324 

92376 

52 

84 

92428 

92480 

92531 

92583 

92634 

92686 

93737 

92788 

92840 

92891 

51 

85 

92942 

92993 

93044 

93095 

93146 

93197 

93247 

93298 

93349 

93399 

51 

86 

93450 

93500 

93551 

93601 

93651 

93702 

93752 

93802 

93852 

93902 

50 

87 

93952 

94002 

94052 

94101 

94151 

94201 

94250 

94300 

94349 

94399 

49 

88 

94448 

94498 

94547 

94596 

94645 

94694 

94743 

94792 

94841 

94890 

49 

89 

94939 

94988 

95036 

95085 

95134 

95182 

95231 

95279 

95328 

95376 

48 

90 

95424 

95472 

95521 

95569 

95617 

95665 

95713 

95761 

95809 

95856 

48 

91 

95904 

95952 

95999 

96047 

96095 

96142 

96190 

96237 

96284 

96332 

48 

92 

96379 

96426 

96473 

96520 

96567 

96614 

96661 

96708 

96755 

96802 

47 

93 

96848 

96895 

96942 

96988 

97035 

97081 

97128 

97174 

97220 

97267 

47 

94 

97313 

97359 

97405 

97451 

97497 

97543 

97589 

97635 

97681 

97727 

46 

95 

97772 

97818 

97864 

97909 

97955 

98000 

98046 

98091 

98137 

98182 

46 

96 

98227 

98272 

98318 

98363 

98408 

98453 

98498 

98543 

98588 

98632 

45 

97 

98677 

98722 

98767 

98811 

98856 

98900 

98945 

98989 

99034 

99078 

45 

■  98 

99123 

99167 

99211 

99255 

99300 

99344 

99388 

99432 

99476 

99520 

44 

99 

99564 

99607 

99651 

99695 

99739 

99782 

99826 

99870 

99913 

99957 

43 

TABLE  II. 


XXIX 


TABLE  IL 

Corrections  for  Dip,  Refraction,  Parallax,  and  Semi-Diameter  and  Dip  and  Refraction, 
to  be  applied  to  the  Observed  Altitude  of  the  Sun's  Lower  Limb,  or  of  a  Star,  to  obtain 
the  True  Altitude.  Barometer  30  inches  =  76.2  centimeters.  Thennometer  50°  F.=  10" 
Centigrade  =  8°  R.     Sims'  Semi-Diameter,  16'  02". 

Height  of  Observer's  Eye,  20  feet  =  6.1  metres. 


>  a 

Correction 

Correction 

Correction 

Observed 
Altitude 

Correction 

Correction 

1^ 

Sun 

+ 

Star 

Sun 

+ 

Star 

Sun 

4- 

Star 

Sun 

+ 

Star 

Sun 

+ 

Star 

0   / 

/  // 

r     // 

O       1 

1    II 

1   II 

o  / 

/  // 

/  /' 

0   / 

1    II 

/   // 

o   / 

/  // 

/  // 

5  00 

1  56 

14  15 

10  00 

6  29 

9  42 

15  00 

8  14 

7  57 

29  00 

10  02 

6  08 

59  00 

11  09 

4  58 

10 

2  12 

13  59 

10 

34 

37 

20 

19 

52 

30  00 

06 

04 

60  00 

10 

57 

20 

27 

44 

20 

39 

32 

40 

23 

48 

31  00 

10 

6  00 

61  00 

11 

55 

30 

41 

30 

30 

43 

28 

16  00 

8  27 

7  44 

32  00 

14 

5  56 

62  00 

12 

54 

40 

55 

16 

40 

48 

23 

20 

32 

39 

33  00 

17 

53 

63  00 

13 

53 

50 

3  08 

03 

50 

52 

19 

40 

36 

35 

34  00 

21 

49 

64  00 

15 

51 

6  00 

3  20 

12  51 

11  00 

6  57 

9  12 

17  00 

8  40 

7  31 

35  00 

10  24 

46 

65  00 

11  16 

50 

10 

32 

39 

10 

7  01 

10 

20 

43 

28 

36  00 

27 

43 

66  00 

17 

49 

20 

43 

28 

20 

05 

06 

40 

47 

24 

37  00 

30 

40 

67  00 

18 

4  48 

30 

54 

17 

30 

09 

02 

18  00 

8  50 

7  21 

38  00 

32 

38 

68  00 

19 

47 

40 

4  04 

07 

40 

13 

8  58 

20 

54 

17 

39  00 

35 

35 

69  00 

20 

45 

50 

14 

11  57 

50 

17 

54 

40 

57 

14 

40  00 

10  37 

5  32 

70  00 

11  21 

44 

7  00 

4  24 

47 

12  00 

7  20 

8  51 

19  00 

9  00 

7  11 

41  00 

39 

30 

71  00 

22 

43 

10 

33 

38 

10 

24 

47 

20 

03 

08 

42  00 

41 

28 

72  00 

23 

42 

20 

42 

29 

20 

28 

43 

40 

06 

05 

43  00 

44 

25 

73  00 

24 

41 

30 

51 

20 

30 

31 

40 

20  00 

9  08 

7  02 

44  00 

46 

23 

74  00 

25 

40 

40 

59 

12 

40 

34 

37 

30 

12 

6  58 

45  00 

10  48 

21 

75  00 

11  26 

4  39 

50 

5  07 

04 

50 

38 

33 

21  00 

9  16 

6  54 

46  00 

50 

19 

76  00 

27 

38 

8  00 

5  15 

10  56 

13  00 

7  41 

8  30 

30 

20 

50 

47  00 

52 

17 

77  00 

28 

37 

10 

22 

49 

10 

44 

27 

22  00 

9  24 

6  46 

48  00 

53 

16 

78  00 

29 

35 

20 

29 

42 

20 

47 

24 

30 

27 

43 

49  00 

55 

14 

79  00 

30 

34 

30 

36 

35 

30 

50 

21 

23  00 

9  31 

6  39 

50  00 

10  56 

5  12 

80  00 

11  31 

33 

40 

43 

28 

40 

53 

18 

30 

34 

36 

51  00 

58 

10 

81  00 

32 

32 

50 

49 

22 

50 

56 

15 

24  00 

9  37 

6  33 

52  00 

59 

08 

82  00 

33 

31 

9  00 

5  55 

10  16 

14  00 

7  58 

8  13 

30 

40 

30 

53  00 

11  01 

07 

83  00 

34 

4  30 

10 

6  01 

10 

10 

8  01 

10 

25  00 

9  43 

6  27 

54  00 

03 

05 

84  00 

35 

29 

20 

07 

04 

20 

04 

07 

30 

45 

25 

55  00 

04 

04 

85  00 

11  36 

28 

30 

13 

9  58 

30 

06 

05 

26  00 

9  48 

6  23 

56  00 

05 

02 

86  00 

37 

27 

40 

18 

53 

40 

09 

02 

27  00 

53 

17 

57  00 

06 

01 

87  00 

37 

26 

50 

24 

47 

50 

11 

8  00 

28  00 

9  58 

6  12 

58  00 

08 

4  59 

88  00 

38 

25 

XXX 


TABLE  III  AND  IV. 


TABLE  IIL 

Correction  for  Height  of  Eye  of  Observer.    To  be  applied  to  the  corrections  from 
Table  II  according  to  the  sign  given. 


Height  of 
Eye 

Correc- 
tion 

Height  of 
Eye 

Correc- 
tion 

Height  of  Eye 

Correc- 
tion. 

Height  of  Eye 

Correc- 

Feet 

Metres 

Feet 

Metres 

Feet 

Metres 

Feet 

Metres 

tion 

/     II 

/    // 

/    // 

/    // 

10 

3.1 

-M  17 

21 

6.4 

-0  06 

32 

9.8 

-1   10 

55 

16.7 

-2  53 

11 

3.4 

+  1  08 

22 

6.7 

-0  13 

33 

10.1 

-1  15 

60 

18.3 

-3  12 

12 

3.7 

+  1  00 

23 

7.0 

-0  19 

34 

10.4 

-1  20 

65 

19.8 

-3  31 

13 

4.0 

+  0  51 

24 

7.3 

-0  25 

35 

10.7 

-1  25 

70 

21.4 

-3  49 

14 

4.3 

+  0  43 

25 

7.6 

-0  31 

36 

11.0 

-1  30 

75 

22,9 

-4  06 

15 

4.6 

+  0  35 

26 

7.9 

-0  37 

37 

11.3 

-1  35 

80 

24.4 

-4  23 

16 

4.9 

+  0  28 

27 

8.2 

-0  43 

38 

11.6 

-1  39 

85 

25.9 

-4  40 

17 

5.2 

+  0  21 

28 

8.5 

-0  48 

39 

11.9 

-1  44 

90 

27.4 

-4  55 

18 

5.5 

+  0  14 

29 

8.9 

-0  54 

40 

12.2 

-1  49 

95 

28.9 

-5  10 

19 

5.8 

+  0  07 

30 

9.2 

-1  00 

45 

13.7 

-2  13 

100 

30.5 

-5  25 

20 

6.1 

0 

31 

9.5 

-1  04 

50 

15.2 

-2  23 

105 

30.8 

-5  40 

TABLE  IV. 

Correction  for  Sun's  Semi-Diameter. 


Jan. 
+  15" 

Feb. 

+  11" 

March 

+  5" 

April 
-4" 

May 
-  11" 

June 
-  16" 

July 
-  15" 

August 
-  11" 

Sept. 
-  5" 

Oct. 

+  4" 

Nov. 
+  11" 

Dec. 

+  16" 

The  corrections  in  Table  II  for  the  Altitude  of  a  Star  may  be  used  for  the  Planets 
also,  as  the  Parallax  is  so  small  that  it  may  ordinarily  be  neglected. 


TABLE  V. 
Altitude  —  Azimuth  Tabic* 


Latitudes 

Azi- 
muths 

,    . 

muths 

0° 

1° 

2 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

o 

1 

0.26 

0.26 

0.26 

1 
0.26 

0.26 

0.26 

0.26 

0.26 

/ 
0.26 

1 
0.26 

o 
1 

2 

0.52 

0.52 

0.52 

0.52 

0.52 

0.52 

0.52 

0.52 

0.52 

0.52 

2 

3 

0.79 

0.79 

0.79 

0.79 

0.78 

0.78 

0.78 

0.78 

0.78 

0.77 

3 

4 

1.05 

1.05 

1.05 

1.05 

1.04 

1.04 

1.04 

1.04 

1.04 

1.03 

4 

5 

1.31 

1.31 

1.31 

1.31 

1.30 

1.30 

1.30 

1.30 

1.29 

1.29 

5 

6 

1.57 

1.57 

1.57 

1.57 

1.56 

1.56 

1.56 

1.56 

1.56 

1.55 

6 

7 

1.83 

1.83 

1.83 

1.83 

1.82 

1.82 

1.82 

1.82 

1.81 

1.81 

7 

8 

2.09 

2.09 

2.09 

2.09 

2.08 

2.08 

2.08 

2.08 

2.08 

2.07 

8 

9 

2.34 

2.34 

2.34 

2.34 

2.34 

2.34 

2.34 

2.33 

2.32 

2.32 

9 

10 

2.60 

2.60 

2.60 

2.60 

2.60 

2.60 

2.60 

2.60 

2.59 

2.58 

10 

11 

2.86 

2.86 

2.86 

2.86 

2.85 

2.88 

2.84 

2.84 

2.83 

2.83 

11 

12 

3.12 

3.12 

3.12 

3.12 

3.11 

3.11 

3.11 

3.10 

3.09 

3.08 

12 

13 

3.43 

3.42 

3.41 

3.40 

3.38 

3.36 

3.35 

3.34 

3.33 

3.33 

13 

14 

3.74 

3.72 

3.70 

3.67 

3.64 

3.62 

3.62 

3.61 

3.60 

3.59 

14 

15 

4.02 

3.99 

3.96 

3.93 

3.90 

3.87 

3.86 

3.85 

3.84 

3.83 

15 

16 

4.30 

4.27 

4.24 

4.20 

4.16 

4.12 

4.11 

4.10 

4.09 

4.08 

16 

17 

4.58 

4.55 

4.50 

4.46 

4.41 

4.37 

4.36 

4.35 

4.34 

4.33 

17 

18 

4.87 

4.82 

4.77 

4.72 

4.67 

4.62 

4.61 

4.60 

4.59 

4.58 

18 

19 

5.17 

5.10 

5.04 

4.98 

4.92 

4.87 

4.86 

4.85 

4.84 

4.83 

19 

20 

5.46 

5.39 

5.32 

5.25 

5.18 

5.11 

5.10 

5.09 

5.08 

5.07 

20 

21 

5.76 

5.68 

5.60 

5.52 

5.44 

5.36 

5.35 

5.33 

5.32 

5.31 

21 

22 

6.06 

5.97 

5.88 

5.79 

5.70 

5.60 

5.59 

5.58 

5.57 

5.55 

22 

23 

6.37 

6.27 

6.16 

6.05 

5.95 

5.84 

5.82 

5.80 

5.79 

5.78 

23 

24 

6.68 

6.56 

6.44 

6.32 

6.20 

6.08 

6.06 

6.04 

6.03 

6.02 

24 

25 

7.00 

6.86 

6.73 

6.62 

6.45 

6.32 

6.30 

6.28 

6.26 

6.25 

25 

26 

7.32 

7.17 

7.02 

6.87 

6.71 

6.55 

6.54 

6.53 

6.52 

6.50 

26 

27 

7.65 

7.47 

7.30 

7.13 

6.96 

6.79 

6.78 

6.76 

6.74 

6.72 

27 

28 

7.97 

7.78 

7.59 

7.40 

7.21 

7.02 

7.01 

6.99 

6.97 

6.95 

28 

29 

7.66 

7.46 

7.24 

7.23 

7.22 

7.20 

7.18 

29 

30 

7.47 

7.46 

7.45 

7.43 

7.41 

30 

( 

jhange  c 

f  Altitw 

ie  in  Ont 

s  Minute 

Azi- 

Azi- 

muths 

muths 

Error  i 

n  the  Fi 

rst  Redu 

ction  Di 

le  to  an 

Error  of 

One  Min 

ute  in  t 

16  Hour 

Angle 

xxxu 


TABLE  V. 
Altitude  —  Azimuth  Table.  —  Continued, 


Azi- 
muths 

Liitit 

udes 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

muths 

0 

1 

1 
0.26 

0.26 

0.26 

0.26 

0.26 

0.25 

/ 
0.25 

0.25 

0.25 

1 
0.25 

0 

1 

2 

0.52 

0.52 

0.52 

0.52 

0.51 

0.51 

0.51 

0.50 

0.50 

0.50 

2 

3 

0.77 

0.77 

0.77 

0.77 

0.76 

0.76 

0.76 

0.75 

0.75 

0.74 

3 

4 

1.03 

1.02 

1.02 

1.02 

1.01 

1.01 

1.01 

1.00 

0.99 

0.99 

4 

5 

1.28 

1.28 

1.27 

1.27 

1.26 

1.26 

1.25 

1.24 

1.24 

1.24 

5 

6 

1.54 

1.54 

1.53 

1.53 

1.52 

1.51 

1.51 

1.50 

1.49 

1.48 

6 

7 

1.80 

1.80 

1.79 

1.78 

1.77 

1.76 

1.75 

1.74 

1.74 

1.73 

7 

8 

2.06 

2.05 

2,04 

2.03 

2.02 

2.02 

2.01 

2.00 

1.99 

1.98 

8 

9 

2.31 

2.30 

2.29 

2.28 

2.27 

2.27 

2.26 

2.25 

2.23 

2.22 

9 

10 

2.57 

2.56 

2.55 

2.54 

2.53 

2.52 

2.50 

2.49 

2.47 

2.46 

10 

11 

2.82 

2.81 

2.80 

2.79 

2.78 

2.77 

2.76 

2.75 

2.73 

2.71 

11 

12 

3.07 

3.05 

3.04 

3.03 

3.02 

3.01 

3.00 

2.99 

2.97 

2.95 

12 

13 

3.32 

3.30 

3.29 

3.28 

3.27 

3.26 

3.25 

3.23 

3.21 

3.19 

13 

14 

3.58 

3.56 

3.54 

3.53 

3.52 

3.51 

3.49 

3.47 

3.45 

3.43 

14 

15 

3.83 

3.81 

3.79 

3.77 

3.76 

3.75 

3.73 

3.71 

3.69 

3.67 

15 

16 

4.07 

4.05 

4.03 

4.01 

4.00 

3.99 

3.97 

3.95 

3.93 

3.91 

16 

17 

4.32 

4.30 

4.28 

4.26 

4.25 

4.23 

4.21 

4.19 

4.17 

4.14 

17 

18 

4.57 

4.55 

4.53 

4.51 

4.49 

4.48 

4.46 

4.44 

4.41 

4.38 

18 

19 

4.81 

4.79 

4.77 

4.75 

4.73 

4.72 

4.70 

4.68 

4.65 

4.62 

19 

20 

5.05 

5.03 

5.01 

4.99 

4.97 

4.96 

4.94 

4.91 

4.88 

4.85 

20 

21 

5.29 

5.27 

5.25 

5.23 

5.21 

5.19 

5.17 

5.14 

5.11 

5.08 

21 

22 

5.53 

5.51 

5.49 

5.47 

5.45 

5.43 

5.40 

5.37 

5.34 

5.31 

22 

23 

5.77 

5.75 

5.73 

5.71 

5.69 

5.66 

5.63 

5.60 

5.57 

5.54 

23 

24 

6.01 

5.98 

5.95 

5.93 

5.91 

5.89 

5.86 

5.83 

5.80 

5.77 

24 

25 

6.24 

6.22 

6.20 

6.17 

6.14 

6.12 

6.09 

6.06 

6.03 

5.99 

25 

26 

6.48 

6.45 

6.42 

6.39 

6.37 

6.35 

6.32 

6.29 

6.26 

6.22 

26 

27 

6.70 

6.67 

6.64 

6.61 

6.59 

6.57 

6.54 

6.51 

6.48 

6.44 

27 

28 

6.93 

6.90 

6.87 

6.84 

6.82 

6.80 

6.77 

6.74 

6.70 

6.66 

28 

29 

7.16 

7.13 

7.10 

7.07 

7.04 

7.02 

6.99 

6.95 

6.91 

6.87 

29 

30 

7.39 

7.36 

7.33 

7.30 

7.27 

7.25 

7.21 

7.17 

7.13 

7.09 

30 

Azi- 

< 

Change  o 

f  Altituc 

le  in  One 

Minute 

Azi- 

muths 

Error 

iu  the  F 

rst  Redi 

iction  Di 

le  to  an  1 

Error  of 

One  Min 

ute  in  tl 

e  Hour 

Angle 

muths 

lAliJ 

^ii;  V. 

xxxm 

Altitude 

-Kz 

fmoth  Table*  —  Continued. 

Azi- 
muths 

Latitudes 

Azi- 
muths 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

o 

1 

0.25 

1 
0.25 

0.25 

0.24 

0.24 

0.24 

0.24 

0.24 

0.23 

0.23 

o 

1 

2 

0.49 

0.49 

0.48 

0.48 

0.47 

0.47 

0.47 

0.46 

0.46 

0.45 

2 

3 

0.73 

0.73 

0.72 

0.72 

0.71 

0.71 

0.71 

0.70 

0.70 

0.69 

3 

4 

0.98 

0.98 

0.97 

0.96 

0.95 

0.95 

0.94 

0.93 

0.92 

0.91 

4 

5 

1.22 

1.21 

1.21 

1.20 

1.19 

.1.18 

1.17 

1.16 

1.15 

1.14 

5 

6 

1.47 

1.46 

1.45 

1,44 

1.43 

1.42 

1.41 

1.40 

1.39 

1.38 

6 

7 

1.71 

1.70 

1.69 

1.68 

1.67 

1.65 

1.64 

1.63 

1.61 

1.59 

7 

8 

1.96 

1.95 

1.94 

1.93 

1.91 

1.89 

1.88 

1.86 

1.84 

1.82 

8 

9 

2.20 

2.19 

2.18 

2.16 

2.14 

2.12 

2.11 

2.09 

2.07 

2.05 

9 

10 

2.45 

2.44 

2.42 

2.40 

2.38 

2.36 

2.34 

2.32 

2.30 

2.28 

10 

11 

2.69 

2.67 

2.65 

2.63 

2.61 

2.59 

2.57 

2.55 

2.53 

2.51 

11 

12 

2.93 

2.91 

2.89 

2.87 

2.85 

2.83 

2.81 

2.79 

2.76 

2.73 

12 

13 

3.17 

3.15 

3.13 

3.11 

3.09 

3.06 

3.04 

3.01 

2.98 

2.95 

13 

14 

3.41 

3.39 

3.37 

3.35 

3.33 

3.29 

3.26 

3.23 

3.20 

3.17 

14 

15 

3.65 

3.63 

3.61 

3.58 

3.55 

3.52 

3.49 

3.46 

3.43 

3.39 

15 

16 

3.89 

3.87 

3.84 

3.81 

3.78 

3.75 

3.72 

3.69 

3.66 

3.62 

16 

17 

4.12 

4.09 

4.06 

4.03 

4.00 

3.97 

3.94 

3.91 

3.87 

3.83 

17 

18 

4.36 

4.33 

4.30 

4.27 

4.24 

4.20 

4.17 

4.13 

4.09 

4.05 

18 

19 

4.59 

4.56 

4.53 

4.49 

4.45 

4.41 

4.38 

4.34 

4.30 

4.26 

19 

20 

4.82 

4.78 

4.74 

4.70 

4.66 

4.62 

4.59 

4.56 

4.52 

4.48 

20 

21 

5.05 

5.00 

4.95 

4.90 

4.85 

4.85 

4.81 

4.77 

4.73 

4.69 

21 

22 

5.28 

5.25 

5.21 

5.17 

5.13 

5.09 

5.05 

5.01 

4.97 

4.92 

22 

23 

5.50 

5.47 

5.43 

5.39 

5.35 

5.31 

5.27 

5.22 

5.17 

5.12 

23 

24 

5.73 

5.69 

5.65 

5.61 

5.57 

5.53 

5.48 

5.43 

5.38 

5.33 

24 

25 

5.95 

5.91 

5.87 

5.83 

5.79 

5.74 

5.69 

5.64 

5.59 

5.54 

25 

26 

6.18 

6.14 

6.10 

6.06 

6.01 

5.96 

5.91 

5.86 

5.81 

5.75 

26 

27 

6.40 

6.36 

6.32 

6.27 

6.22 

6.17 

6.12 

6.07 

6.01 

5.95 

27 

28 

6.62 

6.58 

6.53 

6.48 

6.43 

6.38 

6.33 

6.28 

6.22 

6.16 

28 

29 

6.83 

6.79 

6.74 

6.69 

6.64 

6.59 

6.54 

6.48 

6.42 

6.36 

29 

30 

7.05 

7.00 

6.95 

6.90 

6.85 

6.80 

6.74 

6.68 

6.62 

6.56 

30 

Azi- 

C 

Change  o 

f  Altitud 

e  in  One  Minute 

Azi- 

muths 

Error  i 

n  the  Fii 

St  Reduc 

tion  Du« 

s  to  an  E 

rror  of  One  Minute  in  th< 

5  Hour  Angle 

muths 

XXXIV 


Altitude 


TABLE  V. 
Azimuth  Table. 


Continued* 


Azi- 
muths 

Latitudes 

Azi- 
muths 

30° 

31° 

32° 

33° 

34° 

3.5° 

36° 

37° 

38° 

39° 

o 

1 

0.23 

/ 

0.23 

0.23 

0.23 

/ 

0.22 

/ 
0.22 

/ 
0.22 

0.21 

/ 
0.21 

0.20 

t 
1 

2 

0.45 

0.45 

0.44 

0.44 

0.43 

0.43 

0.42 

0.42 

0.41 

0.41 

2 

3 

0.68 

0.68 

0.67 

0.66 

0.65 

0.64 

0.63 

0.62 

0.61 

0.60 

3 

4 

0.91 

0.90 

0.89 

0.88 

0.87 

0.86 

0.85 

0.84 

0.83 

0.81 

4 

5 

1.13 

1.12 

1.11 

1.10 

1.09 

1.07 

1.05 

1.03 

1.02 

1.01 

5 

6 

1.36 

1.35 

1.34 

1.32 

1.30 

1.28 

1.26 

1.24 

1.23 

1.22 

6 

7 

1.58 

1.57 

1.56 

1.54 

1.52 

1.50 

1.48 

1.46 

1.44 

1.42 

7 

8 

1.81 

1.80 

1.78 

1.76 

1.74 

1.72 

1.70 

1.68 

1.66 

1.63 

8 

9 

2.03 

2.01 

1.99 

1.97 

1.95 

1.92 

1.90 

1.88 

1.86 

1.83 

9 

10 

2.26 

2.24 

2.21 

2.19 

2.16 

2.13 

2.11 

2.09 

2.06 

2.03 

10 

11 

2.48 

2.46 

2.43 

2.40 

2.37 

2.34 

2.31 

2.28 

2.25 

2.22 

11 

12 

2.70 

2.67 

2.64 

2.61 

2.58 

2.55 

2.52 

2.49 

2.46 

2.43 

12 

13 

2.92 

2.89 

2.86 

2.83 

2.80 

2.76 

2.73 

2.70 

2.67 

2.63 

13 

14 

3.14 

3.11 

3.08 

3.05 

3.01 

2.97 

2.94 

2.90 

2.86 

2.82 

14 

15 

3.36 

3.33 

3.30 

3.26 

3.22 

3.18 

3.14 

3.10 

3.06 

3.02 

15 

16 

3.58 

3.55 

3.51 

3.47 

3.43 

3.39 

3.35 

3.31 

3.27 

3.22 

16 

17 

3.79 

3.75 

3.71 

3.67 

3.63 

3.59 

3.55 

3.51 

3.46 

3.41 

17 

18 

4.01 

3.97 

3.93 

3.89 

3.85 

3.80 

3.75 

3.70 

3.65 

3.60 

18 

19 

4.22 

4.18 

4.14 

4.09 

4.04 

4.00 

3.95 

3.90 

3.85 

3.80 

19 

20 

4.44 

4.40 

4.35 

4.30 

4.25 

4.20 

4.15 

4.10 

4.04 

3.98 

20 

21 

4.65 

4.60 

4.55 

4.50 

4.45 

4.40 

4.35 

4.29 

4.23 

4.17 

21 

22 

4.87 

4.82 

4.77 

4.72 

4.66 

4.60 

4.54 

4.48 

4.42 

4.36 

22 

23 

5.07 

5.02 

4.97 

4.92 

4.86 

4.80 

4.74 

4.68 

4.62 

4,55 

23 

24 

5.28 

5.23 

5.18 

5.12 

5.06 

5.00 

4.94 

4.88 

4,81 

4.74 

24 

25 

5.48 

5.43 

5.38 

5.32 

5.26 

5.20 

5.13 

5.06 

4.99 

4.92 

25 

26 

5.69 

5.63 

5.57 

5.51 

5.45 

5.39 

5.31 

5.24 

5.17 

5.10 

26 

27 

5.89 

5.83 

5.77 

5.71 

5.65 

5.58 

5.50 

5.42 

5.35 

5.28 

27 

28 

6.10 

6.04 

5.98 

5.91 

5.84 

5.77 

5.69 

5.61 

5.53 

5.46 

28 

29 

6.30 

6.24 

6.17 

6.10 

6.03 

5.96 

5.88 

5.80 

5.72 

5.64 

29 

30 

6.50 

6.43 

6.36 

6.29 

6.22 

6.15 

6.07 

5.99 

5.91 

5.83 

30 

Jhange  c 

>f  Altitu 

le  in  One 

)  Minute 

Azi- 

Azi- 

muths 

muths 

Error 

in  the  Fi 

rst  Kedu 

ction  Di 

le  to  an  ' 

Crror  of 

One  Min 

ute  in  tl 

le  Hour 

Angle 

TABLE  V. 
Altitude  —  Azimuth  Table*  —  Continued, 


XXXV 


Latitudes 

Azi- 
muths 

Azi- 
muths 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

o 
1 

0.20 

/ 
0.20 

0.20 

0.19 

0.19 

0.19 

0.18 

0.18 

0.18 

/ 
0.18 

0 

1 

2 

0.40 

0.40 

0.39 

0.39 

0.38 

0.37 

0.36 

0.36 

0.35 

0.35 

2 

3 

0.60 

0.59 

0.58 

0.57 

0.56 

0.55 

0.54 

0.53 

0.52 

0.51 

3 

4 

0.80 

0.79 

0.78 

0.77 

0.76 

0.74 

0.73 

0.72 

0.71 

0.69 

4 

5 

1.00 

0.99 

0.98 

0.96 

0.94 

0.92 

0.91 

0.90 

0.88 

0.86 

5 

6 

1.20 

1.19 

1.17 

1.15 

1.13 

1.11 

1.09 

1.07 

1.05 

1.03 

6 

7 

1.40 

1.38 

1.36 

1.34 

1.32 

1.29 

1.27 

1.25 

1.23 

1.20 

7 

8 

1.60 

1.58 

1.56 

1.54 

1.52 

1.48 

1.46 

1.43 

1.40 

1.37 

8 

9 

1.80 

1.78 

1.75 

1.72 

1.69 

1.66 

1.63 

1.60 

1.57 

1.54 

9 

10 

2.00 

1.97 

1.94 

1.91 

1.88 

1.84 

1.81 

1.78 

1.75 

1.71 

10 

11 

2.19 

2.16 

2.13 

2.10 

2.06 

2.02 

1.99 

1.96 

1.92 

1.88 

11 

12 

2.39 

2.36 

2.33 

2.29 

2.25 

2.21 

2.17 

2.13 

2.09 

2.05 

12 

13 

2.59 

2.56 

2,52 

2.48 

2.44 

2.40 

2.36 

2.32 

2.27 

2.22 

13 

14 

2.78 

2.74 

2.70 

2.66 

2.62 

2.57 

2.53 

2.48 

2.43 

2.38 

14 

15 

2.98 

2.94 

2.90 

2.85 

2.80 

2.75 

2.70 

2.65 

2.60 

2.55 

15 

16 

3.17 

3.12 

3.07 

3.02 

2.97 

2.92 

2.87 

2.82 

2.77 

2.72 

16 

17 

3.36 

3.31 

3.26 

3.21 

3.16 

3.10 

3.05 

3.00 

2.94 

2.88 

17 

18 

3.55 

3.50 

3.45 

3.40 

3.34 

3.28 

3.22 

3.16 

3.10 

3.04 

18 

19 

3.74 

3.69 

3.64 

3.59 

3.53 

3.46 

3.40 

3.34 

3.28 

3.21 

19 

20 

3.93 

3.87 

3.81 

3.75 

3.69 

3.63 

3.57 

3.51 

3.44 

3.37 

20 

21 

4.11 

4.05 

3.99 

3.93 

3.87 

3.80 

3.74 

3.67 

3.60 

3.53 

21 

22 

4.30 

4.24 

4.18 

4.11 

4.04 

3.97 

3.90 

3.83 

3.76 

3.69 

22 

23 

4.48 

4.42 

4.35 

4.28 

4.21 

4.14 

4.07 

3.99 

3.91 

3.83 

23 

24 

4.67 

4.60 

4.53 

4.46 

4.39 

4.31 

4.24 

4.16 

4.08 

4.00 

24 

25 

4.85 

4.77 

4.70 

4.63 

4.55 

4.48 

4.40 

4.32 

4.24 

4.16 

25 

26 

5.04 

4.97 

4.89 

4.81 

4.73 

4.65 

4.57 

4.49 

4.41 

4.32 

26 

27 

5.21 

5.14 

5.06 

4.98 

4.90 

4.82 

4.74 

4.65 

4.56 

4.47 

27 

28 

5.38 

5.30 

5.22 

5.14 

5.06 

4.98 

4.89 

4.80 

4.71 

4.62 

28 

29 

5.56 

5.48 

5.40 

5.32 

5.23 

5.14 

5.05 

4.96 

4.87 

4.78 

29 

30 

5.75 

5.66 

5.57 

5.48 

5.39 

5.30 

5.21 

5.12 

5.02 

4.92 

30 

Azi- 

< 

Change  o 

f  Altitm 

ie  in  Om 

Minute 

Azi- 

muths 

Error 

in  the  F 

rst  Redi 

ction  Di 

le  to  an  J 

Error  of 

One  Miu 

ate  in  th 

e  Hour  J 

Ingle 

muths 

XXXVl 


TABLE  V. 
Altitude  —  Azimath  Tabic  —  Continued. 


Latitudes 

Azi- 
muths 

Azi- 

50° 

r^i° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

muths 

0 

1 

0.17 

0.17 

0.16 

0.16 

0.15 

0.15 

0.15 

0.15 

0.15 

o 

1 

2 

0.34 

0.33 

0.33 

0.32 

0.31 

0.30 

0.30 

0.29 

0.28 

2 

3 

0.50 

0.49 

0.48 

0.47 

0.46 

0.45 

0.44 

0.43 

0.42 

3 

4 

0.67 

0.66 

0.65 

0.64 

0.62 

0.60 

0.59 

0.58 

0.56 

4 

5 

0.84 

0.83 

0.81 

0.79 

0.77 

0.75 

0.73 

0.71 

0.69 

5 

6 

1.01 

0.99 

0.97 

0.95 

0.93 

0.90 

0.88 

0.86 

0.84 

6 

7 

1.17 

1.15 

1.13 

1.11 

1.08 

1.05 

1.03 

1.00 

0.97 

7 

8 

1.34 

1.32 

1.29 

1.26 

1.23 

1.20 

1.17 

1.14 

1.11 

8 

9 

1.50 

1.47 

1.44 

1.41 

1.38 

1.35 

1.31 

1.28 

1.25 

9 

10 

1.67 

1.64 

1.61 

1.57 

1.53 

1.49 

1.46 

1.42 

1.38 

10 

11 

1.84 

1.80 

1.76 

1.72 

1.68 

1.64 

1.60 

1.56 

1.52 

11 

12 

2.01 

1.97 

1.93 

1.89 

1.84 

1.79 

1.75 

1.71 

1.66 

12 

13 

2.17 

2.13 

2.09 

2.04 

1.99 

1.94 

1.89 

1.84 

1.79 

1.3 

14 

2.33 

2.28 

2.23 

2.18 

2.13 

2.08 

2.03 

1.98 

1.93 

14 

15 

2.49 

2.44 

2.39 

2.34 

2.29 

2.23 

2.17 

2.12 

2.07 

15 

16 

2.66 

2.61 

2.55 

2.49 

2.43 

2.37 

2.31 

2.25 

2.19 

16 

17 

2.82 

2.76 

2.70 

2.64 

2.58 

2.52 

2.45 

2.39 

2.33 

17 

18 

2.98 

2.92 

2.86 

2.80 

2.73 

2.66 

2.60 

2.53 

2.46 

18 

19 

3.14 

3.08 

3.01 

2.94 

2.87 

2.80 

2.73 

2.66 

2.59 

19 

20 

3.30 

3.23 

3.16 

3.09 

3.02  • 

2.94 

2.87 

2.80 

2.73 

20 

21 

3.46 

3.39 

3.32 

3.24 

3.16 

3.08 

3.01 

2.93 

2.85 

21 

22 

3.62 

3.54 

3.46 

3.38 

3.30 

3.22 

3.14 

3.06 

2.98 

22 

23 

3.75 

3.68 

3.60 

3.52 

3.44 

3.36 

3.28 

3.20 

3.11 

23 

24 

3.92 

3.84 

3.76 

3.68 

3.59 

3.50 

3.41 

3.32 

3.23 

24 

25 

4.07 

3.99 

3.91 

3.82 

3.73 

3.64 

3.54 

3.45 

3.36 

25 

26 

4.23 

4.14 

4.05 

3.96 

3.87 

3.77 

3.68 

3.59 

3.49 

26 

27 

4.38 

4.29 

4.20 

4.11 

4.01 

3.91 

3.80 

3.70 

3.60 

27 

28 

4.53 

4.44 

4.34 

4.24 

4.14 

4.04 

3.94 

3.84 

3.74 

28 

29 

4.68 

4.58 

4.48 

4.38 

4.28 

4.17 

4.07 

3.96 

3.85 

29 

30 

4.82 

4.72 

4.62 

4.52 

4.41 

4.30 

4.19 

4.08 

3.97 

30 

Azi- 

Chan 

ge  of  Alt 

itude  in  ( 

)ne  Miuu 

te 

Azi- 

muths 

Error  in  t 

he  First  1 

ieductioi 

1  Due  to 

in  Error 

of  One  A 

[inute  in 

the  Hou 

r  Angle 

muths 

TABLE  V. 
Altitude  —  Azimuth  Table.  —  Continued, 


XXX  Vll 


Azl- 

mutli8 

Latitudes 

Azi- 

muths 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

o 

1 

0.14 

/ 

0.13 

/ 
0.13 

0.13 

0.12 

0.12 

0.11 

0 

1 

2 

0.27 

0.26 

0.26 

0.25 

0.24 

0.23 

0.22 

2 

3 

0.41 

0.39 

0.38 

0.37 

0.36 

0.35 

0.33 

3 

4 

0.54 

0.52 

0.51 

0.49 

0.47 

0.46 

0.44 

4 

5 

0.67 

0.65 

0.63 

0.61 

0.59 

0.57 

0.55 

5 

6 

0.81 

0.78 

0.76 

0.74 

0.72 

0.69 

0.66 

6 

7 

0.94 

0.91 

0.89 

0.86 

0.83 

0.80 

0.77 

7 

8 

1.08 

1.04 

1.01 

0.98 

0.95 

0.92 

0.88 

8 

9 

1.21 

1.17 

1.14 

1.11 

1.07 

1.03 

0.99 

9 

10 

1.34 

1.30 

1.26 

1.22 

1.18 

1.14 

1.10 

10 

11 

1.48 

1.43 

1.39 

1.35 

1.31 

1.26 

1.21 

11 

12 

1.61 

1.56 

1.52 

1.47 

1.42 

1.37 

1.32 

12 

13 

1.74 

1.69 

1.64 

1.59 

1.54 

1.49 

1.43 

13 

14 

1.87 

1.81 

1.76 

1.71 

1.65 

1.59 

1.53 

14 

15 

2.01 

1.94 

1.88 

1.82 

1.76 

1.70 

1.64 

15 

16 

2.13 

2.07 

2.01 

1.95 

1.89 

1.82 

1.75 

16 

17 

2.26 

2.19 

2.13 

2.06 

1.99 

1.92 

1.85 

17 

18 

2.39 

2.32 

2.25 

2.18 

2.11 

2.04 

1.96 

18 

19 

2.52 

2.44 

2.37 

2.30 

2.22 

2.14 

2.06 

19 

20 

2.65 

2.57 

2.49 

2.41 

2.33 

2.25 

2.17 

20 

21 

2.77 

2.69 

2.61 

2.53 

2.45 

2.36 

2.27 

21 

22 

2.90 

2.81 

2.73 

2.65 

2.56 

2.47 

2.38 

22 

23 

3.02 

2.93 

2.84 

2.75 

2.66 

2.57 

2.48 

23 

24 

3.14 

3.05 

2.96 

2.87 

2.78 

2.68 

2.58 

24 

25 

3.27 

3.17 

3.08 

2.98 

2.88 

2.78 

2.68 

25 

26 

3.39 

3.29 

3.19 

3.09 

2.99 

2.89 

2.78 

26 

27 

3.50 

3.40 

3.30 

3.20 

3.10 

2.99 

2.88 

27 

28 

3.63 

3.52 

3.42 

3.31 

3.20 

3.09 

2.98 

28 

29 

3.74 

3.63 

3.52 

3.41 

3.30 

3.19 

3.08 

29 

30 

3.86 

3.75 

3.64 

3.53 

3.41 

3.29 

3.17 

30 

Change  of  Altitude  in  One  Minute 

Azi- 

Azi- 

muths 

muths 

Error  in  t 

ie  First  Red 

uction  Due  to  an  Error  of  One  Min 

ute  in  the  I 

lour  Angle 

Tabic  VI.  —  Error  in  the  First  Reduction  Dae  to  an  Error 
the  Latitude  Used  in  the  Computation. 


ifVziiniitli 

Difference  between  the  Ass 

lined  Latitude  and  Latitude  by  Observation 

Azimuth 

Ditferen 

ee  between  the  Assumed  Declination  and  the  True  Declination 

Position 
Angle 

1 

/ 
2 

/ 
3 

/ 

4 

1 
5 

1 

6 

1 
10 

20 

1 
30 

40 

50 

60 

Position 
Angle 

0 

5 

0.0 

0.0 

/ 
0.0 

0.01 

0.02 

0.02 

0.04 

0.08 

0.11 

1 

0.15 

0.19 

1 
0.23 

o 

5 

10 

0.01 

0.03 

0.05 

0.06 

0.08 

0.09 

0.15 

0.30 

0.46 

0.61 

0.76 

0.91 

10 

H 

0.02 

0.04 

0.06 

0.07 

0.09 

0.11 

0.18 

0.37 

0.55 

0.73 

0.92 

1,10 

11 

12 

0.02 

0.04 

0.07 

0.09 

0.11 

0.13 

0.22 

0.44 

0.66 

0.87 

1.09 

1,31 

12 

13 

0.03 

0.05 

0.08 

0.10 

0.13 

0.15 

0.26 

0.51 

0.77 

1.03 

1.28 

1,54 

13 

14 

0.03 

0.06 

0.09 

0.12 

0.15 

0.18 

0.30 

0.59 

0.89 

1.19 

1.49 

1.78 

14 

15 

0.03 

0.07 

0.10 

0.14 

0.17 

0.20 

0.34 

0.68 

1.02 

1.36 

1.70 

2,04 

15 

16 

0.04 

0.08 

0.12 

0.15 

0.19 

0.23 

0.39 

0.77 

1.16 

1.55 

1.94 

2.32 

16 

17 

0.04 

0.09 

0.13 

0.17 

0.22 

0.26 

0.44 

0.87 

1.31 

1.75 

2.19 

2.62 

17 

18 

0.05 

0.10 

0.15 

0.20 

0.24 

0.29 

0.49 

0.98 

1.47 

1.96 

2.45 

2.94 

18 

19 

0.05 

0.11 

0.16 

0.22 

0.27 

0.33 

0.54 

1.09 

1.63 

2.18 

2,72 

3.27 

19 

20 

0.06 

0.12 

0.18 

0.24 

0.30 

0.36 

0.60 

1.21 

1.81 

2.41 

3.02 

3.62 

20 

21 

0.07 

0.13 

0.20 

0.27 

0.33 

0.40 

0.66 

1.33 

1.99 

2.66 

3.32 

3.99 

21 

22 

0.07 

0.15 

0.22 

0.29 

0.36 

0.44 

0.73 

1.46 

2.18 

2.91 

3.64 

4.37 

22 

23 

0.08 

0.16 

0.24 

0.32 

0.40 

0.47 

0.80 

1.59 

2.39 

3.18 

3.98 

4.70 

23 

24 

0.09 

0.17 

0.26 

0.35 

0.43 

0.52 

0.86 

1.73 

2.59 

3.46 

4.32 

5.19 

24 

26 

0.09 

0.19 

0.28 

0.37 

0.47 

0.56 

0.94 

1.87 

2.81 

3.75 

4.68 

5.62 

25 

26 

0.10 

0.20 

0.30 

0.40 

0.51 

0.61 

1.01 

2.02 

3.04 

4.05 

5.06 

6.07 

26 

27 

0.11 

0.22 

0.33 

0.44 

0.54 

0.65 

1.09 

2.18 

3.27 

4.36 

5.45 

6.54 

27 

28 

0.12 

0.23 

0.35 

0.47 

0.59 

0.70 

1.17 

2.34 

3.51 

4.68 

5.85 

7.02 

28 

29 

0.13 

0.25 

0.38 

0.50 

0.63 

0.75 

1.25 

2.51 

3.76 

5.02 

6.27 

7.52 

29 

30 

0.13 

0.27 

0.40 

0.54 

0.67 

0.80 

1.34 

2.68 

4.02 

5.36 

6.70 

8,04 

30 

31 

0,14 

0.29 

0.43 

0.57 

0.71 

0.86 

1.43 

2.86 

4,28 

5.71 

7.14 

8.57 

31 

32 

0.15 

0.30 

0.46 

0.61 

0.76 

0.91 

1.52 

3.04 

4.56 

6.08 

7.60 

9.12 

32 

33 

0.16 

0.32 

0.48 

0.65 

0.81 

0.97 

1.61 

3.23 

4.84 

6.45 

8.07 

9.68 

33 

34 

0.17 

0.34 

0.51 

0.68 

0.85 

1,03 

1.71 

3.42 

5.13 

6,84 

8,55 

10.26 

34 

35 

0.18 

0.36 

0.54 

0.72 

0.90 

1.09 

1.81 

3.62 

5.43 

7,23 

9.04 

10.85 

35 

36 

0.19 

0.38 

0.57 

0.76 

0.95 

1.14 

1.91 

3.82 

5.73 

7,64 

9.55 

11.46 

36 

37 

0.20 

0.40 

0.60 

0.81 

1.01 

1.21 

2.01 

4.03 

6.04 

8,05 

10.07 

12.08 

37 

38 

0.21 

0.42 

0.64 

0.85 

1.06 

1.27 

2,12 

4.24 

6.36 

8.48 

10.60 

12.72 

38 

39 

0.22 

0.45 

0.67 

0.89 

1.11 

1.34 

2.23 

4.46 

6.69 

8.91 

11.14 

13.37 

39 

40 

0.23 

0.47 

0.70 

0.94 

1.17 

1.40 

2.34 

4,68 

7.02 

9.36 

11.70 

14.04 

40 

Table  VI  also  shows  the  Error  in  the  First  Reduction  due  to  au  Error  in  the  Declina- 
tion used  in  the  Computation.     Enter  with  M  instead  of  Z. 


Table  Vn. —  Error  in  the  Latitude  Doe  to  an  Error  in 
the  Latitude  Used  in  the  Oimputation. 


Azimuth 

Difference  between  Assumed  Latitude  and  Latitude  by  Observation 

Azimuth 

/ 

1 

/ 

/ 

1 

/ 

/ 

/ 

1 

t 

1 

/ 

1 

2 

3 

4 

5 

6 

10 

20 

30 

40 
/ 

0.15 

50 

60 

o 
5 

/ 
0.0 

0.0 

0.0 

0.01 

0.02 

1 
0.03 

0.04 

0.08 

0.11 

0.19 

0.23 

o 

5 

10 

0.01 

0.03 

0.05 

0.06 

0.08 

0.09 

0.15 

0.30 

0.46 

0.62 

0.77 

0.92 

10 

11 

0.02 

0.04 

0.06 

0.07 

0.09 

0.11 

0.19 

0.38 

0.56 

0.75 

0.94 

1.12 

11 

12 

0.02 

0.04 

0.07 

0.09 

0.11 

0.13 

0.22 

0.44 

0.67 

0.89 

1.12 

1.34 

12 

13 

0.03 

0.05 

0.08 

0.11 

0.13 

0.16 

0.26 

0.52 

0.79 

1.05 

1.32 

1.58 

13 

14 

0.03 

0.06 

0.09 

0.12 

0.15 

0.18 

0.31 

0.62 

0.92 

1.22 

1.53 

1.84 

14 

15 

0.04 

0.07 

0.11 

0.14 

0.18 

0.21 

0.35 

0.70 

1.06 

1.41 

1.75 

2.12 

15 

16 

0.04 

0.08 

0.12 

0.16 

0.20 

0.24 

0.40 

0.80 

1.21 

1.61 

2.02 

2.42 

16 

17 

0.05 

0.09 

0.14 

0.18 

0.23 

0.27 

0.45 

0.90 

1.37 

1.83 

2.28 

2.74 

17 

18 

0.05 

0.10 

0.15 

0.21 

0.26 

0.31 

0.51 

1.02 

1.54 

2.06 

2.57 

3.08 

18 

19 

0.06 

0.11 

0.17 

0.23 

0.29 

0.35 

0.58 

1.16 

1.73 

2.30 

2.88 

3.46 

19 

20 

0.06 

0.12 

0.19 

0.26 

0.32 

0.39 

0.64 

1.28 

1.93 

2.57 

3.21 

3.86 

20 

21 

0.07 

0.14 

0.21 

0.28 

0.36 

0.43 

0.71 

1.42 

2.13 

2.85 

3.56 

4.26 

21 

22 

0.08 

0.15 

0.24 

0.31 

0.39 

0.47 

0.79 

1.58 

2.36 

3.14 

3.93 

4.72 

22 

23 

0.09 

0.17 

0.26 

0.35 

0.43 

0.52 

0.86 

1.72 

2.59 

3.45 

4.32 

5.18 

23 

24 

0.09 

0.19 

0.28 

0.38 

0.47 

0.57 

0.94 

1.88 

2.84 

3.79 

4.73 

5.68 

24 

26 

0.10 

0,20 

0.31 

0.41 

0.52 

0.62 

1.03 

2.06 

3.10 

4.13 

5.17 

6.20 

25 

26 

0.11 

0.22 

0.34 

0.45 

0.56 

0.68 

1.13 

2.26 

3.39 

4.51 

5.63 

6.78 

26 

27 

0.12 

0.24 

0.37 

0.49 

0.61 

0.73 

1.22 

2.44 

3.67 

4.89 

6.12 

7.34 

27 

28 

0.13 

0.27 

0.40 

0.53 

0.66 

0.80 

1.33 

2.66 

3.98 

5.30 

6.63 

7.96 

28 

29 

0.14 

0.29 

0.43 

0.57 

0.72 

0.86 

1.43 

2,86 

4.30 

5.73 

7.17 

8.60 

29 

30 

0.15 

0.31 

0.46 

0.62 

0.77 

0.93 

1.55 

3.10 

4.64 

6.19 

7.74 

9.28 

30 

31 

0.17 

0.33 

0.50 

0.67 

0.83 

1.00 

1.67 

3.33 

5.00 

6.67 

8.33 

10.00 

31 

32 

0.18 

0.36 

0.54 

0.72 

0.90 

1.08 

1.79 

3.58 

5.38 

7.17 

8.96 

10.75 

32 

33 

0.19 

0.38 

0.58 

0.77 

0.96 

1.15 

1.92 

3.85 

5.77 

7.69 

9.62 

11.54 

33 

34 

0.21 

0.41 

0.62 

0.82 

1.03 

1.24 

2.06 

4.12 

6.19 

8.25 

10.31 

12.37 

34 

35 

0.22 

0.44 

0.66 

0.88 

1.10 

1.33 

2.20 

4.42 

6.62 

8.83 

11.04 

13.25 

35 

36 

0.24 

0.47 

0.71 

0.94 

1.18 

1.42 

2.36 

4.72 

7.08 

9.44 

11.80 

14.16 

36 

37 

0.25 

0.50 

0.76 

1.01 

1.26 

1.51 

2.52 

5.04 

7.56 

10.08 

12.60 

15.13 

37 

38 

0.27 

0.54 

0.81 

1.07 

1.35 

1.61 

2.69 

5,38 

8.07 

10.76 

13.45 

16.14 

38 

39 

0.29 

0.57 

0.86 

1.15 

1.43 

1.73 

2.87 

5,74 

8.60 

11.47 

14.34 

17.21 

39 

40 

0.31 

0.61 

0.92 

1.22 

1.53 

1.84 

3.07 

6.13 

9.20 

12.27 

15.34 

18.40 

40 

Table 
Enter  w 


VII  also  .shows 
ith  position  angle 


the  error  in  the  Latitude  due  to  an  error  in  the  Declination 
M  instead  of  Azimuth. 


TABLE  Vin. 
For  Convcrtingf  Arc  into  Time  and  Time  ino  Arc 


0 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

M.  S. 

o 

H.  M. 

' 

M.  S. 

/ 

M.  S. 

' 

M.  S. 

f 

M.  S. 

1 

/ 

M.  S. 

' 

s.^ 

It 

S.^tT 

» 

s.^V 

II 

s-^V 

n 

s.A 

II 

S.  ^'o 

1 

0  4 

31 

2  4 

61 

4  4 

91 

6'  4 

121 

8  4 

151 

10  4 

2 

0  8 

32 

2  8 

62 

4  8 

92 

6  8 

122 

8  8 

152 

10  8 

3 

0  12 

33 

2  12 

63 

4  12 

93 

6  12 

123 

8  12 

153 

10  12 

4 

0  16 

34 

2  16 

64 

4  16 

94 

6  16 

124 

8  16 

154 

10  16 

5 

0  20 

35 

2  20 

65 

4  20 

95 

6  20 

125 

8  20 

155 

10  20 

6 

0  24 

36 

2  24 

66 

4  24 

96 

6  24 

126 

8  24 

156 

10  24 

7 

0  28 

37 

2  28 

67 

4  28 

97 

6  28 

127 

8  28 

157 

10  28 

8 

0  32 

38 

2  32 

68 

4  32 

98 

6  32 

128 

8  32 

158 

10  32 

9 

0  36 

39 

2  36 

69 

4  36 

99 

6  36 

129 

8  36 

159 

10  36 

10 

0  40 

40 

2  40 

70 

4  40 

100 

6  40 

130 

8  40 

160 

10  40 

11 

0  44 

41 

2  44 

71 

4  44 

101 

6  44 

131 

8  44 

161 

10  44 

12 

0  48 

42 

2  48 

72 

4  48 

102 

6  48 

132 

8  48 

162 

10  48 

13 

0  52 

43 

2  52 

73 

4  52 

103 

6  52 

133 

8  52 

163 

10  52 

14 

0  56 

44 

2  56 

74 

4  56 

104 

6  56 

134 

8  56 

164 

10  56 

15 

1  0 

45 

3  0 

75 

5  0 

105 

7  0 

135 

9  0 

165 

11  0 

16 

1  4 

46 

3  4 

76 

5  4 

106 

7  4 

136 

9  4 

166 

11  4 

17 

1  8 

47 

3  8 

77 

5  8 

107 

7  8 

137 

9  8 

167 

11  8 

18 

1  12 

48 

3  12 

78 

5  12 

108 

7  12 

138 

9  12 

168 

11  12 

19 

1  16 

49 

3  16 

79 

5  16 

109 

7  16 

139 

9  16 

169 

11  16 

20 

1  20 

50 

3  20 

80 

5  20 

110 

7  20 

140 

9  20 

170 

11  20 

21 

1  24 

51 

3  24 

81 

5  24 

111 

7  24 

141 

9  24 

171 

11  24 

22 

1  28 

52 

3  28 

82 

5  28 

112 

7  28 

142 

9  28 

172 

11  28 

23 

1  32 

53 

3  32 

83 

5  32 

113 

7  32 

143 

9  32 

173 

11  32 

24 

1  36 

54 

3  36 

84 

5  36 

114 

7  36 

144 

9  36 

174 

11  36 

25 

1  40 

55 

3  40 

85 

5  40 

115 

7  40 

145 

9  40 

175 

11  40 

26 

1  44 

56 

3  44 

86 

5  44 

116 

7  44 

146 

9  44 

176 

11  44 

27 

1  48 

57 

3  48 

87 

5  48 

117 

7  48 

147 

9  48 

177 

11  48 

28 

1  52 

58 

3  52 

88 

5  52 

118 

7  52 

148 

9  52 

178 

11  52 

29 

1  56 

59 

3  56 

89 

5  56 

119 

7  56 

149 

9  56 

179 

11  56 

30 

2  0 

60 

4  0 

90 

6  0 

120 

8  0 

150 

10  0 

180 

12  0 

xl 


TABLE  VIII.  xli 

For  Converting:  Arc  into  Time  and  Time  into  Arc  —  Continued, 


o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

' 

M.  S. 

> 

M.  S. 

/ 

M.  S. 

/ 

M.  S. 

' 

M.  S. 

/ 

M.  S. 

' 

s.^V 

H 

s-A 

It 

s-^V 

" 

s-^ 

" 

s.^V 

II 

s-A 

181 

12  4 

211 

14  4 

241 

16  4 

271 

18  4 

301 

20  4 

331 

22  4 

182 

12  8 

212 

14  8 

242 

16  8 

272 

18  8 

302 

20  8 

332 

22  8 

183 

12  12 

213 

14  12 

243 

16  12 

273 

18  12 

303 

20  12 

333 

22  12 

184 

12  16 

214 

14  16 

244 

16  16 

274 

18  16 

304 

20  16 

334 

22  16 

185 

12  20 

215 

14  20 

245 

16  20 

275 

18  20 

305 

20  20 

335 

22  20 

186 

12  24 

216 

14  24 

246 

16  24 

276 

18  24 

306 

20  24 

336 

22  24 

187 

12  28 

217 

14  28 

247 

16  28 

277 

18  28 

307 

20  28 

337 

22  28 

188 

12  32 

218 

14  32 

248 

16  32 

278 

18  32 

308 

20  32 

338 

22  32 

189 

12  36 

219 

14  36 

249 

16  36 

279 

18  36 

309 

20  36 

339 

22  36 

190 

12  40 

220 

14  40 

250 

16  40 

280 

18  40 

310 

20  40 

340 

22  40 

191 

12  44 

221 

14  44 

251 

16  44 

281 

18  44 

311 

20  44 

341 

22  44 

192 

12  48 

222 

14  48 

252 

16  48 

282 

18  48 

312 

20  48 

342 

22  48 

193 

12  52 

223 

14  52 

253 

16  52 

283 

18  52 

313 

20  52 

343 

22  52 

194 

12  56 

224 

14  56 

254 

16  56 

284 

18  56 

314 

20  56 

344 

22  56 

195 

13  0 

225 

15  0 

255 

17  0 

285 

19  0 

315 

21  0 

345 

23  0 

196 

13  4 

226 

15  4 

256 

17  4 

286 

19  4 

316 

21  4 

346 

23  4 

197 

13  8 

227 

15  8 

257 

17  8 

287 

19  8 

317 

21  8 

347 

23  8 

198 

13  12 

228 

15  12 

258 

17  12 

288 

19  12 

318 

21  12 

348 

23  12 

199 

13  16 

229 

15  16 

259 

17  16 

289 

19  16 

319 

21  16 

349 

23  16 

200 

13  20 

230 

15  20 

260 

17  20 

290 

19  20 

320 

21  20 

350 

23  20 

201 

13  24 

231 

15  24 

261 

17  24 

291 

19  24 

321 

21  24 

351 

23  24 

202 

13  28 

232 

15  28 

262 

17  28 

292 

19  28 

322 

21  28 

352 

23  28 

203 

13  32 

233 

15  32 

263 

17  32 

293 

19  32 

323 

21  32 

353 

23  32 

204 

13  36 

234 

15  36 

264 

17  36 

294 

19  36 

324 

21  36 

354 

23  36 

205 

13  40 

235 

15  40 

265 

17  40 

295 

19  40 

325 

21  40 

355 

23  40 

206 

13  44 

236 

15  44 

266 

17  44 

296 

19  44 

326 

21  44 

356 

23  44 

207 

13  48 

237 

15  48 

267 

17  48 

297 

19  48 

327 

21  48 

357 

23  48 

208 

13  52 

238 

15  52 

268 

17  52 

298 

19  52 

328 

21  52 

358 

23  52 

209 

13  56 

239 

15  56 

269 

17  56 

299 

19  56 

329 

21  56 

359 

23  56 

210 

14  0 

240 

16  0 

270 

18  0 

300 

20  0 

330 

22  0 

360 

24  0 

xlii 


TABLE  IX. 


s 

c 
1 

o 

00 

< 

0 

OOCOOOO<M'-''OCOT»<COMOaOOOOOOC<»'OOOC^t-»C^r^(MOO 

< 

n 

0 

< 

0 

T-<(NtOt^OS00<M— iC<J«0(MOOOOOO<M-*00»-l»OOtO>-'t~CC05 

«010'*COCOCOCOC^C<)C^C^C~<C4r-l-^i-lt-l.-li-Hr-(i-<.-l^H^H-H,— . 

< 

= 

1— l(MC«3C0C0C<5-^-<*<-^-*'^M<'^'^'*-^-^-^lO'O»C>O'OlOiniO 

o 

< 

o 

-Ht^050-H(Mr^CDOOC00300t^OOO<N»'50>COOOC<500Tt<i-it>.rl<rt 

lOTj<Tj)cooocciMlM(M(MiM~rtrtrtrtrtrti-i-Hi-iT-H.-l.-lr-<rt.-i 

< 

E 

J3 

tJ<CDt}<->*<05'— iC<JOOO"<*"0'005COOOC«5moOO(MM<COOOO— ICO 

o 

< 

o 

•<*<t^cr>oort(Moooortt^Tttco-^»ooO'-<'«tioocociiO.-it^(root^ir5<M 

COiOOOfOOt-'^IM— i03GOt-«0»0'<»<'«»<COC<IC^>-lr-i.-<0000505C5 
lO'*COCOCO(M<N(M(N--H-Hrtrtrtr-lr-(r^r-lrt,-lrtrt,-l^^ 

< 

X 

s 

J3 

T-iiOfM-^          rt(MCOCO-*-<*iiOiO                        '-i'^'^^'-«!M<N<M<NIM!M(M 

o 

< 

o 

M00O5'— i»0l-~«050i— lOOI>-t^OO-H->*iGO<Mt^CO«i>Oi— 10010(M00050-^ 

M^'^0<OC0^0500«D»OTt<OOCO(M^.-HOOO>050300000000r~r^t^ 

< 

X 

J3 

oocv3cq-^ict^50c<3a>ioo-^t^oe«5iooooiM-^iot^ooo^cqco->*<»c 

o 

< 

o 

<r>050-<ti^lOf005':0-^lOt-05COl^lMQO-*Ol--'^^OCO-^(NOOOt~lO 

OOtOO»0<MOSt--.»0-<l<C»3e<l-H00050iOOOOOOt^t^t^«OCO<»CDCDiO»OlO 

< 

s 

•*co       i-HCOTfiioio             •-(■-•■— i<Mc^c^(M(Ncococorocococococo-^'<i<-<ti 

0 

< 

o 

000«DiOOu:>OOtOiOi:005COt^(MOOlO(M03<OC<:i— HOt^tO-^CO— cOOiOOt— 

< 

K 

B 

co-^'*-^-^>o»oio»oioiomiomioiO'Oioioiomio»oioioirticioiO'rtu5 

o 

< 

0 

OlOlCiO<0<MC^Tt<QOC«300»C<M03CD-<+i(M^O>OOt^<£>lO-^C«5(M-^-^00000 

oa>'^.-M05a5t^oioiO'^Ti<Tj(coc«:icocofOC<ic<ic<)c<ic<ic^cjc^c<i(Nc^c^'— I"-! 

< 
X 

1 

0 

(Mco'*<ir5ir>t^oca>o-HC<«e<5Tt<\o«ot^ooo»o^e^MTt<i«tDt^ooo50-H(Mco 

rti-<rtF4rt»-ti-(rtrtrtC<ICS|(N{N<MIM<N(Nes|(NC>OCOCOrO 

TABLE  IX. 


xliii 


^3 
is 

(3 


a 

§ 
a 


■^Ot>-'<l<'-<00»0(MOOOiOCOT-iOOO«OlOC«3C<J00500tOlO-<!l<COC^--H-HOC;00 
°     ■^•^COCOCOCNC^IC^lC^T-i.-Hr-i.-i.— iOOOOOO050»05050>0205050>Ci0000 

p<N-^iOt-oiO'-ico'<*<ior^ooa50-HC^co-^'0<ot^r^ooo50-^'-i<Mco'*^io 
'-.--lI-Hr-^>-^I-H(^^c^lC^<^^(^^c^c^(^^coc«^cococo(:ocococol:oco•>»^•>*'■>*^■<l<■<l^■^■^TJ< 


eopoot~-'^<N05t»»ocoi-io5r^«OTt<cO'-ioo300eo»o-^cococ<ir-ioo>oooot- 

C^C^IMi— (1— l>-(000000»0»050505050500aOOOCOOOOOOOOOOOOOt>-t^t^t^ 


^Ir5i0i0i0»0i0i0»0l0l0icu^l0l0i0»0i0l0»0i0l0l0l0*010i0l0i0l0i0i0i0 


00»0C<IO00iffl'*<(MO0050»OT*(<Mi-lO00l^«0>0->*<C0<M.-l,-lO0>0000t^l^C0 


000003050J050500CX)00«3000000t^t^t^t^t^t^t:^t^t^t^CD«OtOCOOCO 


^  C5  C3  O  C3 


J3»0l0>0l0l0ic»0i0«0»0»0l0l0l0»0l0»0i0»0»0l0'0l0>0»0»0l0l0i0»0>0m 


Ot~>OC«5.— lOOO«Cl»OCOC<J>-lOOOr~-CO»OT*(CCCO<Mr-l00050000t~-t^«OCOlO 


cO'-<<Mc<:i-*»ocot:^oooco30'-i 


(MOOOI--U3Tt<(M-H00500I>-CO»C'«l<CO(NT-lT-l00030000t^t^«OiX)lOlO'*-* 


^ioioicio>oio»o»o»oiou:iinio«o'0'Oio»oio»oioioiO'oio>oiomiO'0»oio 


■*l(M-H00500t^tOiO'^CO(MC<l.-H0003000000l^tr^<»COlO»OlOTt<Tt<'*cOCO 


°    cr>c^c<i(ncoco<ncoco(>^c<i(>i(:<t(:<i<^<^c<>c<i(^c<i(^i>tc^(:<t(^c<ic<ie^c^t>i<:^(:^ 


X2lOl0^lOiOlOtOlOlOiOlOlOLOlOlOlOlClOl040lClOlOtOlOlClOiOlOiOiOlO 


xliv 


TABLE  IX. 


6 


S 


o 

< 

iO«OOt^rO-^05t^t-OTj<0«OTt<C<5M'««'iOt-OM 

< 

0 

< 

05COOO«OC^(>lt~lOiOOOC<)00>OCOC<ie^(M'^«DQO'-i»0 

eocoiou:)Tt<-^ri<T}<cccoc»:)cccoc<3ecco<M(MC^csic^(M 

< 

n                                co>oootooe«5-^ir<5evjot-'^05'^a>-<*'ooc^toocot». 

o 

< 

<M-»Jt00»COO»0C^<Ml005lClMOO5asO(M-<*<tOC:Mr^ 

«O«OiOiO-*'*<-*-*C0Cr:C0COC0CO<N<M<NIMIM(MC^lMC^ 

< 

C                                      «O0C>— lO-*t—  0Cl00<O'<^-Ht--C000C000(MCDOC0t^OCC 
J3                                      ■-lrt<M(M(MCOC«5COCOCOCOCCTj<-.*l-<*<Tt<-<*<-<*<-^Tt<-^'ti-* 

0 

CO 

< 

•ocot^cor^t^^ooo3-HO^oor^eoot^05T-HT}<t^rtioo5 

°                         ooo-*ooc»:)rtOO«oioiro<M00500t--toio»rt-<»<rocoM-H 

< 

S                               05<M<»-*i05IMCOIM-HOOi0^t^(Mr^lM500COt^OCOCOO» 

o 

CI 

<t^ 

ioe^-*oeoc«5t-Tf<ioi^^t^»oco(McoM<ir>oo.-iTj<ooiMi^e<i 

°                   r^a5c<:!05":)(M05t^iOc«3(M0050oi^ovo-<jicoco(M  —  — <oo 

< 

o 

< 

COO^lOOOt^-HOOO>(MCO(MOOOOOOOO(N-*t^-H»00>'<*<05»0 

°                   000(M(^eoOOO>OC»5lMOO^OOCOlC-^-^CO(Mrt-HOCTJ050000 
COu:)lO-*l-<*<'<*<COCOCOCOCOlMIM(MOJ(MC-4(M(N(M(M(M-H-Hr-<^ 

< 

X 

C                 lO-^U5Tt(03C<>COCOr-HOO»0^50^tOO-«l<00^-*t^OrO!OGCO 

o 

o 

< 

lOtOlOOS.— l-HTj<<M<MlOC3«0'^MC»5COlOt^OCOt^.— ICO-— lOIMOO 

°        >ocDO'r5l^^o>tOT^^(^ioo2t^co^OTJ<co(^^^'-HOc35CT>oooo^^^^50 

<OlO»OTl<rt(cy3COCOfOCO<M(N<NC^C^C^C^IMC^C<lrtrt^.-(-^rt~ 

< 

X 

p       oor^ococx)05a5r^'*<oiric^i^^ioococOCT>c^-*t^oic^-^50 

o 

o 

< 

CO— lOO-HrOC^COCOTjtb-fMOlt^cOtOt^OJlMiOOOIMI^C^r-lMOO-*—" 

°     ■*lOOO"<tlOt^-*C^OOOt^lCTf<CO(M-H00050000t^t^tDtOlOlOlO 
tOiO-*Tt<-<tlCOCOCOCOC^(MC^C^C^(M<M(N(M-H— <>^r^»-i— i-^-H— ..^ 

< 
X 

pTt<(Mt^t^CqiOCDlOCOOt^rOOO<Mr^-^M<00-H-^COOi— H'^OOOO  — 
C^C^,^          (MCO-^lO          .-<^(M<MC0C0-^'<J<-<*<lOlOlC'O                               ^-^ 

j2rHC<l(MC»5COCOCOCO-^-«*<Tt<T}<Tt<'<*<Tj<Tt(T}<Tl<-^'^-»*l-^lfllOlOlOlO'n 

TABLE  IX. 


xlv 


«0O'^00C«500'^a>mr-<00Tt<i-<00iCC>^05t^Tj<(MO00«0-<l<C-»OC30l 


<  E  ^  t:  2  £2  2  E£  "t: '\2 '^  °£  ® '^ '*' '^  *"=> '=^  "*  ^  f^  "^  ■=>  =^  i^  "^  ■»  oo  c» 


c^(^^c^(^^(^^c^(^^(Nc-^<^^|^^<^^r-^.--l>--lrtrt1-HT-l>-lT-l,--l,-l,-l^rtr-^)-( 


^  COCO<000-HC<50QOO(M'<**0000(>»Tt<;Ot^OOO<MC<:)-<tlCOt^05CDr-H 


T-HO-HOCqQO'>*<OOCOOl— •*'-HOOtO-<*<(NOOOCO-<tl<M005t~COlO 

coiMc^i— I.— ioooo>0503QOoooot^r~r^r^t^co50co<r)toioicioio 


(NC<1(MC<)<N<M(M(M 


—  -~  i«  r^ii  .ii  j^  ''  '^ ■  — V  >-^  ^-^  -^  — ^  •  -  v.^  ^_^  . — ^  V .-  ^-  s^^  1—  \^^  i^_^  1—1  i.^  i.'j 

■^•>*»r5lClO»0  '-I'-i'— l'-i'-i>-l(M<M(M<NC^(MC^COCOCOCO 


^  lO  fcO  lO  lO 


5  °     0505000000t--b--t>-eO«0!CCDlO'OlOlOTfl'^Tj<'^'.^iia<C(3COCOCCCOCO 

^      I  '-lO'O  '-l.-iT-iT-ii-i.-ic<|(M(M(~q(M{M(M(MCOC«3COO0COCOCO 

5  °    oo^-^^|»oolOlOiOlOTtlTJ^TJ^T^TtlMcocococococ^c^c<^c<^l^^e<^(^^ 


x:'0»o»C'0»o»c»oift»ou5>o»c»oio»o»nu5ioioicicio>oioiO'Oioio 


I0mi0ick0l0ici0»0l0l0>0l0l0»0l0l0>0l0l0l0»0»0»0i0l0l0l0 


t"'^i— ioo»ocooooeofo>-<oootD-<i<co'— iooor^co»c'<*'foc<i>-i005 

■^•»l<-*C<3C0C0e«3(>l(M(M<N<M.-<i-li-l-H.-l,-HOOOOOOOOO05 


'-■_(r-(^H,-(r-(C^(M(MC^(M(M(M<MCOCOCOC«5O0C<3CCCOCOCO'*'*Tt<-<l<-^ 


oooiO-HiMc<:j'>#meot^ooo50'-i(NM'<i<ioeot~ooo50'-H(Nc*3Tt<io 


xlvi 


TABLE  IX. 


X 

s 


0 

< 

o 

ro-H<r>oO'«i<-<^POt^(Moow^co<N« 

•^CCCOOt^Tji(MOOOtOiCCO(M— lOOOO 
t^(;0«3«OiO>0»OlC-<ti-^'>»<Tj<Tt<->tlTj<cocO 

< 

B 

J3 

O3CDtDCOtOtXlO000t^iOC^a>iO— •t^C^t^ 
C0'O'-<<NC0-^>r3          ^(Nev>COM<-*lOlO 

rtr-lrtCVJC^(Me^e^c»5COCOCOCOC<3COCOCO 

o 

CO 

< 

O 

OJtDO'^COt—  •<l<fO»OOOC005t^»OTt<Ttl-<*lio 

C0t^C0O>OC0>-iO>t^>OTtic<lrtOO500l^<C 
t^COtOlO>OiOiO-<»'M<-^-^-^-^TttcocOCOCO 

< 

E 
x: 

OQOoOT»<ooo^oa>t^->*<— it^coo5-<^ooco 

.-HCOiO^tN-^lO                 rt<MCOCO'<»<-^lOlO 
.-l»-(rtlM(M(NCS|COCOCCeOcr3C<5COCOC»3CO'^ 

0 

< 

o 

■-H-<nt^oo55Diot^O"<i<'Hooioioiomtooo 

t^<NQ0>0(MO00<r>u:iC0(MO0500t^c0i0-<ti 

oto»oio»0"0-<*i-«j<Tt<-<ti-<j<-^cocococococo 

< 

K 

e 

„ 

050«OOC<)COO'^05tClCOO>iOOiOOi005 
CO          >-iC0-<1''O(>>>-i<— iC^ICOCO-^iOiO 

.-lCS«C<l(M(M(MCOCOCOCOCOCOCOCOCOTt<-»»tTjl 

O 

< 

o 

— iioooooo^Hoot^oo— io>-ioot^r^co«oi>.oo-^ 

CO  <« 

>— iOO-^<M02t--iO-^(N^H0500l>.«DiO-^COCO 
COlOlOiO-*i-*T}(-<ti-^-^COCOCOCOCOCOCOCO 

< 
X 

s 

Si 

CO  — 1 

<M(MM(M(MCOCOCOCOCOOOirOCOCO->*<'^T»<-»J< 

O 

o 

< 

o 

to  05  --H 

(MOC000t^00--(CO(>)O5t^«5tOC0l>.05.-i-* 

<N  m  --< 

t^  to  CD 

t^-<»<— lOOtOTjicO'— iOOOt^tOiO-*COC<)(M-^ 

iOiO'0-<f-^-<*<-<*<T»<-^cococococococococo 

< 

s 

J3 

Tjfco-^'^iot^oot^tci-^i^t^cooiioO'^aicor^-M 

,-(r-((M(M(MM(MCOCOCOCOCOCOCOC<5'<tlrt<-*-^-^Ttl 

^-iCOCO-<*<(N'^OQ005C^CD(M051^CO«OCDt^aj-HTj(t^ 


■-h.-i(MIM<M(MC000COCOCOCOCOCOCOtJ<-<*<'«*<-<*<-^tJ('»*< 


0«DCOCOCOTf<OQ005C»0(N05t^OlCCDt--05-HT»tt^,^ 


_-  i-l.-l(M(M(M(NC«5COCOCOCOCOCOCO'*'^'^'«*<->!l<'>*Tt<-«J<Ttl 


OOt^t^CO-^OOOOO— iiO-^OOOmiO»OCOOOOCOt---Hio 


J3i-lr-i(MC<|C^(MfOCOCOCOCOCOCOCOTt<-^"*TttT*<-<!t<-i^-«t(TtiT*l 


n     00030-H(MfO-<l<»COt^00050'-c(NfO'*»0«Or-OOOSO-H 
°     rtr^<M(N(N<M<Me^(M<N<M(NCOOOCOCOCOfOfOCOCOCOTj<'^ 


TABLE  IX. 


xlvii 


^3 

c 


X 

(—1 

PQ 


c 
o 

a 
~ 

a 

0 
(N 

< 

Titooo.-<Ttiooc^eOrt<c>i-it^MoOT»<ot^eoot^'*ic<«02t^ 

°     t^«OlrtO'^COCO(M<MT-lrHo'c>0203oiodoOo6b-"t^t—  too 
COfOCOCO00COCOCO00C<5COCOCO(NC^C<IC<IC<l(NC^(NC^C^Cl 

< 

K 

C'-i<c>0'«<ooc<)ioo5<M'oa><N-^r^ocoiocx)oco»ooooc» 

C                 ,-1,-..— lC^IM(MCOCOCO-^-^TtliOiOlOlO                              .—(■— 1 

0 

CO 

< 

t~-o>c^inCTicot^c^t^<Mt^cooi«0'-ioo'^'-HOOioeoooo»o 

COCOC»5C<:>C<3COCOCOCOrO<MC^<M(N(M<M<MMC<IC<lC^IMC^(M 

< 

0 

< 

OC0OO'*00C0I:^C000->*<Ot0(M00l0(MOJt0-*T-i00«0'* 

cofocococcroco<^io»<NC^c^c<lc<i(NCi<NC^(rqc<lc<icsic<ics 

< 

CCOt^'-HiOOO— <lCOO-HTt(Oa5(M-^t^05r-l-»tlt00001M»dt^ 

O 

< 

•^t^T-i->*l00C000ir005U:iOCOC0O2COC0Ot^-*<M05t—  icco 

0    (M__oo>a50ooot^t^t-to<r>u:5ioicio-*'>*<'*cocoooco 

■     COCOCOCOC^(N(rqCSC^C^)l>)(N(^l(N<NCSC^C^(NC<C^<NC^C<l 

< 

0 

o 

< 

t^T-HlOOJ-<*<0-^05lOrtl>>Tt<Ot^'^'-lCO":)COOOOtO-<*l(M 

°     OOO50000t^t^tDCD':D>0iOl0Ttl-<*<TliC0i:v3C0C0(MIMIMC<) 
C<3CO(M<MCSIM(MC^CaC^IMC<IC<)C^(NC^C^C<l<M(M(M<M(M<M 

ClOOOr-HlOCXl^HCOCOOS'— (-^5OO5T-HC0»0t^O5'— iMlCt— 05'-l 

0 

< 

rti005'*05-«*<0>u:ir-iOO-^Ot^-*rtOOCO(rO-HOOCD-^(MO 
°     0500J^r^cOCOiOiO'OT}<-<tl-*COCOCO(NC^(M<M'-ii—i,— !.-(.— 1 

< 
X 

COC0C005<M'O00OC0'O00OIMTtlC000O(MTl<c000O'— ICO 

o 

CO 

< 

l0O5-^ai'*O«O(M00Tt<rt00»O(MO5CC>-<tl.-(O5t^lOC0rtO> 

°     t^COCCilO'OlO-*-^COCOC<:i(M(MC<li-ii-i.-H>— 10000005 

< 

ciooo— i-<tit^05C-qTt<t^05'-HCO»ob»05r-<coicr--oooiM-*»o 

o 

< 

03Ttia3-«*<o«0(MQO'<*<— lOOlO(M05CO->*<(M05t^lOCO— <ooo 

°     >Oi0'^'*<-^C0C<2<M(M(M-Hrt^OOOO0505OJ05050500 

< 

e-Hcocoo5-^-*cooorHcoiot^03^iM-<*<<r>ooo5'^ro-*coi^ 

1 

-      IM  CO -^  »0  to  t^  00  0»  O  — 1  (M  iro  Tjt  lO  CO  t^  00  05  O  T-H  (M  C«5  rt<  Ifl 

°    T»< -^  •<*< -^  Tf  ■*  ■>*  TfH  »o  lo  »o  lo  lo  lO  m  lo  io  >o  to  to  CO  to  to  to 

xlviii 


TABLE  IX. 


(3 


,2 
Q 

0 

5 

0 

«>-«»<iOCOt^C<5C»5kOas'^Ot^»0'*<^'««Ot^ 

E 

J2 

--l.-(^H<N(NC^C^C^<>)COCOC^COCOCOCOCOCO 

0 

CO 

< 

0 

cD-Hr^cO'-H0050->*<oo-H005t-coio-*c<:>co<>» 

P 

0 

0 

< 

0 

.— i;OCD'a<t-.COC<)COtO'— lOCO-— lOOO— iCOlOt^ 

< 

E 

0 

< 

0 

OOCOlMOi<— ct^COt^Ol-^OtOTftcOCOCOTjtlOt^-OCO 

< 

S 

X! 

rt.-ir-<(M(MIMC^(MC^JCOCOCOC000COCOC«500-<*<'<*<-^ 

0 

00 

<i 

0 

»r5oot^-*iOr-io50cot^iM05i^coic»ccot^a>^-^oo 

E 

J3 

.-lr-lr-<(M(M(M(MIMCOCOo:iCCiCOCOCOC«2C«3CO'!*<-^Tt<Tl< 

0 

1 

0 

COlCC^OOOliOCOCOOO'CC^CTiOOt^t^OOOl'-HTHt^OC^ 

< 

E 

Si 

OC0C<100^C0-<tiC0(MOt~-'<*<O«0<N00C0t--.<Ml^.-im05 

.-(T-i.— i<Ne^c^c^c^cococofoc«3cccococcco-<i<'«*''<*<'^-^ 

0 

to 

< 

0 

03or^iMc<:iooocoooc^t^rt<^oo>050'^cotooo^ioa> 

< 

a 

J3 

t--.'^f005CC|lOCOiOC«5'-<050<MOOC005'*a>COOO<NCDO(>:i 
com          (MCO-^iO          i-H.— ((MCOCO'^'^'rtiO                 i-H'-iMC^ 

i-H-H— ((M<NM(MC^<rOCOC«3COCOOOCOCOCv5CO'>1<'>4<'^'*<Tl<-^ 

0 

< 

0 

sooc^cDt^-— io>05-^ioocococ<>— i.-H(Mco»or^ocot~-'-<in 

< 

s 

Si 

00»OlO-HlOt^t^50lOCOOt~-MO>lCO»CO'^05<>Ot>-»-i'»t<00 

3 

0 

TABLE  IX. 


xlix 


^3 

is 


X 

s 


5 

c 
o 

o 
ex 

< 

OC0e005C0t^<Mt^<Ml>.C000lO^00 

o 

o 

0 

°    cooa.— lOOOJOsoOGor^-t^cDcocDio 
^^  T^  ^H  Tj<  ^H  CO  CO  CO  CO  CO  CO  CO  CO  co  co 

< 

CcX^COOOfMCDO-^OCC^iOasCJCOOliM 
<-•  m                 T-i^H(M(NCMCOCOCO-^'*i'^iO 

E 

- 

o 

< 

»O00T-llOO5C000'<*<OJlOT-lt^C0OCO 

o 

o 

CO 

o 

00 

°      — lOOCTiOOOOt^t^COCOCOiOiOlO-^ 

■*Tt<Tt<cococococococococococooo 

< 

STl<00(McOO-*OC(MlOaJ(MiCOOOCO 

^             1— i^HC^cqc^cococo-^-^i-^ioio 

s 

„ 

o 

o 

C<5 

< 

0'^oo<N50»-i<r>.-it^cooo»«>-ioo«o 

0 

CO 

o 

O  CO 
00  CO* 

°    oo5oooot--t^cD!r)icio-^-^Tj<coco 
■<*<cocococococococococococococo 

'-          .-1.— lCvlC^(NCOCOCO-*-*-^iOiOiO 

s 

I-H    CO 

o 

Oi 

< 

COO-<*IOOCOOOCOOO'*OI>-COOCOCO 

o 

CO 

0 

00  o  ■* 

t^  co'  03 

r-  r»  CD 

°     OOOOl^cOCOiOLOTf<Tt<Tj<cOCOfOlM'(M 

cococococococococococococococo 

< 

CCOt^'— ilOO5(MCOO2(M»O0C— i^t^O 
'-'.— 1.— i<MCsl(MCOCOCO'*'«f-<*iOlO»0 

e 

r-l  CD  -"tl 

o 

X 

< 

<^^coo^oolOOlr>(^^QOu:l'-^oo>n(N 

o 

CD 
CO 

0 

CD  t^  i-H   1-H 

t^  (m'  o>  cd' 

t^  t^  CD  CD 

°     t^COCO»OlO-*i-*COCO!N(M(M^r-,^ 

COCOCOCOCOCOCOCOCOCOCOCOCOCOCO 

< 

pooiMcoococoosc^ioor^-^t^oco 

^.-.(MMCOCOCOCOTjH-^i^iiOiOlO 

a 

T-l  CD  lO  O 

T-l    >-l    ,-(    (M 

0 

< 

)t>irHC0.-HC0(M00'*OCOC005l0C0l— 1 

0 

CO 

0 

n<  ■^  t~  1^  IM 

!>.'  (M  00  iC  CO 
t^  t^  CD  CD  CO 

°      u:>lOTjlTt<COCO(NIM<Mrt«Oo"oO 

COCOCOCOCOCOCOCOCOCOCOCOCOCOCO 

< 

CCOCOO-^I^OCOt005(M-^t^OC-^lO 
^C<l(MCOCOCOTtl'*iTt<-<j(ioiC»0 

e 

(M  t-.  lO  rt  ■* 

IM  -^          ^ 

t-l  >-l  — 1  <M  (N 

o 

< 

cooocooocoCT>iO'-ir^-*<.-it^»0(Ma> 

0 

CO 

° 

i-l  O  CO  CO  1^  ■* 

t--.  IM  00  >0  <N  O 

!>.  r^  CD  CD  CD  CD 

°      -^COCOC^fM^^^OOOOlOJOSOO 
COCOCOCOCOCOCOCOCOCOCO<N<M(M(M 

< 

pt^O-^lt^OCOCOOJC^lOt^OC^lOt-^ 
^<MCOCOCO-*-<*<-<*<-<*<lOlOiO 

a 

(M  t^  CO  -H  -^f*  CO 
i-<  O  -H  iM  <N  cq 

o 

< 

03-<*<05iO.— (t^COOlOMOiCDCOOOO 

0 

CO 
CO 

0 

0>  t^  05  00  (M  05  05 

CO  -h'  t^  TlH  IM  OJ  t^ 

t^  t^  CO  CO  CO  lO  »o 

°      M<M^^rt000502C15GOOOOOOOb- ' 
COCOCOCOCOCOCOC^C^CJOIC^IMC^IIM 

< 

X 

p-HlO0C^-*it^O5(MlO00OC0l0t^O 
^COCOCO'<*"'!t<'*-*lOmiO                               "—I 

E 

CO  OO  t^  (N  »0  !>.  t^ 

(M  •<*<          1-1  IM  CO 

.-1  1-1  rt  <N  M  <M  IM 

„    -Hc^jfO'^iocot^ooojo-^iMco-^tn 

"      ir5lOlO»OlOiO»OmiOCOOCOOCOCO 

o 

•*  lO  CO  l^  00  05  o 

ro  CO  CO  CO  CO  CO  ^^ 

TABLE  IX. 


u:i05»flt-»'^00>005'^OOOt>.eOOt»OOOCOC005C<5t^<Nt-.C^ 


^,_(,_i,_,,-((MC^(M(NiM(roirocccoeocococococc'^'<l<-*'^-^-<i< 


tO>-cMO300OC<500'flC0'— lOO'-l<M-<*<<005(N«50i005'«*<0 


_S-rtrti-4(MIM<N<M(MCOOOCOfOS»3COCOCOOOC<5-^'<*<'>!tl-»«lTi<Tl<-^ 


0005iO-*'OOOC»305l~-»0'<*<'*-^iOt^05(Mi005f»5t^<Mt^C^OO 


C-*02<M-^"*'^CO'-l05(r!COOtO(Mt^C«:>OOC«500COt^C^«DOOO 


^3 


X 

t— t 

a 


lO'— lO5OCCC0-*-H00t-»l^00O3'-<C0lO00(M<»Ol005»0O«O 


00<Mt~--<MOO«C'"^iO»OCDt^05'-H'>S<00'— I'OOlCO'O'-'COCO 


'-iiOO«OTt(C^»-lT-HC<)COlCt-^OCOt-»'-<lOOlOOlC(Mt^C005 


jSMC^ICOCOCOCCCOCOCOCOCOCO'^'*'*''^'*'^"^'^'^'*'*''*''^ 


TABLE  IX. 


^3 


a 


5 

0 

< 

o 

03050«OlOt^'-Ht--'«*<M--iM(MCO»rtOO'^ 

< 

E 

o 

< 

o 

CXDt^t^C^.— iCor-(M05r^«D«DCO-H05<MiOOO 

< 
X 

Si 

o 

< 

o 

tD«0-^050003IMt>--<*l(Nr-iOOC^CO»OOOIMiO 

< 
X 

s 

0>OCOO>IM-*lOlCTf<COT-4050000tOC005U:) 

0 

< 

o 

Ttl(Mrt>0-<*<lCOOC005t^lO»0»CCOl^05(Ml005CO 

03lO(M03t^>OrO(M00500t^cOlO'<tiCOCO<N'-<'-< 

< 

X 

s 

OiOCOOOIM-^l-^TtlTtlC^OOOlOC^OSiOfMt^COa) 

o 

< 

o 

C>J0500(MO^^'«l<00-^<MO0505O'— ICO<000(MOO 

< 
X 

s: 

OlOCOOO(MCO'*<T(<fOc^ociOlO<NOO-<*<rt(r)(MOOCO 

1— (1— 1— <.— ic^<M(M(NC^coco<rococococococo-^Tf<-^ 

o 

n 

< 

o 

Ot^lOOOeO«D05COCT>COu:)-*lCO->!tliCt^l3>(MCD05C«200 

05'*l'-lOOCO'^(M'-i0200t^OlOTj<COlM'— Ir-I0050i00 

< 

X 

s 

o 

< 

o 

oo-*'^":i<M<M-^05-^'-H05ooooooo5^cocoa>coi^-Hco 

< 

X 

S 

o>ocoooe<ii>:i-*r»<iro'-i05i---*ot^coo5ico«o-Hco^H 

o 

< 

0 

«O'-h00'— cOOOOO'*05«D'*iM<N<NCOOt^05(MCOO-*05'^ 

00-*000»OCO<MOOOt^iClO'*C«3lM^0020JOOOOt~-<OCO 

< 
X 

E 

_„„_  „,^  ,^,,,,  ^, ..................    .^  ^  ^  ^  ^      1 

0 

(MfO'^i050l^00050'HC^C«:i'^"50t-00050'-i<MCOTt<lC 

Latitude  0°  Declination  North  or  South. 

Declinations. 


Hour  1     no 
Angles  1     " 

1° 

2° 

3°    1    4° 

5° 

6°         7° 

8°    1    9° 

10° 

11° 

Hour 
Angles 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

'       // 

/        n 
n 

/ 

II 

If 

// 

5 
23 
53 

II 
22.4 

II 

59 
57 
52 

4 

4  59 

19  55 
44  50 

II 
18.68 

4  16 
17  03 
38  23 

II 
15.99 

1     II 

3  43 
14  54 
33  32 
59  36 

II 
13.97 

1      II 

3  18 
13  14 
29  46 
52  54 

II 
12.40 

1      II 

2  59 
1153 
26  44 
47  32 

II 
11.14 

1     II 

2  42 
10  46 
24  14 
43  06 

II 
10.10 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.351 
02 

1.271 

38 

1.203 
85 

1.145 
20 

1.093 
42 

1.046 
89 

1.004 
32 

Log. 

Limit 

0 

1 

3 

5 

7 

8 

9 

10 

11 

12 

13 

14 

Min- 
utes 

Merid- 
ian. 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17°  1    18° 

19° 

20° 

21° 

22° 

23° 

Horn- 
Angles 

Min. 

1      II 

1     II 

/      // 

/      II 

1     II 

1     II 

/      II 

1     II 

/      // 

/      // 

1      II 

/      // 

Min. 

4 

2  28 

2  16 

2  06 

157 

150 

142 

137 

131 

126 

122 

1  18 

1  14 

4 

8 

9  52 

9  04 

8  24 

7  49 

7  18 

6  51 

6  27 

6  05 

5  45 

5  27 

5  11 

4  56 

8 

12 

22  11 

20  24 

18  55 

17  35 

16  26 

15  25 

14  30 

13  41 

12  56 

12  17 

11  40 

1106 

12 

16 

39  25 

36  16 

33  37 

31  17 

29  14 

27  23 

25  46 

24  19 

23  00 

2151 

20  44 

19  46 

16 

20 

56  40 

52  32 

48  52 

45  40 

42  48 

40  16 

38  00 

35  56 

34  08 

32  24 

30  52 

20 

24 

65  46 

61  38 

57  59 

54  43 

5145 

49  10 

46  40 

44  27 

24 

28 

83  54 

78  55 

74  29 

70  26 

66  54 

63  30 

60  30 

28 

32 

82  56 

79  01 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

1) 

II 

II 

Ajh 

9.24 

8.50 

7.88 

7.33 

6.85 

6.42 

6.04 

5.70 

5.39 

5.12 

4.86 

4.63 
0.665 

A,h 

Log. 

0.965 

0.929 

0.896 

0.865 

0.835 

0.807 

0.781 

0.755 

0.731 

0.709 

0.686 

Log. 

67 

42 

53 

10 

69 

54 

04 

87 

59 

27 

64 

58 

Limit 

15 

16 

17 

18 

19 

20 

21 

22 

24 

24 

25 

26 

Min- 
utes 

Merid- 
ian 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

Alti- 
tudes 

Latitude  0°  Declination  North  or  South. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Miu. 

1         tr 

/      II 

/      II 

/      II 

/      // 

/      II 

1      II 

/      II 

/      II 

/      // 

/      /' 

1      II 

Min. 

4 

1  10 

107 

1  04 

1  02 

0  59 

0  57 

0  54 

0  52 

0  51 

0  48 

0  46 

0  45 

4 

8 

4  43 

4  30 

4  18 

4  06 

3  56 

3  47 

3  38 

3  30 

3  21 

3  13 

3  06 

2  59 

8 

12 

10  35 

10  06 

9  40 

9  14 

8  51 

8  30 

8  10 

7  51 

7  32      7  15 

6  59 

6  43 

12 

16 

18  49 

17  58 

17  12 

16  26 

15  45 

15  06 

14  30 

13  57 

13  24    12  53 

12  25 

11  57 

16 

20 

29  24 

28  04 

26  52 

25  40 

24  36 

23  36 

22  40 

2148 

20  56    20  08 

19  24 

18  40 

20 

24 

42  20 

40  25 

38  41 

36  58 

35  26 

33  59 

32  38 

31  23 

30  091  29  00 

27  56 

26  53 

24 

28 

57  38 

55  01 

52  40 

50  18 

48  13 

46  15 

44  26 

42  44 

41  01 

39  28 

38  02 

36  35 

28 

32 

75  16 

7151 

68  47 

65  42 

62  58 

60  25 

58  02 

55  49 

53  35 

51  32 

49  40 

47  47 

32 

36 

79  43 

76  28 

73  26 

70  38 

67  50 

65  14 

62  51 

60  29 

36 

40 

90  40 

87  12 

83  44 

80  32 

77  36 

74  40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

.  ,  . 

60 

II 

II 

II 

II 

II 

n 

if 

II 

II 

II 

n 

n 

Ajh 

4.41 

4.21 

4.03 

3.85 

3.69 

3.54 

3.40 

3.27 

3.14 

3.02 

2.91 

2.80 

A,h 

Log. 

0.644 

0.624 

0.605 

0.585 

0.567 

0.549 

0.531 

0.514 

0.496 

0.480 

0.463 

0.447 

Log. 

44 

28 

31 

46 

03 

00 

48 

55 

93 

01 

89 

16 

Limit 

27 

28 

29 

30 

31 

32 

33 

33 

34 

35 

36 

37 

Min- 
utes 

Merid- 
ian 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/      // 

/      II 

/      /' 

/      // 

/      II 

1      II 

1      II 

/      II 

1      II 

1      II 

1      II 

Min. 

4 

0  43 

0  42 

0  40 

0  38 

0  38 

0  36 

0  35 

0  34 

0  32 

0  31 

0  30 

0  29 

4 

8 

2  53 

2  47 

2  41 

2  35 

2  30 

2  25 

2  19 

2  15 

2  10 

2  05 

2  01 

157 

8 

12 

6  29 

6  15 

6  01 

5  49 

5  37 

5  26 

5  14 

5  03 

4  52 

4  43 

4  34 

4  23 

12 

16 

1131 

1109 

10  43 

10  19 

9  59 

9  38 

9  18 

9  01 

8  40 

8  21 

8  06 

7  49 

16 

20 

18  00 

17  24 

16  44 

16  08 

15  36 

15  04 

14  32 

14  04 

13  32 

13  04 

12  40 

12  12 

20 

24 

25  55 

25  04 

24  06 

23  14 

22  28 

2142 

20  56 

20  16 

19  29 

18  49 

18  14 

17  34 

24 

28 

35  17 

34  06 

32  48 

31  38 

30  34 

29  32 

28  29 

27  34 

26  32 

25  37 

24  50 

23  55 

28 

32 

46  05 

44  32 

42  50 

41  18 

39  56 

38  34 

37  12 

36  00 

34  39 

33  27 

32  26 

31  13 

32 

36 

58  19 

56  23 

54  13 

52  16 

50  33 

48  49 

47  06 

45  35 

43  51 

42  20 

41  02 

39  32 

36 

40 

72  00 

69  36 

66  56 

64  32 

62  24 

60  16 

58  08 

56  16 

54  08 

52  16 

50  40 

48  48 

40 

44 

87  07 

84  13 

80  59 

78  05 

75  30 

72  55 

70  21 

68  05 

65  30 

63  14 

61  18 

59  03 

44 

48 

96  23 

92  56 

89  51 

86  47 

83  42 

81  01 

77  57 

75  16 

72  58 

70  16 

48 

52 

105  27 

10151 

98  14 

95  05 

91  29 

88  20 

85  38 

82  28 

52 

56 

106  06 

102  26 

99  181 

95  39 

56 

60 

114  00 

109  48 

60 

II 

n 

II 

II 

II 

II 

II 

II 

II 

II 

n 

II 

Ajh 

2.70 

2.61 

2.51 

2.42 

2.34 

2.26 

2.18 

2.11 

2.03 

1.96 

1.90 

1.83 

A,h 

Log. 

0.431 

0.416 

0.399 

0.383 

0.369 

0.354 

0.338 

0.324 

0.307 

0.292 

0.278 

0.262 

Log. 

36 

64 

67 

82 

22 

11 

46 

28 

50 

26 

75 

45 

Limit 

38 

39 

40 

41 

42 

43 

44 

45 

46 

46 

47 

48 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

Latitude  0°  Declination  North  or  South. 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

1      /I 

/      // 

/      // 

/      // 

/      // 

1      II 

/      // 

1      II 

/      // 

1      II 

/     // 

/      II 

Min. 

4 

0  28 

0  27 

0  27 

0  25 

0  24 

0  23 

0  22 

0  22 

0  21 

0  20 

0  19 

0  19 

4 

8 

154 

150 

145 

142 

1  38 

135 

1  32 

1  28 

124 

1  22 

1  19 

115 

8 

12 

4  16 

4  06 

3  57 

3  49 

3  40 

3  34 

3  24 

3  17 

3  10 

3  05 

2  57 

2  50 

12 

16 

7  33 

7  18 

7  03 

6  47 

6  32 

6  18 

6  06 

5  51 

5  38 

5  27 

5  15 

5  02 

16 

20 

1148 

1124 

1100 

10  36 

10  12 

9  52 

9  32 

9  08 

8  48 

8  32 

8  12 

7  52 

20 

24 

16  59 

16  25 

15  51 

15  16 

14  41 

14  12 

13  43 

13  09 

12  41 

12  17 

11  48 

11  20 

24 

28 

23  08 

22  21 

2133 

20  47 

20  00 

19  21 

18  42 

17  54 

17  15 

16  44 

16  05 

15  25 

28 

32 

30  13 

29  11 

28  09 

27  08 

26  07 

25  16 

24  25 

23  23 

22  31 

21  51 

21  00 

20  08 

32 

36 

38  14 

36  56 

35  39 

34  21 

33  03 

3158 

30  53 

29  36 

28  31 

27  39 

26  34 

25  30 

36 

40 

47  12 

45  36 

44  00 

42  24 

40  48 

39  28 

38  08 

36  32 

35  12 

34  08 

32  48 

31  28 

40 

44 

57  07 

55  10 

53  15 

51  18 

49  22 

47  45 

46  08 

44  13 

42  36 

41  18 

39  41 

38  05 

44 

48 

67  56 

65  38 

63  21 

6103 

58  45 

56  50 

54  55 

52  36 

50  41 

49  09 

47  14 

45  18 

48 

52 

79  46 

77  04 

74  21 

71  39 

68  57 

66  42 

64  27 

6144 

59  29 

57  41 

55  26 

53  10 

52 

56 

92  31 

89  22 

86  15 

83  06 

79  58 

77  21 

74  44 

71  37 

69  00 

66  54 

64  17 

61  41 

56 

60 

106  12 

102  36 

99  00 

95  24 

91  48 

88  48 

85  48 

82  12 

79  12 

76  48 

73  48 

70  48 

60 

n 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

1.77 

1.71 

1.65 

1.59 

1.53 

1.48 

1.43 

1.37 

1.32 

1.28 

1.23 

1.18 

A,h 

Log. 

0.247 

0.233 

0.217 

0.201 

0.184 

0.170 

0.155 

0.136 

0.120 

1.107 

0.089 

0.071 

Log. 

97 

00 

48 

40 

69 

26 

34 

72 

57 

21 

91 

88 

Limit 

49 

50 

51 

53 

54 

56 

57 

58 

59 

60 

62 

64 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

Declination 

^• 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1      II 

1      II 

1      II 

1      II 

/    // 

1      II 

1    II 

1      II 

/      // 

/      // 

/      // 

1      II 

Min. 

4 

0  18 

0  17 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

Oil 

4 

8 

1  12 

1  10 

1  07 

104 

101 

0  58 

0  55 

0  53 

0  51 

0  48 

0  45 

0  42 

8 

12 

2  42 

2  37 

2  30 

2  24 

2  19 

2  11 

2  05 

159 

154 

148 

1  42 

136 

12 

16 

4  50 

4  39 

4  26 

4  16 

4  05 

3  53 

3  43 

3  33 

3  22 

3  12 

3  02 

2  52 

16 

20 

7  32 

7  16 

6  56 

6  40 

6  24 

6  04 

5  48 

5  32 

5  16 

5  00 

4  44 

4  28 

20 

24 

10  51 

10  28 

9  59 

9  36 

9  13 

8  44 

8  21 

7  58 

7  35 

7  12 

6  49 

6  26 

24 

28 

14  46 

14  15 

13  35 

13  04 

12  33 

11  54 

1122 

10  51 

10  20 

9  48 

9  17 

8  45 

28 

32 

19  17 

18  36 

17  45 

17  04 

16  23 

15  32 

14  51 

14  10|  13  29 

12  48 

12  07 

1126 

32 

36 

24  25 

23  33 

22  28 

2136 

20  44 

19  39 

18  48'   17  56^  17  04 

16  12 

15  20 

14  29 

36 

40 

30  OS 

29  04 

27  44 

26  40 

25  36 

24  16 

23  12 

22  08 

21  04 

20  00 

18  56 

17  52 

40 

44 

36  28 

35  10 

33  33 

32  16 

30  58 

29  21 

28  05 

26  47 

25  29 

24  12 

22  54 

21  38 

44 

48 

43  23 

41  51 

39  56 

38  24;  36  52 

34  57 

33  24 

3152 

30  18 

28  46 

27  14 

25  43 

48 

52 

50  55 

49  07 

46  52 

45  04 

43  16 

41  01 

39  12 

37  24 

35  36 

33  48 

32  00 

30  11 

52 

56 

59  04 

56  58 

54  21 

52  16 

50  10 

47  33 

45  29 

43  23 

41  17 

39  12 

37  06 

35  02 

56 

60 

67  48 

65  24 

62  24 

60  00 

57  36 

54  36 

52  12 

49  48 

47  24 

45  00 

42  36 

40  12 

60 

II 

II 

II 

II 

n 

II 

// 

II 

II 

II 

II 

II 

Ajh 

1.13 

1.09 

1.04 

1.00 

0.96 

0.91 

0.87 

0.83 

0.79 

0.75 

0.71 

0.67 

Ajh 

Log. 

0.053 

0.037 

0.017 

0.00 

9.982 

9.959 

9.939 

9.919 

9.897 

9.875 

9.851 

9.826 

Log, 

08 

43 

03 

27 

04 

52 

08 

63 

06 

26 

07 

Limit 

66 

68 

70 

72 

74 

77 

79 

81 

83 

85 

87 

89 

Min- 
utes 

Merid- 
ian 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

Alti- 
tudes 

4. 


Latitude  1°  Declination  Same  Name* 


Di-xi.ix 

VTIOX.- 

Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9°    i    10°      11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
23 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 
II 

// 

/ 

II 

// 

1 
II 

// 

II 

// 

1 

II 

// 

II 

5 
23 

II 
22.4 

II 

58 
54 

0 

1     II 

4  59 
19  53 

II 
18.64 

4  15 
17  00 
38  17 

II 
15.95 

/      // 

3  43 
14  51 
33  26 
59  26 

II 
13.93 

3  18 
13  11 
29  40 
52  44 

II 
12.36 

2  58 
1150 
26  38 
47  22 

II 
11.10 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.350 
25 

1.270 
45 

1.202 
76 

1.143 
95 

1.092  1.045 
02        32        ^ 

Limit 

2 

0 

1 

3 

5 

7 

8 

9 

10 

11 

12 

13 

Min- 
utes 

Merid- 
ian 

89 

o 

90 

o 

89 

o 

88 

o 

87 

o 

86° 

85 

o 

84° 

83° 

82° 

81° 

80° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

t      II 

/      // 

1      II 

r        II 

1     II 

/      // 

1      II 

/      // 

/      // 

/      // 

/    // 

Min. 

4 

2  41 

2  27 

2  15 

2  06 

156 

149 

1  42 

136 

131 

i3b 

121 

1  17 

4 

8 

10  44 

9  49 

9  03 

8  22 

7  47 

7  16 

6  49 

6  25 

6  03 

5  42 

5  25 

5  08 

8 

12 

24  09 

22  05 

20  20 

18  49 

17  30 

16  20 

15  20 

14  25 

13  36 

12  52 

12  12 

11  34 

12 

16 

42  55 

39  15 

36  08 

33  27 

3106 

29  04 

27  16 

25  39    24  12 

22  52 

21  40l  20  34 

16 

20 

56  28 

52  16 

48  36 

45  24 

42  36 

40  04^  37  48 

35  44 

33  52'  32  08 

20 

24 

65  23 

61  21 

57  42 

54  26 

5128 

48  46 

46  17 

24 

28 

83  31 

78  32 

74  05 

70  02 

66  23 

62  59 

28 

32 

82  15 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

// 

II 

"  -? 

// 

II 

II 

Ajh 

10.06 

9.20 

8.47 

7.84 

7.29 

6.81 

6.39 

6.01 

5.67 

5.36 

5.08 

4.82 

A,h 

Log. 

1.002 

0.963 

0.927 

0.894 

0.862 

0.833 

0.805 

0.778 

0.753 

0.729 

0.705 

0.683 

Log. 

6  J 

79 

88 

32 

73 

15 

50 

87 

58 

16 

86 

05 

Limit 

14 

15 

16 

17 

18 

19 

20 

21 

23 

24 

25 

26 

Min- 
utes 

Merid- 
ian 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

Latitude  J°  Declination  Same  Name, 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

1      II 

1      II 

1      II 

/      // 

/      II 

1     II 

/      II 

/      // 

1     II 

/      // 

/      // 

Min. 

4 

1  13 

1  10 

107 

103 

101 

0  59 

0  56 

0  54 

0  51 

0  50 

0  47 

0  46 

4 

8 

4  54 

4  40 

4  27 

4  15 

4  05 

3  54 

3  45 

3  36 

3  27 

3  19 

3  11 

3  04 

8 

12 

11  01 

10  29 

10  02 

9  35 

9  10 

8  47 

8  25 

8  05 

7  45 

7  27 

7  11 

6  55 

12 

16 

19  35 

18  39 

17  50 

17  01 

16  18 

15  37 

14  59 

14  23 

13  47 

13  17 

12  45 

12  17 

16 

20 

30  3& 

-29  08 

27  52 

26  36 

25  28 

24  24 

23  24 

22  28 

21  32 

20  44 

19  56 

19  12 

20 

24 

44  04 

4157 

40  08 

38  18 

36  41 

35  09 

33  42 

32  21 

3100 

29  52 

28  42 

27  39 

24 

28 

59  59 

57  06 

54  37 

52  09 

49  55 

47  49 

45  52 

44  02 

42  13 

40  38 

39  05 

37  38 

28 

32 

78  20 

74  34 

71  20 

68  06 

65  11 

62  27 

59  54 

57  31 

55  08 

53  04 

51  02 

49  09 

32 

36 

79  04 

75  49 

72  48 

69  46 

67  11 

64  35 

62  13 

36 

40 

89  52 

86  08 

82  56 

79  44 

76  48 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

'I 

II 

II 

II 

n 

II 

II 

Aih 

4.59 

4.37 

4.18 

3.99 

3.82 

3.66 

3.51 

3.37 

3.23 

3.11 

2.99 

2.88 

A,li 

Log. 

0.661 
81 

0.640 

48 

0.621 

18 

0.600 
97 

0.582 
06 

0.563 

48 

0.545 
31 

0.527 
63 

0.509 
20 

0.492 
76 

0.475 
67 

0.459 
39 

Log. 

Limit 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

36  ' 

Min- 
utes 

Merid- 
ian 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Mm. 

/       // 

/      II 

1      II 

/      // 

/      II 

1      II 

/      // 

/      // 

/      // 

/      // 

/      // 

1      If 

Min. 

4 

0  44 

0  43 

0  41 

0  39 

0  38 

0  37 

0  35 

0  35 

0  33 

0  32 

0  30 

0  30 

4 

8 

2  58 

2  51 

2  45 

2  39 

2  33 

2  28 

2  22 

2  17 

2  13 

2  08 

2  03 

159 

8 

12 

6  39 

6  24 

6  10 

5  58 

5  44 

5  32 

5  20 

5  09 

4  58 

4  48 

4  38 

4  28 

12 

16 

11  49 

1124 

10  58 

10  34 

10  12 

9  52 

9  28 

9  11 

8  50 

8  32 

8  14 

7  56 

16 

20 

18  28 

17  48 

17  08 

16  32 

15  56 

15  24 

14  48 

14  20 

13  48 

13  20 

12  52 

12  24 

20 

24 

26  35 

25  38 

24  40 

23  48 

22  57 

22  11 

21  19 

20  39 

19  52 

19  12 

18  31 

17  52 

24 

28 

36  12 

34  53 

33  35 

32  25 

31  14 

30  11 

29  01 

28  05 

27  03 

26  08 

25  14 

24  18 

28 

32 

47  17 

45  34 

43  52 

42  20 

40  47 

39  25 

37  53 

36  41 

35  20 

34  08 

32  57 

31  44 

32 

36 

59  50 

57  41 

55  31 

53  34 

5138 

49  54 

47  57 

46  27 

44  43 

43  12 

41  41 

40  11 

36 

40 

73  52 

71  12 

68  32 

66  08|  63  44 

61  36 

59  12 

57  20 

55  12 

53  20 

5128 

49  36 

40 

44 

86  10 

82  56 

80  01 

77  07 

74  32 

71  38 

69  23 

66  48 

64  32 

62  16 

60  01 

44 

48 

95  14 

91  46 

88  42 

85  15;  82  33 

79  29 

76  48 

74  07 

7125 

48 

52 

107  42 

104  06 

100  03 

96  53 

93  17 

90  08 

86  59 

83  49 

52 

53 

108  12 

104  32 

100  52 

97  13 

56 

60 

111  36 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

" 

II 

II 

Ajh 

2.77 

2.67 

2.57 

2.48 

2.39 

2.31 

2.22 

2.15 

2.07 

2.00 

1.93 

1.86 

A,h 

Log. 

0.442 

0.426 

0.409 

0.394 

0.378 

0.363 

0.346 

0.332 

0.315 

0.301 

0.285 

0.269 

Log. 

48 

51 

93 

45 

40 

61 

35 

44 

97 

03 

56 

51 

Limit 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

46 

47 

Min- 
utes 

Merid- 
ian 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

Latitude  J°  Decimation  Same  Name. 


Declination.^ 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  29 

155 

4  19 

7  41 

12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

81  07 

94  05 

108  00 
II 

1.80 

/      // 

0  27 

151 

4  09 

7  28 

11  32 

16  36 

22  37 

29  32 

37  22 

46  08 

55  49 

66  24 

77  58 

90  25 

103  48 
II 

1.73 

I  II 

0  27 

1  47 
4  00 
7  08 

II  08 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 
II 

1.67 

1     II 

0  26 

142 

3  51 

6  53 

10  44 

15  28 

21  02 

27  28 

34  47 

42  56 

5157 

61  49 

72  33 

84  09 

96  36 

II 

1.61 

1      II 

0  25 

140 

3  45 

6  39 

10  24 

14  59 

20  23 

26  37 

33  42 

41  36 

50  20 

59  54 

70  18 

8132 

93  36 

II 

1.56 

1      II 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 
II 

1.50 

1      II 

0  22 

133 

3  28 

6  08 

9  36 

13  49 

18  49 

24  35 

31  06 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 

II 

1.44 

/      II 

0  22 

129 

3  20 

5  56 

9  16 

13  21 

18  10 

23  43 

30  02 

37  04 

44  51 

53  22 

62  38 

72  39 

83  24 
II 

1.39 

0  22 

126 

3  13 

5  43 

8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

51  27 

60  23 

70  02 

80  24 
II 

1.34 

1      II 

0  21 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 

II 

1.29 

/     // 

0  20 

120 

2  59 

5  17 

8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
II 

1.24 

/      // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

3144 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

Min. 
A 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.255 
27 

0.238 
05 

0.222 
72 

0.206 
83 

0.193 
12 

0.176 
09 

0.158 
36 

0.143 
01 

0.127 
10 

0.110 
59 

0.093 
42 

0.075 
55 

Log. 

Limit 

48 

49 

51 

52 

53 

55 

57 

57 

58 

59 

62 

64 

Min- 
utes 

Merid- 
ian 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

Alti- 
tudes 

Declin.\tions. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

1      II 

/      // 

/      // 

/      // 

/      // 

1      II 

1      II 

/      // 

/      // 

/      // 

1      II 

Min. 

4 

0  19 

0  18 

0  17 

0  16 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

Oil 

Oil 

4 

8 

1  13 

1  10 

107 

104 

1  02 

0  58 

0  56 

0  54 

0  51 

0  49 

0  46 

0  43 

8 

12 

2  45 

2  38 

2  31 

2  25 

2  20 

2  13 

2  07 

2  01 

155 

150 

1  44 

137 

12 

16 

4  55 

4  42 

4  29 

4  19 

4  08 

3  55 

3  45 

3  35 

3  25 

3  14 

3  04 

2  54 

16 

20 

7  40 

7  20 

7  00 

6  44 

6  28 

6  08     5  52     5  36 

5  20 

5  04 

4  48 

4  32 

20 

24 

1103 

10  34 

10  05 

9  42 

9  18 

8  50     8  27      8  04 

7  41 

7  18 

6  55 

6  32 

24 

28 

15  01 

14  22 

13  43 

13  12 

12  41 

1202'  1130    10  58i  10  27 

9  56 

9  25     8  53 

28 

32 

19  37 

18  46 

17  55 

17  14 

16  34 

15  42    15  Oil  14  20    13  39 

12  58 

12  17    11  36 

32 

36 

24  51 

23  46 

22  41 

21  49 

20  57 

19  52 

19  01    18  09    17  17 

16  25 

15  33    14  42 

36 

40 

30  40 

29  20 

28  00 

26  56 

25  52 

24  32 

23  28    22  24    21  20|  20  16 

19  12    18  08     40 

44 

37  07 

35  30 

33  53 

32  35 

31  18 

29  41 

28  24 

27  06    25  49 

24  31 

23  14    21  57      44 

48 

44  09 

42  14 

40  19 

38  47 

37  15 

35  20 

33  47 

32  15 

30  43 

29  09 

27  37    26  06     48 

52 

5149 

49  34 

47  19 

45  31 

43  43 

4128 

39  39 

37  51 

36  03 

34  15 

32  27j  30  38     52 

56 

60  07 

57  30 

54  53 

52  47 

50  42 

48  05 

46  00 

43  54 

4149 

39  43 

37  38    35  33     56 

60 

69  00 

66  00 

63  00 

60  36 

58  12 

55  12 

52  48 

50  24 

48  00 

45  36 

43  12 

40  48 

60 

II 

II 

II 

II 

II 

// 

// 

// 

II 

It 

" 

II 

Ajh 

1.15 

1.10 

1.05 

1.01 

0.97 

0.92 

0.88 

0.84 

0.80 

0.76 

0.72 

0.68 

A,h 

Log. 

0.060 

0.041 

0.021 

0.004 

9.986 

9.963 

9.944 

9.924 

9.903 

9.880 

9.857 

9.832 

Log. 

70 

39 

19 

32 

77 

79 

48 

28 

09 

81 

33 

51 

Limit 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

86 

88 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24°      23°      22° 

21° 

20° 

Alti- 
tudes 

Latitude  1°  Declination  Contrary  Nams 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

10° 

11° 

Hour 

Auglea 

Mln. 

1       II 

/       // 

1      II 

1     II 

1      II 

1      II 

1      II 

1        II 

1      II 

/      // 

/     // 

1      II 

Min. 

4 

5  59 

4  59 

4  16 

3  44 

3  18 

2  59 

2  42 

2  28 

4 

8 

23  58 

19  57 

17  04 

14  56 

13  16|  11  55 

10  48 

9  54 

8 

12 

38  27 

33  36 

29  50 

26  48 

24  18 

22  15 

12 

16 

53  02 

47  40 

43  14 

39  33 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

" 

» 

II 

n 

// 

II 

A,h 

22  Al 

18.71 

16.02 

14.00 

12.43 

11.17 

10.13 

9.27 

Ajh 

Log. 

1.351 

1.272 

1.204 

1.146 

1.094  1.048 

1.005 

0.967 

Log. 

60 

07 

66 

13 

47        05        61 

08 

Limit 

1 

3 

5 

1 

8 

9 

10 

11 

12 

13 

14 

15 

Min- 
utes 

Merid- 
ian 

89 

0 

88 

0 

87 

0 

86 

0 

85° 

8 

4° 

83 

o 

82° 

81° 

50° 

79 

0 

78 

0 

Alti- 
tudes 

Declination.s. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23 

Hour 
Angles 

Min. 

1       II 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

/       n     1 

//    1 

II 

/      // 

/      // 

Min. 

4 

2  17 

2  06 

158 

150 

143 

137 

131 

126 

123 

1  18 

1  15 

1  11 

4 

8 

9  07 

8  26 

7  51 

7  20 

6  53 

6  29 

6  07 

5  48 

5  29 

5  13 

4  58 

4  45 

8 

12 

20  30 

18  58 

17  40 

16  31 

15  29 

14  36 

13  45 

13  02    1 

2  21|  1 

144 

11  11 

10  40 

12 

16 

36  26 

33  45 

3124 

29  21 

27  31 

25  56 

24  27 

23  10    2 

1  59    2 

0  52 

19  53 

18  56 

16 

20 

56  56 

52  44 

49  04 

45  52 

43  00 

40  32 

38  12 

36  12    3 

4  20    3 

2  36 

3104 

29  36 

20 

24 

66  03 

6155 

58  22 

55  00 

52  07    A 

9  27    4 

6  57 

44  45 

42  37 

24 

28 

84  17 

79  27 

74  53 

70  58    6 

7  17    6 

3  54 

60  53 

58  01 

28 

32 

..       8 

3  27 

79  31 

75  47 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

8.54 

7.91 

7.36 

6.88 

6.45 

6.08 

5.73 

5.43     5 

.15     4 

.89 

4.66 

4.44 

A,h 

Log. 

0.931 

0.898 

0.866 

0.837 

0.809 

0.783 

0.758 

0.734  0 

.711   0 

.689 

0.668 

0.647 

Log. 

46 

18 

88 

59 

56 

90 

15 

80 

81 

31 

39 

38 

Limit 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

Min- 
utes 

Merid- 
ian 

77 

3 

76 

3 

75 

D 

74 

D 

73 

3 

72 

3 

71 

0 

70 

°  1 

B9 

° 

58° 

67 

0 

66 

0 

Alti- 
tudes 

Latitude  \°  Declination  Contrary  Name. 


Df.clixatioxs. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

t        n 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      //    /      // 

Min. 

4 

108 

105 

102 

0  59 

0  57 

0  54 

0  53 

0  51 

0  49 

0  47 

0  46     0  44 

4 

8 

4  32 

4  20 

4  09 

4  00 

3  49 

3  40 

3  31 

3  23 

3  16 

3  08 

3  02     2  56 

8 

12 

10  11 

9  45 

9  20 

8  57 

8  36 

8  14 

7  55 

7  38 

7  21 

7  04 

6  49 

6  35 

12 

16 

18  05 

17  19 

16  36 

15  55 

15  16 

14  38 

14  05 

13  34 

13  03 

12  32 

12  07 

11  41 

16 

20 

28  16 

27  04 

25  56 

24  52 

23  52 

22  52 

22  00 

21  12 

20  24 

19  36 

18  56 

18  16 

20 

24 

40  42 

38  59 

37  21 

35  48 

34  22 

32  55 

31  41 

30  32 

29  23 

28  13 

27  16    26  18 

24 

28 

55  24 

53  03 

50  50 

48  45 

46  47 

44  50 

43  07 

41  33 

39  59 

38  25 

37  06    35  48 

28 

32 

72  22 

69  17 

66  23 

63  40 

6106 

58  33 

56  19 

54  16 

52  13 

50  11    48  28 

46  46 

32 

36 

77  20 

74  05 

71  17 

68  42 

66  06 

63  30!  61  21 

59  11 

36 

40 

9128 

88  00 

84  48 

8136 

78  24 

75  44 

73  04 

40 

44 

88  24 

44 

48 

48 

52 

52 

56 

56 

60 

60 

1/ 

rr 

II 

II 

II 

II 

II 

II 

II 

II 

II 

It 

A,h 

4.24 

4.06 

3.89 

3.73 

3.58 

3.43^ 

^3.30 

3.18 

3.06 

2.94 

2.84 

2.74 

A,h 

Log. 

0.627 

0.608 

0.589 

0.571 

0.553 

0.535 

0.518 

0.502 

0.485 

0.468 

0.453 

0.437 

Log. 

37 

53 

95 

71 

88 

29 

51 

43 

72 

35 

32 

75 

Limit 

28 

29 

30 

31 

32 

33 

34 

34 

35 

36 

37 

38 

Min- 
utes 

Merid- 
ian 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1     II 

/      // 

1      II 

/      // 

1      II 

/      // 

/      // 

/      // 

1      II 

/      // 

/      // 

/      // 

Min, 

4 

0  43 

0  41 

0  39 

0  38 

0  36 

0  35 

0  35 

0  33 

0  32 

0  30 

0  30 

0  29 

4 

8 

2  49 

2  43 

2  38 

2  32 

2  27 

2  22 

2  17 

2  13 

2  08 

2  03 

159 

155 

8 

12 

6  20 

6  07 

5  55 

5  41 

5  30 

5  18 

5  08 

4  58 

4  48 

4  38 

4  28 

4  19 

12 

16 

11  16 

10  53 

10  29 

10  07 

9  46 

9  26 

9  08 

8  50 

8  32 

8  14 

7  56 

7  41 

16 

20 

17  36 

17  00 

16  24 

15  48 

15  16 

14  44 

14  16 

13  48 

13  20 

12  52 

12  24 

12  00 

20 

24 

25  21 

24  29 

23  37 

22  45 

21  59 

21  13 

20  33 

19  52 

19  12 

18  31 

17  52 

17  17 

24 

28 

34  29 

33  19 

32  09 

30  58 

29  56 

28  53 

27  57 

27  03 

26  08 

25  14 

24  18 

23  31 

28 

32 

45  03 

43  31 

4159 

40  27 

39  05 

37  43 

36  31 

35  20 

34  08 

32  57 

3144 

30  43 

32 

36 

57  02 

55  05 

53  08 

51  12 

49  28 

47  44 

46  14 

44  43 

43  12 

4141 

40  11 

38  53 

36 

40 

70  24 

68  00 

65  36 

63  12 

61  04 

58  56 

57  04 

55  12 

53  20 

51  28 

49  36 

48  00 

40 

44 

85  11 

82  17 

79  22 

76  39 

73  53 

71  18 

69  03 

66  48 

64  32 

62  16 

60  01 

58  05 

44 

48 

94  28 

91  00 

87  56 

84  52 

82  10 

79  29 

76  48 

74  07 

7125 

69  07 

48 

52 

106  48 

103  12 

99  36 

96  26 

93  17 

90  08 

86  59 

83  49 

81  07 

52 

56 

108  12 

104  32 

100  52 

97  13 

94  05 

56 

60 

111  36 

108  00 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.64 

2.55 

2.46 

2.37 

2.29 

2.21 

2.14 

2.07 

2.00 

1.93 

1.86 

1.80 

A,h 

Log. 

0.421 

0.406 

0.390 

0.374 

0.359 

0.344 

0.330 

0.315 

0.301 

0.285 

0.269 

0.255 

Log. 

60 

54 

94 

75 

84 

39 

41 

97 

03 

56 

51 

27 

Limit 

38 

39 

40 

41 

41 

42 

43 

44 

45 

46 

47 

48 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

Latitude  1°  Decimation  Contrary  Name. 


Declinations. 


Hour 

Angles 

48°  1   49° 

50° 

51° 

52° 

53° 

54° 

55°      56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t       If 

0  28 

152 

4  11 

7  25 

11  36 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

104  24 

ir 

1.74 

/      // 

0  27 

147 

4  02 

7  10 

11  12 

16  08 

2157 

28  40 

36  18 

44  48 

54  13 

64  30 

75  42 

87  49 

100  48 
II 

1.68 

r        II 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
II 

1.62 

0  25 
140 
3  45 

6  39 
10  24 
14  59 
20  23 
26  37 
33  42 
41  36 
50  20 
59  54 
70  18 
81  32 

93  36 

II 

1.56 

/      // 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 
90  36 
II 

1.51 

t      II 

0  23 

1  34 
3  31 
6  13 
9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
II 

1.46 

t      II 

0  22 

130 

3  23 

6  01 

9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 

1.41 

1      II 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

81  36 

1.36 

1      1/ 

0  21 

1  23 
3  08 
5  36 
8  44 

12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 
II 

1.31 

1      It 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 
16  28 
21  30 
27  13 
33  36 
40  39 
46  23 
56  47 
65  51 
75  36 

1.26 

/      If 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

/      If 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

Log. 

-0.240 
55 

0.225 
31 

0.209 
52 

0.193 
12 

0.178 
98 

0.164 
35 

0.149 
22 

0.133 
54 

0.117 

27 

0.100 
37 

0.082 
79 

0.068 
19 

Log. 

Limit 

49 

50 

52 

54 

55 

56 

57 

59 

60 

62 

64 

66 

Min- 
utes 

Merid- 
ian 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

1      II 

1      * 

1      II 

1      II 

/      // 

/      // 

/      // 

/      // 

f      II 

1         u 

1      If 

Min. 

4 

0  18 

0  17 

0  16 

0  15 

0  15 

0  14 

0  14 

0  13 

0  12 

0  12 

oil 

Oil 

4 

8 

1  11 

109 

106 

103 

101 

0  58 

0  55 

0  53 

0  51 

0  48 

0  45 

0  42 

8 

12 

2  41 

2  36 

2  28 

2  23 

2  17 

2  11 

2  05 

159 

154 

148 

1  42 

1  36 

12 

16 

4  47 

4  36 

4  24 

4  13 

4  03 

3  53 

3  43 

3  33 

3  22 

3  12 

3  02 

2  52 

16 

20 

7  28 

7  12 

6  52 

6  36 

6  20 

6  04 

5  48 

5  32 

5  16 

5  00 

4  44 

4  28 

20 

24 

10  46 

10  22 

9  53 

9  30 

9  07 

8  44 

8  21 

7  58 

7  35 

7  12 

6  49 

6  26 

24 

28 

14  38 

14  07 

13  28 

12  57 

12  25 

1154 

1122 

10  51 

10  20 

9  48 

9  17 

8  45 

28 

32 

19  06 

18  26 

17  35 

16  54 

16  13 

15  32 

14  51 

14  10 

13  29 

12  48 

12  07 

1126 

32 

36 

24  12 

23  20 

22  15 

2123 

20  31 

19  39 

18  48 

17  56 

17  04 

16  12 

15  20 

14  29 

36 

40 

29  52 

28  48 

27  28 

26  24 

25  20 

24  16 

23  12 

22  08 

2104 

20  00 

18  56 

17  52 

40 

44 

36  09 

34  51 

33  14 

3156 

30  39 

29  21 

28  05 

26  47 

25  29 

24  12 

22  54 

2138 

44 

48 

43  00 

41  28 

39  33 

38  01 

36  29 

34  57 

33  24 

31  52 

30  18 

28  46 

27  14 

25  43 

48 

52 

50  28 

48  40 

46  25 

44  37 

42  49 

4101 

39  12 

37  24 

35  36 

33  48 

32  00 

30  11 

54 

56 

58  33 

56  27 

53  50 

5144 

49  39 

47  33 

45  29 

43  23 

41  17 

39  12 

37  06 

35  02 

56 

60 

67  12 

64  48 

6148 

59  24 

57  00 

54  36 

52  12 

49  48 

47  24 

45  00 

42  36 

40  12 

60 

II 

II 

II 

II 

II 

If 

II 

II 

II 

II 

II 

II 

Ajh 

1.12 

1.08 

103 

0.99 

0.95 

0.91 

0.87 

0.83 

0.79 

0.75 

0.71 

0.67 

A,h 

Log. 

0.049 

0.033 

0.012 

9.995 

9.977 

9.959 

9.939 

9.919 

9.897 

9.875 

9.851 

9.826 

Log. 

22 

42 

84 

64 

72 

04 

52 

08 

63 

06 

26 

07 

Limit 

67 

69 

71 

73 

75 

77 

80 

82 

84 

86 

90 

93 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

10 


Latitude  2°  Decimation  Same  Name* 

DkC'LI  NATIONS. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

// 

n 

/ 

n 

1 

/ 

// 

/        n 

II 

II 

/      // 

5  58 
23  50 

II 
22.35 

1      II 

4  57 
19  50 

II 
18.59 

1      II 

4  14 
16  57 
38  10 

II 
15.90 

/      // 

3  42 
14  49 
33  20 

II 
13.89 

1      II 

3  17 
13  08 
29  32 
52  32 

II 
12.31 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.349 

28 

1.269 

28 

1.201 
40 

1.142 
70 

1.090 
26 

Log. 

Limit 

3 

1 

0 

1 

3 

5 

7 

8 

9 

10 

11 

12 

Min- 
utes 

>rerid- 
ian 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

1      II 

1      II 

/      // 

/      II 

/      // 

1      II 

'      " 

'      " 

/      // 

/      // 

'      " 

Min. 

4 

2  57 

2  40 

2-27 

2  14 

2  05 

156 

149 

142 

135 

130 

1  25 

121 

4 

8 

1147 

10  41 

9  46 

9  00 

8  19 

7  44 

7  14 

6  46 

6  22 

6  00 

5  40 

5  23 

8 

12 

26  31 

24  03 

2159 

20  14 

18  43 

17  24 

16  15 

15  14 

14  20 

13  30 

12  46 

12  06 

12 

16 

47  09 

42  45 

39  05 

35  58 

33  17 

30  56 

28  53 

27  06 

25  28 

24  02 

22  42 

21  30 

16 

20 

56  12 

52  00 

48  20 

45  08 

42  20 

39  48 

37  32 

35  28 

33  36 

20 

24 

64  59 

60  58 

57  18 

54  03 

5105 

48  23 

24 

28 

82  59 

78  01 

73  34 

69  31 

65  51 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

Aih 

11.05 

10.02 

9.16 

8.43 

7.80 

7.25 

6.77 

6.35 

5.97 

5.63 

5.32 

5.04 

A,h 

Log. 

1.043 

1.000 

0.961 

0.925 

0.892 

0.860 

0.830 

0.802 

0.775 

0.750 

0.725 

0.702 

Log. 

36 

87 

90 

83 

09 

34 

59 

77 

97 

51 

91 

43 

Limit 

13 

14 

15 

16 

17 

18 

19 

20 

22 

23 

24 

25 

Min- 
utes 

Merid- 
ian 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

Alti- 
tudes 

Latitude  2°  Declination  Same  Name. 


11 


Declinations. 


Hour      24°       25° 
Angles     **         "" 

26° 

27°      28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

5 
11 
20 
31 
45 
62 
81 

It 
4.7 

16 
)7> 
30 
26 
56 
59 
34 
45 

9 

1 

4 
10 
19 
30 
43 
59 
77 

4.5 

// 

13 
51 
55 

25 
20 
41 
27 
39 

5 

1 

1 

4 
10 
18 
28 
41 
56 
74 

n 

4.3 

// 

10 
38 
25 
31 
56 
40 
42 
04 

4 

1 

1( 

4 

9 
17 
27 
39 
54 
70 

// 

4.1 

37 

36 

40 
36 
45 
05 
39 

4 

1 

1( 

4 

9 
16 
26 
37 
51 
67 

II 
3.9 

// 

)3 

12 
29 
51 
20 
55 
37 
25 

5 

1( 

4 

9 
16 
25 
36 
49 
64 

II 
3.7 

II 

30 
32 
35 
37 
12 
17 
24 
31 

8 

0, 
3 

8 
15 
24 
34 

47 
61 

78 

II 
3.6 

58 
51 

41 
27 
38 
46 
18 
46 
12 

2 

0  55 
3  43 
8  20 

14  48 
23  08 
33  18 
45  21 
59  14 
74  57 
92  32 

II 
3.47 

/      II 

0  53 
3  33 

7  59 
14  13 

22  12 
3158 
43  31 
56  50 
7156 
88  48 

II 
3.33 

/      II 

0  51 
3  25 
7  41 
13  39 
2120 
30  43 
4149 
54  37 
69  07 
85  20 

II 
3.20 

/      // 

0  49 

3  17 

7  22 

13  06 

20  28 
29  28 
40  07 
52  24 
66  19 
8152 

3.07 

t      II 

0  47 
3  09 
7  05 
12  35 
19  40 
28  19 
38  33 
50  21 
63  43 
78  40 

II 
2.95 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.680 
34 

0.658 
01 

0.637 
49 

0.617 
00 

0.596 
60 

0.577 
49 

0.558 
71 

0.540 
33 

0.522 
44 

0.505 
15 

0.487 
14 

0.469 
82 

Log. 

Limit 

26 

27 

28 

29 

30 

31 

31 

32 

33 

34 

35 

36 

Min- 
utes 

Merid- 
ian 

68 

o 

67 

o 

66 

o 

65 

o 

64 

o 

63 

o 

62 

o 

61° 

60 

o 

59 

° 

58 

o 

57 

o 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

'     " 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

/      // 

'      " 

Min. 

4 

0  46 

0  43 

0  42 

0  40 

0  39 

0  38 

0  36 

0  35 

0  34 

0  32 

0  31 

0  30 

4 

8 

3  02 

2  55 

2  48 

2  42 

2  37 

2  30     2  26 

2  20 

2  15 

2  10 

2  05 

2  01 

8 

12 

6  49 

6  33 

6  18 

6  04 

5  52 

5  38 

5  27 

5  15 

5  03 

4  52 

4  43 

4  32 

12 

16 

12  07 

11  39 

11  14 

10  48 

10  24 

10  02 

9  41 

9  21 

9  01 

8  40 

8  21 

8  04 

16 

20 

18  56 

18  12 

17  32 

16  52 

16  16 

15  40 

15  08 

14  36 

14  04 

13  32 

13  04 

12  36 

20 

24 

27  16 

26  12 

25  15 

24  17 

23  25 

22  34 

2147 

2102 

20  16 

19  29 

18  49 

18  09 

24 

28 

37  06 

35  41 

34  22 

33  04 

3153 

30  42 

29  40 

28  37 

27  34 

26  32 

25  37 

24  42 

28 

32 

48  28 

46  36 

44  53 

43  11 

41  39 

40  06 

38  45 

37  22 

36  00 

34  39 

33  27 

32  15 

32 

36 

6121 

58  58 

56  49 

54  39 

52  42 

50  46 

49  02 

47  19 

45  35 

43  51 

42  20 

40  50 

36 

40 

75  44 

72  48 

70  08 

67  28 

65  04 

62  40 

60  32 

58  24 

56  16 

54  08 

52  16 

50  24 

40 

44 

88  05 

84  52 

8138 

78  43 

75  50 

73  15 

70  40 

68  05 

65  30 

63  14 

60  59 

44 

48 

93  42 

90  14 

87  10 

84  05 

8101 

77  57 

75  16 

72  34 

48 

52 

105  54 

102  18 

98  41 

95  05 

91  29 

88  20 

85  10 

52 

56 

106  06 

102  26 

98  47 

56 

60 

113  24 

60 

II 

II 

II 

II 

II 

// 

II 

II 

II 

II 

// 

II 

A,h 

2.84 

2.73 

2.63      2.53 

2.44 

2.35      2.27 

2.19 

2.11 

2.03 

1.96 

1.89 

A,h 

Log. 

0.453 

0.436 

0.419 

0.403 

0.387 

0.371    0.356 

0.340 

0.324 

0.307 

0.292 

0.276 

Log. 

32 

16 

96 

12 

39 

07 

03 

44 

28 

50 

26 

46 

Limit 

37 

38 

39 

40 

41 

42 

43 

44 

45 

45 

46 

47 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51°  1    50° 

49° 

48° 

47° 

46°  1    45° 

Alti- 
1  tudes 

12 


Latitude  2^  Declination  Same  Name. 


DliCLlNATIONS. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55°  1  56° 

52° 

58° 

59° 

Hour 
Angles 

Min. 

/   // 

1       n 

1     II 

/  II 

'  It 

1     II 

/  // 

/  II 

/  // 

1     II 

1     II 

1     II 

Miu. 

4 

0  29 

0  28 

0  27 

0  27 

0  25 

0  24 

0  23 

0  22 

0  22 

0  21 

0  20 

0  19 

4 

8 

157 

153 

149 

145 

141 

137 

134 

130 

127 

123 

120 

117 

8 

12 

4  23 

4  14 

4  05 

3  56 

3  48 

3  39 

3  31 

3  23 

3  16 

3  07 

3  00 

2  54 

12 

16 

7  49 

7  30 

7  15 

7  00 

6  44 

6  29 

6  13 

6  01 

5  48 

5  33 

5  20 

5  10 

16 

20 

12  12 

11  44 

1120 

10  56 

10  32 

10  08 

9  44 

9  24 

9  04 

8  40 

8  20 

8  04 

20 

24 

17  34 

16  54 

16  19 

15  45 

15  10 

14  36 

14  01 

13  32  13  04 

12  29 

12  00 

1137 

24 

28 

23  55 

23  00 

22  13 

2125 

20  39 

19  52 

19  05 

18  26  17  46 

16  59 

16  20 

15  49 

28 

32 

31  13 

30  02 

29  01 

27  59 

26  58 

25  56 

24  55 

24  04  23  12 

22  11 

2120 

20  39 

32 

36 

39  32;  38  01 

36  43 

35  26 

34  08 

32  50 

31  32 

30  27  29  23 

28  05 

27  00 

26  08 

36 

40 

48  48!  46  56 

45  20 

43  44 

42  08 

40  32 

38  56 

37  36  36  16 

34  40 

33  20 

32  16 

40 

44 

59  03 

56  47 

54  51 

5255 

50  59 

49  03 

47  06 

45  29  43  53 

4157 

40  20 

39  02 

44 

48 

70  16 

67  33 

65  15 

62  58 

60  40 

58  22 

56  04 

54  09 

52  13 

49  55 

48  00 

46  28 

48 

52 

82  28 

79  19 

76  37 

73  54 

71  12 

68  30 

65  48 

63  33 

61  17 

58  35 

56  20 

54  32 

52 

56 

95  39 

9159 

88  51 

85  43 

82  35 

79  27 

76  18 

73  41 

7105 

67  57 

65  20 

63  14 

56 

60 

109  48 

105  36 

102  00 

98  24 

94  48 

91  12 

87  36 

84  36 

8136 

78  00 

75  00 

72  36 

60 

n 

n 

II 

II 

II 

II 

II 

/' 

II 

II 

II 

II 

A,h 

1.83 

1.76 

1.70 

1.64 

1.58 

1.52 

1.46 

1.41 

1.36 

1.30 

1.25 

1.21 

A,h 

Log. 

0.262 

0.245 

0.230 

0.214 

0.198 

0.181 

0.164 

0.149 

0.133 

0.113 

0.096 

0.082 

Log. 

45 

51 

45 

84 

66 

84 

35 

22 

54 
58 

94 

91 

79 

Limit 

48 

49 

50 

52 

53 

55 

56 

57 

59 

61 

63 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65°   66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Miu. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  II 

0  19 

1  14 

2  47 
4  57 
744 

11  09 

15  09 

19  47 

25  04 

30  56 

37  26 

44  32 

52  16 

60  38 

69  36 
II 

1.16 

1     II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

1      II 

0  17 

108 

2  33 

.  4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
II 

1.06 

/  II 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

II 

1.02 

1      II 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

1     II 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
II 

0.93 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 

0.89 

1     II 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 

50  24 

II 

0.84 

/  // 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/  II 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 

II 

0.76 

1     II 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 

15  33 

19  12 

23  14 

27  37 

32  27 

37  38 

43  12 
II 

0.72 

1     II 

Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

1136 

14  42 

18  08 

2157 

26  06 

30  38 

35  33 

40  48 
II 

0.68 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.064 
46 

0.045 
32 

0.025 
31 

0.008 
60 

9.986 

77 

9.968 

48 

9.949 
39 

9.924 

28 

80 

9.903 
09 

9.880 
81 

9.857 
33 

9.832 
51 

Log. 

Limit 

65 

67 

69 

71 

73 

75 

78 

82 

84 

86 

88 

Min- 
utes 

Merid- 
ian 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

Alti- 
tudes 

Latitude  2°  Decimation  Contrary  Name. 


13 


DkclixatiuNs. 


Hour 
Augles 

0° 

1° 

2= 

3° 

4°    1    5° 

1 

6° 

70     j     go 

90 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,li 

1 

ff 

ff 

1 
11 

n 

1 

5 
23 

■■ 
22.4 

59 
59 

S 

1      II 

5  00 
19  59 

18.73 

1 

17 
38 

16.0 

II 

17 
07 
30 

4 

3 
14 
33 
59 

14.0 

44 
57 
39 
49 

2 

'3 
13 
29 
53 

II 
12.4 

19 
17 
53 
07 

5 

I  II 

2  59 

II  56 
26  51 
47  45 

... 

" 
11  19 

1     II 

2  43 
10  50 
24  23 
43  21 

10.16 
1.006 
89 

14 

79° 

2  28 

9  55 

22  18 

39  38 

... 
9.29 

'      II 

2  17 

9  08 

20  33 

36  31 

57  04 

II 
8.56 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.351 
80 

7 

1.272!  1.205 

54         20 

T        10 

1.146 
75 

1.095 
17 

12 

1.048 

83 



13 

0.968 
02 

0.932 

47 

Log. 

Limit 

3 

4 

5 

11 

15        16 

Min- 
utes 

Merid- 
ian.    ' 

88° 

87° 

86° 

85° 

84°      83° 

82° 

81° 

80° 

78°  1    77° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

1   20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

'       " 

'      " 

'      " 

1      II 

,      II 

'      " 

t           ff 

'      II 

>      II 

'      // 

Min. 

4 

2  06 

1  58 

1  50 

143 

1  38 

1  32 

1  27 

1  23 

118 

1  15 

111 

108 

4 

8 

8  27 

7  53 

7  22 

6  55 

6  30 

6  09 

5  50 

5  31 

5  14 

5  00 

4  47 

4  34 

8 

12 

f  9  02 

17  44 

16  35 

15  34 

14  38 

13  50 

13  07 

12  26 

1149 

11  15 

10  44 

10  15 

12 

16 

33  50 

31  32 

29  29 

27  38 

26  02 

24  34 

23  17 

22  06 

20  59 

20  01 

19  04 

18  13 

16 

20 

52  52 

49  16 

46  04 

43  12 

40  40 

38  24 

36  24 

34  32 

32  48 

31  16 

29  48 

28  28 

20 

24 

66  20 

62  12 

58  34 

55  18 

52  25 

49  44 

47  14 

45  02 

42  53 

40  59 

24 

28 

79  42 

75  16 

71  21 

67  41 

64  18 

61  17 

58  25 

55  48 

28 

32 

... 

80  02 

76  18 

72  53 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

" 

ff 

II 

II 

" 

II 

" 

II 

// 

II 

II 

A,h 

7.93 

7.39 

6.91 

6.48 

6.10 

5.76 

5.46 

5.18 

4.92 

4.69 

4.47 

4.27 

A,h 

Log. 

0.899 

0.868 

0.839 

0.811 

0.785 

0.760 

0.737 

0.714 

0  691 

0.671'  0.650 

0.630 

Log. 

27 
17 

64 
18 

48 

58 

33 

42 

19 
23 

33 

97 

17 

31 

43 

Limit 

19 

20 

21 

22 

24 

25 

26 

27 

28 

Min- 
utes 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

Alti- 
tudes 

14 


Latitude  2°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

1       n 

28° 

29° 

30° 

31° 

32° 

33°  }   34° 

35° 

1      II 

1  Hour 
Angles 

Miu. 

1       II 

'      " 

/        n 

/      II 

/      // 

1     II 

/     II 

'      II 

1       II  ,  1       n 

1 

Min. 

4 

1  05i     1  02 

1  00     0  58 

0  55 

0  53 

0  51 

0  49 

0  47 

0  46!     0  44 

0  43 

4 

8 

4  22'     4  10 

4  01      3  51 

3  43 

3  33 

3  26 

3  18 

3  10 

3  04'     2  58 

2  51 

8 

12 

9  49'    9  25 

9  02     8  39'     8  20 

7  59 

7  42 

7  25 

7  10 

6  53;     6  39 

6  24 

12 

16 

17  27    16  43 

16  02'  15  25    14  48 

14  13 

13  42 

13  11 

12  42 

12  15    11  49 

11  24 

16 

20 

27  16   26  08 

25  04    24  04'  23  08 

22  12 

21  24 

20  36 

19  52 

19  08    18  28 

17  48 

20 

24 

39  16 

37  38 

36  06^  34  40    33  18 

3158 

30  49 

29  40 

28  36 

27  33    26  35 

25  38 

24 

28 

53  27 

51  14 

49  08|  47  10   45  21 

43  31 

4157 

40  23 

38  57 

37  30   36  12 

34  53 

28 

32 

69  48 

66  54 

64  10^  61  36    59  14 

56  50 

54  47 

52  44 

50  52 

48  59'  47  17 

45  34 

32 

36 

77  59 

74  57 

7156 

69  20 

66  45 

64  22 

62  00 

59  50 

57  41 

36 

40 

92  32 

88  48 

85  36 

82  24 

79  28 

76  32 

73  52 

71  12 

40 

44 

86  10 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

// 

It 

n 

n 

II 

II 

II 

tt 

'/ 

II 

II 

A,h 

4.09 
0.611 

3.92 

3.76 

3.61 

"0.557 

3.47 
0.540 

3.33 
0.522 

3.21 

3.09 

2.98 

2.87 

2.77 

2.67 

A,h 

Log. 

0.593,  0.575 

0.506 

0.489 

0.474 

0.457!  0.442 

0.426 

Log. 

72 

29!        19 

51 

33 

44 

51 

96 

22 

88 1        48 

51 

Limit 

29 

30    1    31 

32 

33 

34 

35 

36 

37 

38    1    39 

39 

Min- 
utes 

Merid- 
ian 

64° 

63°  1   62° 

61° 

60° 

59° 

58° 

57° 

56° 

55°  i   54° 

53° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36°  i   37°  1   38°  '   39° 

1                      1 

40°  {   41° 

42° 

43° 

1     II 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/        "  i  '        '/      '        "  i  '        " 

/      II  \  1     II 

1     II 

1      II 

1     II 

/      II  I  1     II 

1 

Min. 

4 

0  4l!     0  39     0  38     0  37 

0  36 

0  35 

0  34 

0  32 

0  31 

0  30 

0  29;    0  28 

4 

8 

2  45     2  40:     2  35     2  28 

2  24 

2  19 

2  14 

2  10 

2  05 

2  01 

1  57;     1  54 

8 

12 

6  12     5  59     5  47!     5  34 

5  24 

5  12 

5  02!     4  52 

4  43 

4  34 

4  23 

4  16 

12 

16 

1100    10  37[  10  17,     9  54 

9  36 

9  16 

8  58l     8  40 

8  21 

8  06 

7  49 

7  33 

16 

20 

17  12    16  36    16  04    15  28|  15  00 

14  28 

14  00    13  32 

13  04 

12  40 

12  12 

11  48 

20 

24 

24  46 

23  54'  23  08    22  17    21  36 

20  50 

20  10'  19  29 

18  49 

18  14 

17  34 

16  59 

24 

28 

33  43 

32  33'  31  30   30  19    29  24 

28  21 

27  26    26  32 

25  37 

24  50 

23  55 

23  08 

28 

32 

44  02 

42  30   41  08    39  35    38  24 

37  02 

35  50'  34  39 

33  27 

32  26 

31  13 

30  13 

32 

36 

55  44 

53  47   52  03   50  07!  48  36 

46  53 

45  22    43  51 

42  20 

41  02 

39  32 

38  14 

36 

40 

68  48 

66  24    64  16   61  52'  60  00 

57  52 

56  00   54  08 

52  16 

50  40 

48  48 

47  12 

40 

44 

83  15 

80  20   77  45   74  52    72  36 

70  02 

67  46j  65  30 

63  14 

61  18 

59  03 

57  07 

44 

48 

95  37   92  33 

89  05   86  24 

83  19 

80  38i  77  57 

75  16 

.72  58 

70  16 

67  56 

48 

52 

104  33  101  24 

97  47 

94  38   91  29 

88  20 

85  38 

82  28 

79  46 

52 

56 

...     106  06 

102  26 

99  18 

95  39 

92  31 

56 

60 

114  00 

109  48 

106  12 

60 

// 

// 

II 

" 

II 

n 

II          II 

" 

II 

// 

II 

A,h 

2.58 

2.49 

2.41 

2.32 

2.25 

2.17 

2.10     2.03 

1.96 

1.90 

1.83 

177 

A,h 

Log. 

0.396 

0.382   0.365J  0.352 

0.336 

0.322;  0.307 

0.292 

0.278 

0.262   0.247 

Log. 

62 

20|        02 

49l        18 

46 

22        50 

26 

75 

45j       97 

Limit 

39 

40    1    41 

42 

42 

43 

44        45 

46 

46 

48 

49 
41° 

Min-' 
utes 

Merid- 
ian 

52° 

51° 

50° 

49°  1   48° 

47° 

46°  I   45° 

44° 

43° 

42° 

Alti- 
tudes 

Latitude  2°  Declination  Contrary  Name. 


15 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Mill. 

/   // 

/   n 

1     II 

/   // 

1     II 

/  // 

1      II 

/  // 

1     II 

1     II 

1      II 

/  II 

Min. 

4 

0  27 

0  27 

0  26 

0  25 

0  23 

0  22 

0  22 

0  22 

0  20 

0  20 

0  19 

0  19 

4 

8 

150 

1  46 

1  42 

139 

136 

1  33 

129 

1  26 

123 

120 

1  17 

1  14 

8 

12 

4  06 

3  59 

3  50 

3  42 

3  35 

3  28 

3  20 

3  13 

3  06 

3  00 

2  53 

2  47 

12 

16 

7  18 

7  05 

6  50 

6  34 

6  21 

6  08 

5  56 

5  43 

5  30 

5  20 

5  07 

4  57 

16 

20 

11  24 

11  04 

10  40 

10  16 

9  56 

9  36 

9  16 

8  56 

8  36 

8  20 

8  00 

7  44 

20 

24 

16  25 

15  57 

15  22 

14  47 

14  18 

13  49 

13  21 

12  52 

12  23 

12  00 

11  31 

11  09 

24 

28 

22  21 

21  41 

20  54 

20  07 

19  29 

18  49 

18  10 

17  30 

16  52 

16  20 

15  41 

15  09 

28 

32 

29  11 

28  19 

27  18 

26  17 

25  26 

24  35 

23  43 

22  52 

22  01 

21  20 

20  29 

19  47 

32 

36 

36  56 

35  52 

34  34 

33  16 

32  11 

31  06 

30  02 

28  57 

27  52 

27  00 

25  55 

25  04 

36 

40 

45  36 

44  16 

42  40 

4104 

39  44 

38  24 

37  04 

35  44 

34  24 

33  20 

32  00 

30  56 

40 

44 

55  10 

53  34 

5138 

49  41 

48  04 

46  27 

44  51 

43  14 

4137 

40  20 

38  43 

37  26 

44 

48 

65  38 

63  44 

6126 

59  08 

57  13^  55  18 

53  22 

51  27 

49  32 

48  00 

46  05 

44  32 

48 

52 

77  04 

74  48 

72  06 

69  24 

67  09  j  64  54 

62  38 

60  23 

58  08 

56  20 

54  05 

52  16 

52 

56 

89  22 

86  46 

83  38 

80  29 

77  52  75  15 

72  39 

70  02 

67  25 

65  20 

62  43 

60  38 

56 

60 

102  36 

99  36 

96  00 

92  24 

89  24 

86  24 

83  24 

80  24 

77  24 

75  00 

72  00 

69  36 

60 

n 

If 

II 

n 

II 

II 

II 

II 

II 

II 

II 

II 

Aih 

1.71 

1.66 

1.60 

1.54 

1.49 

1.44 

1.39 

1.34 

1.29 

1.25 

1.20 

1.16 

Ajh 

Log. 

0.233 

0.220 

0.204 

0.187 

0.173 

0.158 

0.143 

0.127 

0.110 

0.096 

0.079 

0.064 

Log. 

00 

11 

12 

52 

19 

36 

01 

10 

59 

91 

18 

46 

Limit 

50 

51 

53 

55 

56 

57 

58 

60^ 

61 

63 

65 

67 

Min- 
utes 

Merid- 
ian 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1       II 

1     II 

1      II 

/  // 

1     II 

>      It 

1      II 

1      II 

/   // 

1     II 

1     II 

1     II 

Min. 

4 

0  18 

0  17 

0  16 

0  15 

0  15 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

Oil 

4 

8 

1  11 

108 

105 

102 

100 

0  57 

0  55 

0  52 

0  50 

0  47 

0  45 

0  43 

8 

12 

2  39 

2  34 

2  27 

2  22 

2  16 

2  10 

2  04 

158 

152 

147 

142 

137 

12 

16 

4  45 

4  34 

4  21 

4  10 

4  00 

3  50 

3  40 

3  30 

3  19 

,3  09 

3  02 

2  54 

16 

20 

7  24 

7  08 

6  48 

6  32 

6  16 

6  00 

5  44 

5  28 

5  12 

4  56 

4  44 

4  32 

20 

24 

10  40 

10  16 

9  48 

9  24 

9  01 

8  38 

8  16 

7  53 

7  29 

7  06 

6  49 

6  32 

24 

28 

14  30 

13  59 

13  20 

12  49 

12  17 

1146 

11  14 

10  43 

10  12 

9  40 

9  17 

8  53 

28 

32 

18  56 

18  16 

17  24 

16  44 

16  03 

15  22 

14  40 

13  59 

13  19 

12  38 

12  07 

11  36 

32 

36 

23  59 

23  07 

22  02 

21  10 

20  18 

19  26 

18  35 

17  43 

16  51 

15  59 

15  20 

14  42 

36 

40 

29  36 

28  32 

27  12 

26  08 

25  04 

24  00 

22  56 

21  52 

20  48 

19  44 

18  56 

18  08 

40 

44 

35  49 

34  32 

32  55 

3137 

30  19 

29  02 

27  45 

26  28 

25  10 

23  52 

22  54 

2157 

44 

48 

42  37 

41  05 

39  10 

37  38 

36  06 

34  34 

33  01 

31  29 

29  55 

28  23 

27  14 

26  06 

48 

52 

50  01 

48  13 

45  58 

44  10 

42  22 

40  34 

38  45 

36  57 

35  09 

33  21 

32  00 

30  38 

52 

56 

58  01 

55  56 

53  19 

51  13 

49  07 

47  02 

44  57 

42  52 

40  46 

38  40 

37  06 

35  33 

56 

60 

66  36 

64  12 

61  12 

58  48 

56  24 

54  00 

5136 

49  12 

46  48 

44  24 

42  36 

40  48 

60 

" 

II 

II 

II 

II 

II 

It 

II 

II 

II 

II 

II 

A,h 

1.11 

1.07 

1.02 

0.98 

0.94 

0.90 

0.86 

0.82 

0.78 

0.74 

0.71 

0.68 

A,h 

Log. 

0.045 

0.029 

0.008 

9.991 

9.973 

9.954 

9.934 

9.913 

9.892 

9.869 

9.851 

9.832 

Log. 

32 

38 

60 

23 

13 

24 

50 

81 

09 

23 

26 

51 

Limit 

69 

70 

72 

74 

76 

78 

80 

82 

84 

86 

90 

93 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

Alti- 
tudes 

k; 


Latitude  3°  Declination  Same  Name. 

Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

// 

// 

t 

H 

// 

// 

1 

n 

// 

1 

// 

1 

// 

// 

t 

// 

// 

»     // 

5  56 
23  46 

II 
22.28 

/     // 

4  57 

19  46 

II 
18.53 

/     // 

4  14 

16  54 
38  01 

II 
15.84 

1     II 

3  42 

14  45 

33  11 

II 
13.83 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.347 
92 

1.267 

88 

1.199 
76 

1.140 

82 

Log. 

Limit 

4 

2 

1 

0 

1 

3 

5 

7 

8 

9 

10 

11 

Min- 
utes 

Merid- 
ian 

87°      88° 

89°      90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      II 

1     II 

'     // 

1     II 

/     // 

/      // 

'     // 

'      // 

/      // 

/      // 

1      II 

/      // 

Min. 

4 

3  16 

2  56 

2  39 

2  26 

2  14 

2  04 

155 

147 

1  41 

134 

129 

124 

4 

8 

13  05 

1144 

10  38 

9  43 

8  56 

8  16 

7  42 

7  11 

6  43 

6  18 

5  57 

5  38 

8 

12 

29  26 

26  24 

23  56 

2151 

20  07 

18  36 

17  18 

16  09 

15  07 

14  13 

13  24 

12  41 

12 

16 

42  32 

38  53 

35  45 

33  04 

30  46 

28  43 

26  53 

25  15 

23  48 

22  31 

16 

20 

55  52 

5140 

48  04 

44  52 

42  00 

39  28 

37  12 

35  12 

20 

24 

64  36 

60  29 

56  50 

53  34 

50  41 

24 

28 

82  19 

77  22 

72  53 

69  00 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

/' 

II 

n 

Ajh 

12.26 

11.00 

9.97 

9.11 

8.38 

7.75 

7.21 

6.73 

6.30 

5.92 

5.58 

5.28 

A,h 

Log. 

1.088 

1.041 

0.998 

0.959 

0.923 

0.889 

0.857 

0.828 

0.799 

0.772 

0.746 

0.722 

Log. 

49 

39 

70 

52 

24 

30 

94 

02 

34 

32 

63 

63 

Limit 

12 

13 

14 

15 

17 

18 

19 

20 

22 

23 

24 

25 

Min- 
utes 

Merid- 
ian 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

Alti- 
tudes 

Latitude  3°  Declination  Same  Name. 


17 


Declination 

-. 

Hour 
Ajigles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min, 

/       n 

/     It 

/       n 

/     II 

/          H 

1     II 

1     II 

1     II 

1     II 

1     II 

/      // 

1     II 

Min. 

4 

120 

1  16 

1  12 

109 

106 

102 

100 

0  57 

0  54 

0  52 

0  51 

0  48 

4 

8 

5  20 

5  04 

4  49 

4  35 

4  22 

4  10 

4  00 

3  49 

3  40 

3  31 

3  22 

3  14 

8 

12 

12  00 

1124 

10  49 

10  19 

9  50 

9  23 

8  59 

8  36 

8  14 

7  54 

7  35 

7  16 

12 

16 

2120 

20  13 

19  15 

18  21 

17  30 

16  41 

15  57 

15  16 

14  38 

14  02 

13  29 

12  56 

16 

20 

33  20 

3136 

30  04 

28  40 

27  20 

26  04 

24  56 

23  52 

22  52 

2156 

2104 

20  12 

20 

24 

48  00 

45  30 

43  18 

41  17 

39  22 

37  32 

35  54 

34  22 

32  55 

3135 

30  21 

29  05 

24 

28 

65  20 

6154 

58  56 

56  11 

53  34 

5106 

48  52 

46  47 

44  50 

43  00 

41  17 

39  36 

28 

32 

80  54 

76  58 

73  23 

69  58 

66  44 

63  50 

6106 

58  33 

56  09 

53  55 

5143 

32 

36 

77  20 

74  05 

7104 

68  16 

65  27 

36 

40 

9128 

87  44 

84  16 

80  48 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

5.00 

4.74 

4.51 

4.30 

4.10 

3.91 

3.74 

3.58 

3.43 

3.29 
0.517 

3.16 

3.03 

Ajh 

Log. 

0.698 

0.675 

0.654 

0.633 

0.612 

0.592 

0.572 

0.553 

0.535 

0.499 

0.481 

Log. 

97 

78 

18 

47 

78 

18 

87 

88 

29 

20 

69 

44 

Limit 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

Min- 
utes 

Merid- 
ian 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

Declinations. 


Hour 
Ajigles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1       II 

/      // 

/      // 

/     // 

1     II- 

/      // 

/      II 

1     II 

1     II 

1     II 

1     II 

1      II 

Min. 

4 

0  46 

0  45 

0  43 

0  41 

0  40 

0  38 

0  37 

0  35 

0  35 

0  33 

0  32 

0  30 

4 

8 

3  06 

2  59 

2  52 

2  46 

2  40 

2  34 

2  28 

2  23 

2  17 

2  13 

2  08 

2  03 

8 

12 

6  59 

6  43 

6  27 

6  13 

6  00 

5  46 

5  34 

5  21 

5  09 

4  58 

4  48 

4  38 

12 

16 

12  25 

1157 

1129 

1103 

10  40 

10  14 

9  54 

9  31 

9  11 

8  50 

8  34 

8  14 

16 

20 

19  24 

18  40 

17  56 

17  16 

16  40 

16  00 

15  28 

14  52 

14  20 

13  48 

13  20 

12  52 

20 

24 

27  56 

26  53 

25  50 

24  52 

24  00 

23  02 

22  17 

2124 

20  39 

19  52 

19  12 

18  31 

24 

28 

38  02 

36  35 

35  09 

33  51 

32  40 

3122 

30  19 

29  09 

28  05 

27  03 

26  08 

25  14 

28 

32 

49  40 

47  47 

45  54 

44  12 

42  40 

40  58 

39  35 

38  04 

36  41 

35  20 

34  08 

32  57 

32 

36 

62  51 

60  29 

58  07 

55  57 

54  00 

5150 

50  07 

48  10 

46  27 

44  43 

43  12 

4141 

36 

40 

77  36 

74  40 

7144 

69  04 

66  40 

64  00 

6152 

59  28 

57  20 

55  12 

53  20 

5128 

40 

44 

86  48 

83  34 

80  40 

77  26 

74  52 

7157 

69  23 

66  48 

64  32 

62  16 

44 

48 

96  00 

92  10 

89  05 

85  38 

82  33 

79  29 

76  48 

74  07 

48 

52 

104  33 

100  30 

96  53 

93  17 

90  08 

86  59 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.91 

2.80 

2.69 

2.59 

2.50 

2.40 

2.32 

2.23 

2.15 

2.07 

2.00 

1.93 

Aih 

Log. 

0.463 

0.447 

0.429 

0.413 

0.397 

0.380 

0.365 

0.348 

0.332 

0.315 

0.301 

0.285 

Log. 

89 

16 

75 

30 

94 

21 

49 

30 

44 

97 

03 

56 

Limit 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

Min- 
utes 

Merid- 
ian 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

18 


Latitwdc  3°  Decimation  Same  Name. 


Declinations. 


Hour 
AngleB 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/  // 

0  30 

1  59 
4  28 
7  56 

12  24 
17  52 
24  18 
3144 
40  11 
49  36 
60  01 
71  25 
83  49 
97  13 
111  36 

1.86 

1      If 

0  28 

155 

4  18 

7  38 

1156 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 

1.79 

/  // 

0  27 

150 

4  08 

7  20 

11  28 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 
II 

1.72 

I  II 

0  27 
146 
3  59 
7  05 

II  04 
15  57 
21  41 
28  19 
35  52 
44  16 
53  34 
63  44 
74  48 
86  46 
99  36 

1.66 

1     II 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 
II 

1.60 

1      II 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

0  23 
135 
3  34 

6  18 
9  52 
14  12 
19  21 
25  16 
31  58 
39  28 
47  45 
56  50 
66  42 
77  21 
88  48 

1.48 

r       II 

0  22 

132 

3  24 

6  06 

9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

71  37 

82  12 

II 

1.37 

1     II 

0  21 

124 

3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
II 

1.32 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
II 

1.27 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.269 
51 

0.252 
85 

0.235 
53 

0.220 
11 

0.204 
12 

0.187 
52 

0.170 
26 

0.155 
34 

0.136 
72 

0.120 
57 

0.103 
80 

0.086 
36 

Log. 

Limit 

48 

49 

50 

51 

53 

55 

56 

57 

58 

59 

61 

63 

Min- 
utes 

Merid- 
ian 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

l'.12 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

1.07 

0  16 
106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 

1.03 

1      II 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 
II 

0.98 

1     II 
0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 
55  48 

0.93 

1     II 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 
II 

0.89 

1     II 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

1     II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

1      II 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

0.77 

0  11 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

0  11 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

11  46 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

4124 

II 

0.69 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.068 
19 

0.049 
22 

0.029 
38 

0.012 
84 

9.991 
23 

9.968 

48 

9.949 
39 

9.929 
42 

9.908 
49 

9.886 
49 

9.863 
32 

9.838 
85 

Log. 

Limit 

65 

67 

69 

71 

72 

75 

77 

79 

81 

83 

85 

87 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

Latitude  3°  Declination  Gjntrary  Name. 


19 


Declinations. 

Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Mill. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

II 

1      II 
II 

1      II 

5  59 
23  59 

II 
22.48 

/      // 

5  00 
20  00 

II 
18.74 

4  17 
17  07 
38  31 

II 
16.05 

1 

1 
3 

II 

3  44 

4  59 
3  42 

It 
.04 

1 

1 
2 

12 

ii 

3  19 

3  19 
9  56 

II 
Al 

1      II 

2  59 

1158 

.  26  54 

II 
11.21 

1      II 

2  43 
10  51 
24  26 
43  26 

10.18 

1     II 

2  29 

9  56 

22  20 

39  44 

9.31 

1     II 

2  17 
9  09 
20  36 
36  36 
57  12 

8.58 

1      II 

2  07 

8  29 

19  07 

33  57 

53  04 

// 
7.96 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.351 
80 

1.272 
77 

1.205 
48 

1.147 
37 

1.095 

87 

1.049 
61 

1.007 
75 

0.968 
95 

0.933 
49 

0.900 
91 

Log. 

Limit 

4 

5 

6 

8 

10 

11 

12 

13 

14 

15 

16 

17 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

7fi°      ^J*^^" 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      II 

/      II 

1      II 

/      // 

/      // 

1      II 

1     II 

/      // 

1      II    1     II 

'      " 

1     II 

Min. 

4 

158 

150 

144 

138 

132 

127 

123 

1  19 

1  15      1  12      1  09 

106 

4 

8 

7  55 

7  23 

6  57 

6  32 

6  11 

5  51 

5  33 

5  16 

5  02     4  48     4  35 

4  23 

8 

12 

17  47 

16  38 

15  37 

14  42 

13  54 

13  10 

12  29 

1153 

1120    10  48    10  19 

9  53 

12 

16 

3137 

29  34 

27  47 

26  10 

24  42 

23  22 

22  11 

2107 

20  08 

19  12    18  21 

17  35 

16 

20 

49  24 

46  12 

43  24 

40  52 

38  36 

36  32 

34  40 

33  00 

3128 

30  00   28  40 

27  28 

20 

24 

66  31 

62  30 

58  51 

55  35 

52  36 

49  55 

47  31 

45  19 

43  12 

41  17 

39  34 

24 

28 

80  06 

75  40 

7137 

67  57 

64  41 

6141 

58  48 

56  11 

53  50 

28 

32 

80  33 

76  48 

73  23 

70  18 

32 

36 

' 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

'/ 

II 

II 

II 

" 

II 

II 

II 

// 

II 

" 

II 

Ajh 

7.41 

6.93 

6.51 

6.13 

5.79 

5.48 

5.20 

4.95 

4.72 

4.50 

4.30 

4.12 

A,h 

Log. 

0.869 

82 

0.840 
73 

0.813 
58 

0.787 
46 

0.762 
68 

0.738 
78 

0.716 
00 

0.694 
61 

0.673 
94 

0.653 
21 

0.633 
47 

0.614 
90 

Log. 

Limit 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

Min- 
utes 

Merid- 
ian 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

20 


Latitude  3°  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min.      ' 

II 

1     II 

/      // 

/      II 

/      // 

/      II 

/      // 

1     II 

/      // 

/     // 

1     II 

1      II 

Min. 

4 

1  03 

100 

0  59 

0  55 

0  54 

0  52 

0  50 

0  48 

0  46 

0  45 

0  43     0  42! 

4 

8 

4  12 

4  03 

3  53 

3  44 

3  35 

3  28 

3  19 

3  13 

3  05 

2  59 

2  53 

2  47 

8 

12 

9  29 

9  06 

8  44 

8  23 

8  04 

7  47 

7  29 

7  13 

6  58 

6  43 

6  29 

6  15 

12 

16        1 

6  51 

16  10 

15  32 

14  53 

14  20 

13  49 

13  19 

12  51 

12  22 

1157 

1131 

1109 

16 

20        2 

6  20 

25  16 

24  16 

23  16 

22  24 

2136 

20  48 

20  04 

19  20 

18  40 

18  00 

17  24 

20 

24       3 

7  55 

36  23 

34  57 

33  30 

32  16 

3106 

29  58 

28  54 

27  50 

26  53 

25  55 

25  04 

24 

28       S 

137 

49  32 

47  33 

45  37 

43  54 

42  20 

40  46 

39  20 

37  54 

36  35 

35  17 

34  06 

28 

32       6 

7  25 

64  41 

62  07 

59  34 

57  20 

55  18 

53  14 

51  22 

49  30 

47  47 

46  05 

44  32 

32 

36 

78  38 

75  23 

72  35 

69  59 

67  24 

65  01 

62  38 

60  29 

58  19 

56  23 

36 

40 

•  • 

89  36 

86  24 

83  12 

80  16 

77  20 

74  40 

72  00 

69  36 

40 

44 

. .  • 

87  07 

84  13 

44 

48 

48 

52 

. .: 

52 

56 

56 

60 

.  • 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

II 

" 

A,h      3 

.95 

3.79 

3.64 

3.49 

3.36 

3.24 

3.12 

3.01 

2.90 

2.80 

2.70 

2.61 

A,h 

Log.      ^ 

.596 

0.578 

0.561 

0.542 

0.526 

0.510 

0.494 

0.478 

0.462 

0.447 

0.431 

0.416 

Log. 

60 

64 
31 

10 
31 

83 
32 

34 

55 

15 

57 

40 

16 

36 

64 

Limit 

30 

33 

34 

36 

36 

37 

38 

39 
53° 

39 

Min- 
utes 

Merid- 
ian. 

B3° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

52° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

1      II 

Hour 
Angles 

Min. 

1      II 

1     II 

1      II 

1     II 

1     II 

/      // 

/      II 

1     II 

/       n 

/     // 

1     II 

Min. 

4 

0  40 

0  39 

0  38 

0  36 

0  35 

0  34 

0  33 

0  31 

0  30 

0  30 

0  29 

0  28 

4 

8 

2  41 

2  37 

2  31 

2  26 

2  21 

2  16 

2  12 

2  07 

2  03 

2  00 

1  55      1  52 

8 

12 

6  03 

5  52 

5  40 

5  29 

5  17 

5  06 

4  57 

.    4  47 

4  38 

4  29 

4  19      4  12 

12 

16 

10  45 

10  24 

10  04 

9  43 

9  23 

9  06 

8  47 

8  29 

8  14 

7  59      7  41      7  28 

16 

20 

16  48 

16  16 

15  44 

15  12 

14  40 

14  12 

13  44 

13  16 

12  52 

12  28    12  00    11  40 

20 

24    , 

24  12 

23  25 

22  40 

21  53 

2107 

20  27 

19  47 

19  06 

18  31 

17  57    17  17 

16  48 

24 

28 

32  56 

3153 

30  50 

29  48 

28  45 

27  50 

26  55 

26  01 

25  14 

24  26    23  31 

22  52 

28 

32 

43  00 

41  39 

40  16 

38  55 

37  33 

36  21 

35  09 

33  58 

32  57 

31  55    30  43 

29  52 

32 

36 

54  26 

52  42 

50  59 

49  15 

47  31 

46  01 

44  30 

42  59 

4141 

40  241  38  53 

37  48 

36 

40 

67  12 

65  04 

62  56 

60  48 

58  40 

56  48 

54  56 

53  04 

5128 

49  52    48  00 

46  40 

40 

44 

81  19 

78  43 

76  09 

73  34 

70  59 

68  44 

66  28 

64  12 

62  16 

60  21 

58  05 

56  28 

44 

48 

93  42 

90  37 

87  33 

84  29 

8146 

79  06 

76  25 

74  07 

71  48 

69  07 

67  10 

48 

52 

106  21 

102  45 

99  09 

95  59 

92  50   89  41 

86  59 

84  16 

8107 

78  52 

52 

56 

104  01 

100  52 

97  45 

94  05 

91  28 

56 

60 

.  . . 

112  12 

108  00 

105  00 

60 

II 

II 

II 

II 

II 

II 

// 

II 

" 

" 

II 

" 

A,h 

2.52 

2.44 

2.36 

2.28 

2.20 

2.13 

2.06 

1.99 

1.93 

1.87 

1.80 

1.75 

A,h 

Log. 

0.410 

0.387 

0.372 

0.357 

0.342 

0.328 

0.313 

0.298 

0.285 

0.271 

0.255 

0.243 

Log. 

40 

39 

91 

93 

42 

38 

87 

85 

56 

84 

27 

04 
50 

Limit 

40 

41 

42 

43 

43 

44 

45 

46 

47 

48 

49 

Min- 
utes 

Merid- 
ian 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

Alti- 
tudes 

Latitude  3°  Decimation  Contrary  Name. 


21 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

1     II 

0  23 

134 

3  32 

6  16 

9  48 

14  06 

19  13 

25  06 

3145 

39  12 

47  26 

56  27 

66  15 

76  50 

88  12 

1.47 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Mill. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

I  ■     It 

0  27 

148 
4  03 
7  13 

II  16 
16  14 
22  05 
28  50 
36  31 
45  04 
54  32 
64  53 
76  09 
88  20 

101  24 

1.69 

1        n 

0  26 

144 

3  54 

6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 

1.63 

t          H 

0  25 

141 

3  48 

6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/   // 

0  24 

1  37 
3  39 
6  39 

10  08 
14  36 
19  52 
25  56 
32  50 
40  32 
49  03 
58  22 
68  30 
79  27 
91  12 
II 

1.52 

1      II 

0  22 
131 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  22 

64  00 

74  13 

85  12 
II 

1.42 

1     II 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
II 

1.37 

1     II 

0  21 
124 
3  10 
5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
II 

1.32 

1     II 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 

1.28 

1      II 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

I  II 

0  19 

1  16 

2  51 
5  05 
7  56 

II  26 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
71  24 

// 

1.19 

1     II 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

5122 

59  35 

68  24 
II 

1.14 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.227 
89 

0.212 
19 

0.198 
66 

0.181 
84 

0.167 
32 

0.152 
29 

0.136 

72 

0.120 
57 

0.107 
21 

0.089 
91 

0.075 
55 

0.056 
90 

Log. 

Limit 

51 

52 

54 

55 

56 

57 

59 

61 

62 

65 

67 

69 

Min- 
utes 

Merid- 
ian 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29°   28° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

1     II 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
II 

1.06 

1     II 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

1.02 

/   // 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
II 

0.93 

1      II 
0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 
II 

0.89 

I  II 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

II  06 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 

5100 

II 

0.85 

1      II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 

II 

0.81 

1      II 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

1      II 
0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 

44  24 

II 

0.74 

1     II 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 

II 

0.70 

I  II 

Oil 
0  42 
135 
2  49 
4  24 
6  21 
8  37 

II  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 

39  36 
II 

0.66 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.041 
39 

0.025 
31 

0.008 
60 

0.986 

77 

9.968 
48 

9.949 
39 

9.929 
42 

9.908 
49 

9.892 
09 

9.869 
23 

9.845 
10 

9.819 
54 

Log. 

Limit 

70 

71 

73 

75 

77 

78 

81 

83 

85 

87 

90 

93 

Min- 
utes 

Merid- 
ian 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

Alti- 
tudes 

22 


Latitude  4°  Decimation  Same  Name. 


rjECLINATIOXS. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

II 

1      II 
II 

II 

// 

II 

// 

1 

II 

// 

1 
II 

// 

/ 

n 

II 

II 

1 

1     II 

5  55 
23  41 

II 
22.20 

/     II 

4  55 
19  41 

II 
18.45 

1      II 

4  12 

16  50 

37  53 

II 
15.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.346 
35 

1.266 
00 

1.198 
11 

Log. 

Limit 

5 

4 

2 

1 

0 

2 

3 

5 

7 

8 

9 

10 

Min- 
utes 

Merid- 
ian 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

1     II 

1      II 

/      // 

1      II 

1     II 

1      II 

1      II 

1      II 

/      // 

/      // 

/      // 

Min. 

4 

3  40 

3  15 

2  55 

2  38 

2  25 

2  13 

2  03 

155 

147 

1  40 

134 

129 

4 

8 

14  42 

13  01 

1140 

10  34 

9  40 

8  53 

8  13 

7  38 

7  07 

6  40 

6  16 

5  55 

8 

12 

33  03 

29  17 

26  16 

23  49 

2145 

19  59 

18  29 

17  11 

16  02 

15  00 

14  07 

13  18 

12 

16 

46  40 

42  19 

38  39 

35  33 

32  51 

30  33 

28  30 

26  40 

25  05 

23  38 

16 

20 

55  32 

5120 

47  44 

44  32 

^2  40^ 

39  12 

36  56 

20 

24 

64  08 

60  00 

56  27 

53  11 

24 

28 

8140 

76  50 

72  23 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

Ajh 

13.77 

12.20 

10.94 

9.92 

9.06 

8.33 

7.70 

7.16 

6.68 

6.25 

5.88 

5.54 

A,h 

Log. 

1.138 

1.086 

1.039 

0.996 

0.957 

0.920 

0.886 

0.854 

0.824 

0.795 

0.769 

0.743 

Log. 

93 

36 

02 

51 

13 

65 

49 

91 

78 

88 

38 

51 

Limit 

11 

12 

13 

15 

16 

17 

18 

19 

20 

21 

22 

23 

Min- 
utes 

Merid- 
ian 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

Alti- 
tudes 

Latitttde  4°  Declination  Same  Name. 


23 


Declinations. 


Hour  i    ntp 
Angles     ^* 

25° 

26°      27° 

28°  1    29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

i 

5 

1 
5 
2 
2 
4 
0 
8 

// 
.2 

II 

23 
35 
33 
19 
52 
12 
21 

3 

1 

\ 

\ 
i 

4 

1 
5 
1 
1 
3 
7 
4 

// 
.9 

» 

19 
16 

53 
07 
00 
31 
41 

5 

] 
4 

1 
5 
1 
0 
1 
5 
1 
0 

II 
.7 

// 

15 

01 
17 
03 
20 
07 
25 
13 

0 

1 

] 
] 

A 

4 

K 

7 
4 

1 

4 
0 
9 
9 
2 
8 
6 

// 
.4 

// 

11 

47 
44 
04 
48 
53 
25 
18 

7 

1 

] 

2 
4 
S 
7 

4 

1 
4 
0 

8 
8 
0 
5 
2 

// 
.2 

08 
32 

12 
08 
20 
48 
32 
32 

5 

1 

] 

e 

4 

1 
4 
9 
7 
7 
8 
2 
9 

// 
.0 

05 
19 
43 
17 
00 
53 
55 
07 

5 

1 

1 
4 
9 
16 
25 
37 
50 
66 

3.8 

II 
02 

08 
17 
31 
48 
09 
34 
03 

7 

1      II 

0  59 
3  57 
8  53 
15  47 
24  40 
35  31 
48  21 
63  09 
79  55 

II 
3.70 

1     II 

0  57 
3  47 
8  30 
15  06 
23  36 
33  59 
46  15 
60  25 
76  28 

3.54 

1      II 

0  54 
3  37 

8  08 
14  28 
22  36 
32  33 
44  18 
57  51 
73  14 
90  24 

II 
3.39 

1      II 

0  52 

3  28 

7  48 

13  52 

2140 

31  12 

42  28 

55  28 

70  12 

86  40 

II 
3.25 

1     II 

0  50 
3  19 
7  29 
13  19 
20  48 
29  58 
40  46 
53  14 
67  24 
83  12 

II 
3.12 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.718   0.694 
50'        61 

0.672 
10 

0.650 
31 

0.628 
39 

0.607 
46 

0.587 
71 

0.568 
20 

0.549 
00 

0.530 
20 

0.511 
88 

0.494 
15 

Log. 

Limit       24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

Min- 
utes 

Merid- 
ian 

70° 

( 

59 

3 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     II 

/      // 

/      // 

1      II 

/      // 

/     // 

1      II 

1     II 

1     II 

1     II 

1     II 

/      II 

Min. 

4 

0  47 

0  46 

0  44 

0  43 

0  41 

0  39 

0  38 

0  36 

0  35 

0  34 

0  32 

0  31 

4 

8 

3  11 

3  04 

2  57 

2  49 

2  43 

2  38 

2  31 

2  26 

2  20 

2  15 

2  10 

2  05 

8 

12 

7  11 

6  53 

6  38 

6  21 

6  07 

5  55 

5  40 

5  29 

5  15 

5  03 

4  52 

4  43 

12 

16 

12  45 

12  15    11  46 

11  19 

10  53 

10  29 

10  04 

9  43 

9  21 

9  01 

8  40 

8  21 

16 

20 

19  56 

19  08    18  24 

17  40    17  00'  16  24 

15  44 

15  12    14  36 

14  04 

13  32 

13  04 

20 

24 

28  42 

27  33'  26  30 

25  27    24  29    23  37 

22  40!  21  53    21  02 

20  16 

19  29 

18  49 

24 

28 

39  05 

37  30|  36  04;  34  37!  33  19    32  09 

30  50j  29  48    28  37 

27  34 

26  32 

25  37 

28 

32 

5102 

48  59    47  06    45  13|  43  31    4159 

40  16    38  55    37  22 

36  00 

34  39 

33  27 

32 

36 

64  35 

62  00   59  37!  57  15 

55  05    53  08 

50  59    49  15 

47  19 

45  35 

43  51 

42  20 

.36 

40 

79  44 

76  32 

73  36 

70  40 

68  00    65  36 

62  56 !  60  48 

58  24 

56  16 

54  08 

52  16 

40 

44 

85  31 

82  17 

79  22 

76  09 

73  34 

70  40 

68  05 

65  30 

63  14 

44 

48 

94  28 

90  37 

87  33 

84  05 

8101 

77  57 

75  16 

48 

52 

106  21 

102  45 

98  41 

95  05 

9129 

88  20 

52 

56 

56 

60 

60 

II 

/r 

It 

II 

// 

II 

// 

II 

II 

II 

II          II 

A,h 

2.99 

2.87 

2.76 

2.65 

2.55 

2.46 

2.36 

2.28 

2.19 

2.11 

2.03      1.96 

Ajh 

Log. 

0.475 

0.457    0.440 

0.423 

0.406'  0.390 

0.372 

0.357 

0.340 

0.324 

0.307    0.292 

67 

88        91 

25 

54        94'        91 

93 

44 

28 

50 

26    ^"^• 

Limit 

36 

37 

38 

39 

40       41 

42 

43 

44 

44 

45 

4fi       Min- 
*"        utes 

Merid- 
ian 

58° 

57°  1    56" 

55°      54°  1   53° 

52° 

51°      50° 

49° 

48° 

4.70      Alti- 
*'        tudes 

24 


Latitude  4°  Decimation  Same  Name* 


Declinations. 


Hour 
Augles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

1     It 

/      II 

/      II 

/      // 

/     II 

1     II 

/     // 

'      " 

/      // 

/      // 

'      " 

'      // 

Min. 

4 

0  30 

0  29 

0  28 

0  27 

0  26 

0  25 

0  24 

0  23 

0  22 

0  22 

0  20 

0-19 

4 

8 

2  01 

156 

152 

148 

143 

1  40      1  36 

1  33 

1  29 

126 

122 

1  19 

8 

12 

4  32 

4  22 

4  12 

4  03 

3  53 

3  45 

3  36 

3  29 

3  20 

3  13 

3  05 

2  57 

12 

16 

8  04 

7  46 

7  28 

7  13 

6  55 

6  39 

6  24 

6  11 

5  56 

5  43 

5  27 

5  15 

16 

20 

12  36 

12  08 

1140 

11  16 

10  48 

10  24 

10  00 

9  40 

9  16 

8  56 

8  32 

8  12     20 

24 

18  09 

17  29 

16  48 

16  14 

15  34 

14  59 

14  24 

13  55 

13  21 

12  52 

12  17 

11  48     24 

28 

24  42 

23  47 

22  52 

22  05 

21  10 

20  23^   19  36 

18  57 

18  10 

17  30 

16  44 

16  05      28 

32 

32  15 

3103 

29  52 

28  50 

27  38 

26  37    25  36 

24  45 

23  43 

22  52 

2151 

21  00     32 

36 

40  50 

39  19 

37  48 

36  31 

35  00 

33  42    32  24 

31  19 

30  02 

28  57 

27  39 

26  34,     36 

40 

50  24 

48  32 

46  40 

45  04 

43  12 

41  36   40  00 

38  40 

37  04 

35  44 

34  08 

32  48     40 

44 

60  59 

58  44 

56  28 

54  32 

52  17 

50  20;  48  24 

46  47 

44  51 

43  14 

41  18 

39  4l!     44 

48 

72  34 

69  53 

67  10 

64  53 

62  12 

59  54    57  36 

55  41 

53  22 

5127 

49  09 

47  14     48 

52 

85  10 

82  01 

78  52 

76  09 

73  00 

70  18 

67  36 

65  21 

62  38 

60  23 

57  41 

55  26     52 

56 

98  47 

95  08 

91  28 

88  20 

84  41 

8132 

78  24 

75  37 

72  39 

70  02 

66  54 

64  17     56 

60 

113  24 

109  12 

105  00 

10124 

97  12 

93  36 

90  00 

87  00 

83  24 

80  24 

76  48 

73  48     60 

" 

II 

II 

" 

II 

// 

II 

II 

II 

II 

" 

// 

Ajh 

1.89 

1.82 

1.75 

1.69 

1.62 

1.56 

1.50 

1.45 

1.39 

1.34 

1.28 

1.23 

A,h 

Log. 

0.276 

0.260 

0.243 

0.227 

0.209 

0.193 

0.176 

0.161 

0.143 

0.127 

0.107 

0.089 

Log. 

46 

07 

04 

89 

52 

12 

09 

37 

01 

10 

21 

91 

Limit 

47 

48 

49 

50 

51 

53 

55 

56 

57 

58 

60 

62 

Min- 
utes 

Merid- 
ian 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

oco       Alti- 
•^3        tudes 

Deci>inations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1     II 

/     It 

1     II 

/      II 

1     II 

1     II 

1      II 

/      // 

1     II 

1     II 

/      // 

/      // 

Min. 

4 

0  19 

0  18 

0  17 

0  17 

0  15 

0  15 

0  14 

0  14 

0  13 

0  12 

Oil 

Oil 

4 

8 

1  15 

1  12 

109 

107 

103 

100 

0  57 

0  55 

0  52 

0  50 

0  47 

0  44 

8 

12 

2  50 

2  42 

2  36 

2  30 

2  23 

2  16 

2  10 

2  04 

158 

151 

145 

139 

12 

16 

5  02 

4  50 

4  36 

4  26 

4  13 

4  00 

3  50 

3  40 

3  30 

3  17 

3  07 

2  57 

16 

20 

7  52 

7  32 

7  12 

6  56 

6  36 

6  16 

6  00 

5  44 

5  28 

5  08 

4  52 

4  36 

20 

24 

1120 

10  51 

10  22 

9  59 

9  30 

9  01 

8  38 

8  16 

7  53 

7  23 

7  00 

6  38 

24 

28 

15  25 

14  46 

14  07 

13  35 

12  57 

12  17 

1146 

11  14 

10  43 

10  04 

9  33 

9  01 

28 

32 

20  08 

19  17 

18  26 

17  45 

16  54 

16  03 

15  22 

14  40 

13  59 

13  09 

12  28 

11  46 

32 

36 

25  30 

24  25 

23  20 

22  28 

2123 

20  18 

19  26 

18  35 

17  43 

16  38 

15  46 

14  55 

36 

40 

31  28 

30  08 

28  48 

27  44 

26  24 

25  04 

24  00 

22  56 

21  52 

20  32 

19  28 

18  24 

40 

44 

38  05 

36  28 

34  51 

33  33 

3156 

30  19 

29  02 

27  45 

26  28 

24  51 

23  33 

22  16 

44 

48 

45  18 

43  23 

4128 

39  56 

38  01 

36  06 

34  34 

33  01 

3129 

29  32 

28  00 

26  29 

48 

52 

53  10 

50  55 

48  40 

46  52 

44  37 

42  22 

40  34 

38  45 

36  57 

34  42 

32  54 

3105 

52 

56 

6141 

59  04 

56  27 

54  21 

5144 

49  07 

47  02 

44  57 

42  52 

40  15 

38  09 

36  04 

56 

60 

70  48 

67  48 

64  48 

62  24 

59  24 

56  24 

54  00 

5136 

49  12 

46  12 

43  48 

4124 

60 

II 

II 

" 

II 

K 

If 

n 

II 

II 

n 

n 

A 

A,h 

1.18 

1.13 

1.08 

1.04 

0.99 

0.94 

0.90 

0.86 

0.82 

0.77 

0.73 

0.69 

A,h 

Log. 

0.071 

0.053 

0.033 

0.017 

9.995 

9.973 

9.954 

9.934 

9.913 

9.886 

9.863 

9.838 

Log. 

88 

08 

42 

03 

64 

13 

24 

50 

81 

49 

32 

85 

Limit 

64 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

86 

Min- 
utes 

Merid- 
ian 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

Alti- 
tudes 

Latitude  4°  Declination  Contrary  Name. 


25 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 
II 

// 

1 

5 
23 

II 
22.4 

II 

59 
59 

7 

5  00 
19  59 

. . . 

II 
18.73 

4 

17 
38 

II 
16.0 

II 

17 
07 
31 

5 

1      II 

3  45 
14  59 
33  42 

II 
14.04 

1 

3 
13 

29 

II 
12.4 

// 

19 
19 
56 

7 

2 

11 
26 

II 
11.2 

II 

59 

58 
56 

2 

1     II 

2  43 
10  52 
24  27 
43  29 

II 
10.19 

/     // 

2  29 

9  57 

22  23 

39  49 

II 
9.33 

/      // 
2  18 
9  10 
20  38 
36  42 
57  20 

II 
8.60 

/      // 

2  07 

8  30 

19  08 

34  00 

53  08 

II 
7.97 

1      II 

158 

7  56 

17  50 

3142 

49  32 

n 

7.43 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.351 
60 

1.272 
54 

1.205 

48 

1.147 
37 

1.095 

87 

1.049 
99 

1.008 
17 

0.969 
88 

0.934 
50 

0.901 
46 

0.870 
99 

Log. 

Limit 

6 

7 

8 

9 

11 

12 

13 

14 

15 

16 

17 

18 

Min- 
utes 

Merid- 
ian 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

1     II 

1      II 

1     II 

1     II 

/      // 

/      // 

1     II 

/      II 

1      II 

/      II 

1     II 

Min. 

4 

151 

144 

139 

133 

128 

123 

1  19 

1  16 

1  12 

109 

107 

103 

4 

8 

7  24 

6  58 

6  33 

6  12 

5  53 

5  35 

5  18 

5  04 

4  50 

4  37 

4  25 

4  14|      8 

12 

16  41 

15  40 

14  45 

13  56 

13  13 

12  33 

1156 

11  23 

10  52 

10  23 

9  56 

9  32      12 

16 

29  39 

27  52 

26  15 

24  48 

23  31 

22  19 

21  12 

20  13 

19  20 

18  29 

17  40 

16  56 

16 

20 

46  20 

43  32 

4100 

38  44 

36  44 

34  52 

33  08 

31  36 

30  12 

28  52 

27  36 

26  28 

20 

24 

66  43 

62  41 

59  03 

55  47 

52  54 

50  12 

47  42 

45  30 

43  29 

4134 

39  45 

38  06 

24 

28 

80  21 

75  55 

72  00 

68  21 

64  57 

61  54 

59  12 

56  35 

54  05 

5153 

28 

32 

80  54 

77  19 

73  53 

70  39 

67  46 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

6.95 

6.53 

6.15 

5.81 

5.51 

5.23 

4.97 

4.74 

4.53 

4.33 

4.14 

3.97 

A,h 

Log. 

0.841 

0.814 

0.788 

0.764 

0.741 

0.718 

0.696 

0.675 

0.656 

0.636 

0.617 

0.598 

Log. 

98 

91 

88 

18 

15 

50 

36 

78 

10 

49 

00 

79 

Limit 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

Alti- 
tudes 

26 


Latitude  4°  Declination  Contrary  Name. 


DiXLIXATIONS. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

101 

0  59 

0  56 

0  54 

0  52 

/     II 
0  51 

/      II 
0  48 

1      II 
0  46 

1      II 
0  45 

1     II 
0  43 

1      II 
0  43 

1      II 
0  41 

Min. 
4 

8 

4  04 

3  54 

3  45 

3  37 

3  29 

3  21 

3  14 

3  07 

3  01 

2  55     2  49 

2  43 

8 

12 

9  08 

8  47 

8  27 

8  08 

7  50 

7  33 

7  16 

7  02 

6  47 

6  33 

6  20 

6  07 

12 

16 

16  16 

15  37 

15  01 

14  28 

13  54 

13  27 

12  56 

12  30 

12  05 

1139 

11  16 

10  53 

16 

20 

25  24 

24  24 

23  28 

22  36 

2144 

2100 

20  12 

19  32 

18  52 

18  12 

17  36 

17  00 

20 

24 

36  35 

35  09 

33  48 

32  33 

31  18 

30  15 

29  05 

28  07 

27  10 

26  12 

25  21 

24  29 

24 

28 

49  47 

47  49 

46  00 

44  18 

42  36 

41  09 

39  36 

38  18 

36  59 

35  41 

34  29 

33  19 

28 

32 

65  01 

62  27 

60  04 

57  51 

55  38 

53  45 

5143 

50  01 

48  18    46  36!  45  03 

43  31 

32 

36 

79  04 

76  02 

73  14 

70  25 

68  03 

65  27 

63  17 

61  08    58  58 

57  02 

55  05 

36 

40 

90  24 

86  56 

84  00 

80  48 

78  08 

75  28 

72  48 

70  24 

68  00 

40 

44 

. . . 

88  05 

85  11 

82  17 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

// 

II 

II 

n 

II 

II 

A,h 

3.81 

3.66 

3.52 

3.39 

3.26 

3.15 

3.03 

2.93 

2.83 

2.73 

2.64 

2.55 

A,h 

Log. 

0.580 

0.563 

0.546 

0.530 

0.513 

0.498 

0.481 

0.466 

0.451 

0.436 

0.521 

0.406 

Log. 

92 

48 

54 

20 

22 

31 

44 

87 

79 

16 

60 

54 

Limit 

31 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

40 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56°  1    55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43°  !   44° 

45° 

46°  1   47° 

Hour 
Angles 

Min. 

/       // 

1     II 

/      // 

/      II 

1      II 

/      // 

/      // 

/      // 

1      II 

/      // 

/      "  1  '      " 

Min. 

4 

0  39 

0  38 

0  37 

0  35 

0  35 

0  33 

0  32 

0  31 

0  30 

0  30 

0  28     0  27 

4 

8 

2  39 

2  32 

2  28 

2  23 

2  18 

2  14 

2  09 

2  05 

2  01 

158 

154 

150 

8 

12 

5  56 

5  43 

5  32 

5  21 

5  11 

5  01 

4  51 

4  43 

4  34 

4  25 

4  17 

4  08 

12 

16 

10  32 

10  09 

9  52 

9  31 

9  13 

8  55 

8  37 

8  21 

8  06 

7  51 

7  35,     7  20 

16 

20 

16  28 

15  52 

15  24 

14  52 

14  24 

13  56 

13  28 

13  04    12  40 

12  16    11  52'   11  28 

20 

24 

23  42 

22  51 

22  11 

2124 

20  45 

20  04 

19  24 

18  49:   18  14 

17  40    17  05    16  31 

24 

28 

32  17 

3106 

30  11 

29  09 

28  13 

27  19 

26  24 

25  37    24  50 

24  02    23  16    22  29 

28 

32 

42  10 

40  37 

39  25 

38  04 

36  51 

35  40 

34  28 

33  27    32  26 

31  24   30  23    29  21 

32 

36 

53  21 

5125 

49  54 

48  10 

46  40 

45  09 

43  38 

42  20    41  02 

39  45    38  27    37  09 

36 

40 

65  52 

63  28 

61  36 

59  28 

57  36 

55  44 

53  52 

52  16    50  40 

49  04    47  28!  45  52 

40 

44 

79  42 

76  48 

74  32 

7157 

69  42 

67  26 

65  11 

63  14    61  18 

59  22    57  26|  55  30 

44 

48 

94  51 

91  23 

88  42 

85  38 

82  56 

80  15 

77  34 

75  16 

72  58 

70  39    68  19    66  01 

48 

52 

107  15 

104  06 

100  30 

97  20 

94  11 

9102 

88  20 

85  38 

82  55    80  13 

77  31 

52 

56 

99  18 

96  10    93  02 

89  54 

56 

60 

106  48 

103  12 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

// 

II 

/» 

A,h 

2.47 

2.38 

2.31 

2.23 

2.16 

2.09 

2.02 

1.96 

1.90 

1.84 

1.78 

1.72 

A  jh 

Log. 

0.392 

0.376 

0.363 

0.348 

0.334 

0.320 

0.305 

0.292 

0.278 

0.264 

0.250 

0.235 

Log. 

70 

58 

61 

30 

45 

15 

35 

26 

75 

82 

42 

53 

Limit 

41 

42 

43 

44 

44 

45 

46 

47 

48 

49 

50 

51 

Min- 
utes 

Merid- 
ian 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tudes 

Latitude  4°  Declination  Contrary  Name. 


27 


Declinations, 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 

32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   n 

0  27 

1  46 
3  59 
7  05 

1104 

15  57 

2141 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

86  46 

99  36 
II 

1.66 

/  // 

0  26 

142 

3  51 

6  53 

10  44 

15  28 

2102 

27  28 

34  47 

42  56 

5157 

6149 

72  33 

84  09 

96  36 
II 

1.61 

1     II 

0  25 

140 

3  45 

6  39 

10  24 

14  59 

20  23 

26  37 

33  42 

4136 

50  20 

59  54 

70  18 

8132 

93  36 
II 

1.56 

/  II 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 
II 

1.50 

1      II 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
II 

1.45 

/  // 

0  22 

130 

3  23 

6  01 

9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 
II 

1.41 

1     II 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

81  36 
II 

1.36 

I     II 

0  21 

1  23 
3  08 
5  36 
8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 
II 

1.31 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 

II 

1.26 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  29 

63  46 

73  12 
II 

1.22 

/   // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

3128 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

1     It 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
55  55 
59  04 

67  48 
II 

1.13 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.220 
11 

0.206 
83 

0.193 
12 

0.176 
09 

0.161 
37 

0.149 

22 

0.133 
54 

0.117 

27 

0.100 
37 

0.086 
36 

0.071 

88 

0.053 
08 

Log. 

Limit 

52 

53 

55 

56 

57 

58 

60 

62 

63 

65 

67 

68 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1      II 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

41  51 

49  07 

56  58 

65  24 
II 

1.09 

1     II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/  II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

II 

1.01 

1     II 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
II 

0.93 

I  II 
0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

II  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 

II 

0.89 

I  II 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

II  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

1      II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 

II 

0.81 

1     II 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

II 

0.77 

1      II 

Oil 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

1     II 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

31  33 

36  35 

42  00 

II 

0.70 

/  // 

0  11 

0  42 

136 

2  52 

4  28 

6  26 

8  45 

11  26 

14  29 

17  52 

2138 

25  43 

30  11 

35  02 

40  12 

II 

0.67 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.037 
43 

0.021 
19 

0.004 
32 

9.986 
77 

9.968 
48 

9.949 
39 

9.929 
42 

9.908 
49 

9.886 
49 

9.863 
32 

9.845 
10 

9.826 
07 

Log. 

Limit 

70 

72 

74 

76 

77 

79 

81 

83 

85 

87 

90 

93 

Min- 
utes 

Merid- 
ian 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

Alti- 
tudes 

28 


Latitude  5°  Declination  Same  Name. 
Declinations. 


Hour  I 
Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Limit 


Merid- 
ian 


5  59 
23  57 


22.44 


1.351 
02 


85° 


86= 


2° 


87° 


88°      89 


90° 


6« 


89° 


88° 


87° 


86' 


10° 


5  54 
23  34 


11° 


22.10 


1.344 
39 


4  54 
19  36 


18.37 


1.264 
11 


Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Min- 
utes 


85° 


o JO    I  Alti- 
*'*      I  tudes 


Declinations. 


Hour 

Angles 

2° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

n 

1     It 

/      // 

1     II 

1      II 

1      II 

/      II 

1      II 

1      II 

1      II 

1      II 

/      // 

Min. 

4 

4  11 

3  39      3  15 

2  54 

2  38 

2  24 

2  12 

2  03 

1  54 

146 

1  39 

133       4 

8        1 

6  45 

14  36 

12  56 

1136 

10  30 

9  36 

8  50 

8  09 

7  34 

7  04 

6  37 

6  13,       8 

12        3 

7  41 

32  51 

29  06 

26  06 

23  38 

21  36 

19  51 

18  20 

17  02 

15  54 

14  53 

13  59i     12 

16 

46  25 

42  02 

38  24 

35  17 

32  36 

30  18 

28  18 

26  27 

24  53      16 

20 

55  08 

50  56 

47  20 

44  12 

4120 

38  52      20 

24 

63  39 

59  31 

55  58      24 

28 

8101 

76  11 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

ir 

n 

II 

" 

II 

II 

// 

II 

II 

II 

II 

A,h    U 

).70 

13.69 

12.13 

10.88 

9.85 

9.00 

8.27 

7.64      7.10 

6.63 

6.20 

5.83 

A,h 

Log.      ^ 

L.195 

1.136 

1.083 

1.036 

0.993 

0.954 

0.917 

0.883,  0.851 

0.821 

0.792 

0.765 

Log. 

90 

40 

86 

63 

44 

24 

51 

09 
18 

26 

51 

39 

67 

Limit 

10 

11 

13 

14 

15 

16 

17 

19 

20 

21 

22 

Min- 
utes 

Merid- 
ian    ' 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

790    1   Alti- 
'^     'tudes 

Latitude  5°  Declination  Same  Name. 


29 


Declinations. 


Hour 
Angles     ' 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min.      ' 

// 

t           It 

1      II 

1     II 

1      II 

1      II 

1      II 

1      II 

1      II 

1      II 

1     II 

/      // 

Min. 

4 

127 

123 

1  18 

1  15 

1  10 

107 

1  04 

101 

0  59 

0  55 

0  54 

0  51 

4 

8 

5  52 

5  31 

5  14 

4  57 

4  43 

4  30 

4  17 

4  05 

3  53 

3  44 

3  34 

3  25 

8 

12        1 

3  11 

12  26 

1147 

11  09 

10  37 

10  06 

9  37 

9  10 

8  45 

8  23 

8  01 

7  41 

12 

16       2 

3  25 

22  06 

20  57 

19  51 

18  51 

17  58 

17  07 

16  18 

15  35 

14  53 

14  15 

13  39 

16 

20       3 

6  36 

34  32 

32  44 

3100 

29  28 

28  04 

26  44 

25  28 

24  20 

23  16 

22  16 

21  20 

20 

24       5 

2  42 

49  44 

47  08 

44  39 

42  26 

40  25 

38  30 

36  41 

35  03 

33  30 

32  04 

30  43 

24 

28       7 

145 

67  41 

64  10 

60  45 

57  46 

55  01 

52  24 

49  55 

47  41 

45  37 

43  38 

4149 

28 

32 

79  21 

75  26 

7151 

68  26 

65  11 

62  17 

59  34 

57  00 

54  37 

32 

36 

78  51 

75  23 

72  09 

69  07 

36 

40 

89  04 

85  20 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h     5 

.49 

5.18 

4.91 

4.65 

4.42 

4.21 

4.01 

3.82 

3.65 

3.49 

3.34 
0.523 

3.20 

Ajh 

Log.      0 

.739 

0.714 

0.691 

0.667 

0.645 

0.624 

0.603 

0.582 

0.562 

0.542 

0.505 

Log. 

57 

33 

OS 

45 

42 

28 

14 

06 

29 

83 

75 

15 

Limit 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

Min- 
utes 

Merid-      r 
ian 

^1° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/        // 

/      // 

1      II 

1      II 

1      II 

1      II 

1      1, 

1      II 

1      II 

/      // 

'      " 

'      // 

Min. 

4 

0  49 

0  47 

0  45 

0  43 

0  42 

0  40 

0  38 

0  37 

0  36 

0  35 

0  33 

0  31 

4 

8 

3  17 

3  09 

3  01 

2  54 

2  47 

2  41 

2  35 

2  28 

2  24 

2  17 

2  13 

2  07 

8 

12 

7  22 

7  05 

6  47 

6  32 

6  15 

6  01 

5  49 

5  34 

5  23 

5  09 

4  58 

4  47 

12 

16 

13  06 

12  35 

12  05 

1136 

1109 

10  43 

10  19 

9  54 

9  33 

9  11 

8  50 

8  29 

16 

20 

20  28 

19  40 

18  52 

18  08 

17  24 

16  44 

16  08 

15  28 

14  56 

14  20 

13  48 

13  16 

20 

24 

29  28 

28  19 

27  10 

26  07 

25  04 

24  06 

23  14 

22  17 

2130 

20  39 

19  52 

19  06 

24 

28 

40  07 

38  33 

36  59 

35  33 

34  06 

32  48 

3138 

30  19 

29  16 

28  05 

27  03 

26  01 

28 

32 

52  24 

50  21 

48  18 

46  25 

44  32 

42  50 

41  18 

39  35 

38  14 

36  41 

35  20 

33  58 

32 

36 

66  19 

63  43 

6108 

58  45 

56  23 

54  13 

52  16 

50  07 

48  23 

46  27 

44  43 

42  59 

36 

40 

8152 

78  40 

75  28 

72  32 

69  36 

66  56 

64  32 

6152 

59  44 

57  20 

55  12 

53  04 

40 

44 

87  46 

84  13 

80  59 

78  05 

74  52 

72  16 

69  23 

66  48 

64  12 

44 

48 

96  23 

92  56 

89  05 

86  01 

82  33 

79  29 

76  25 

48 

52 

104  33 

100  57 

96  53 

93  17 

89  41 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.07 

2.95 

2.83 

2.72 

2.61 

2.51 

2.42 

2.32 

2.24 

2.15 

2.07 

1.99 

A,h 

Log. 

0.487 

0.469 

0.451 

0.434 

0.416 

0.399 

0.383 

0.365 

0.350 

0.332 

0.315 

0.298 

Log. 

14 

82 

79 

57 

64 

67 

82 

49 

25 

44 

97 

85 

Limit 

35 

36 

37 

38 

39 

40 

41 

42 

43 

43 

44 

45 

Min- 
utes 

Merid- 
ian 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

Latitude  5°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

48= 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59°  1 

Hour 
Angles 

Min. 

t       n 

t      If 

/      // 

/      // 

1     II 

/      // 

/      II 

/      // 

1      II 

/      // 

1     II 

/     // 

Min, 

4 

0  30 

0  30 

0  28 

0  27 

0  27 

0  25 

0  24 

0  23 

0  22 

0  22 

0  21 

0  20 

4 

8 

2  02 

158 

154 

150 

145 

141 

137 

134 

1  30 

126 

123 

1  20 

8 

12 

4  37 

4  26 

4  17 

4  06 

3  57 

3  48 

3  39 

3  31 

3  23 

3  14 

3  07 

3  00 

12 

16 

8  11 

7  54 

7  35 

7  18 

7  03 

6  44 

6  29 

6  13 

6  01 

5  46 

5  33 

5  20* 

16 

20 

12  48 

12  20 

1152 

1124 

1100 

10  32 

10  08 

9  44 

9  24 

9  00 

8  40 

8  20 

20 

24 

18  26 

17  46 

17  05 

16  25 

15  51 

15  10 

14  36 

14  01 

13  32 

12  58 

12  29 

12  00 

24 

28 

25  06 

24  10 

23  16 

22  21 

2133 

20  39 

19  52 

19  05 

18  26 

'  17  38 

16  59 

16  20 

28 

32 

32  46 

3134 

30  23 

29  11 

28  09 

26  58 

25  56 

24  55 

24  04 

23  02 

22  11 

21  20 

32 

36 

4128 

39  58 

38  27 

36  56 

35  39 

34  08 

32  50 

31  32 

30  27 

29  10 

28  05 

27  00 

36 

40 

51  12 

49  20 

47  28 

45  36 

44  00 

42  08 

40  32 

38  56 

37  36 

36  00 

34  40 

33  20 

40 

44 

6157 

59  42 

57  26 

55  10 

53  15 

50  59 

49  03 

47  06 

45  29 

43  34 

4157 

40  20 

44 

48 

73  44 

7102 

68  19 

65  38 

63  21 

60  40 

58  22 

56  04 

54  09 

5150 

49  55 

48  00 

48 

52 

86  32 

83  22 

80  13 

77  04 

74  21 

71  12 

68  30 

65  48 

63  33 

60  50 

58  35 

56  20 

52 

56 

100  21 

96  42 

93  02 

89  22 

86  15 

82  35 

79  27 

76  18 

73  41 

70  34 

67  57 

65  20 

56 

60 

111  00 

106  48 

102  36 

99  00 

94  48 

91  12 

87  36 

84  36 

8100 

78  00 

75  00 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.92 

1.85 

1.78 

1.71 

1.65 

1.58 

1.52 

1.46 

1.41 

1.35 

1.30 

1.25 

A,h 

Log. 

0.283 

0.267 

0.250 

0.233 

0.217    0.198 

0.181 

0.164 

0.149 

0.130 

0.113 

0.096 

Log. 

30 

17 

42 
43 

00 

48 

66 

84 

35 

22 

33 

94 

91 

Limit 

46 

47 

49 

50 

52 

54 

55 

56 

57 

59 

61 

Min- 
utes 

Merid- 
ian 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36°  ; 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1       II 

/      // 

/      II 

/      II 

/      // 

/      // 

1      II 

1      II 

/      II 

/      // 

1      II 

/      II 

Min. 

4 

0  19 

0  19 

0  17 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

4 

8 

1  16 

1  13 

1  10 

107 

104 

101 

0  58 

0  55 

0  52 

0  50 

0  47 

0  45 

8 

12 

2  51 

2  44 

2  37 

2  31 

2  24 

2  17 

2  11 

2  04 

1  58 

152 

147 

141 

12 

16 

5  05 

4  52 

4  39 

4  29 

4  16 

4  03 

3  53 

3  40 

3  30 

3  19 

3  09 

2  59 

16 

20 

7  56 

7  36 

7  16 

7  00 

6  40 

6  20 

6  04 

5  44 

5  28 

5  12 

4  56 

4  40 

20 

24 

1126 

10  57 

10  28 

10  05 

9  36 

9  07 

8  44 

8  16 

7  53 

7  29 

7  06 

6  43 

24 

28 

15  33 

14  53 

14  15 

13  43 

13  04 

12  25 

11  54 

11  14 

10  43 

10  12 

9  40 

9  09 

28 

32 

20  18 

19  27 

18  36 

17  55 

17  04 

16  13 

15  32 

14  40 

13  59 

13  19 

12  38 

1157 

32 

36 

25  43 

24  38 

23  33 

22  41 

2136 

20  31 

19  39 

18  35 

17  43 

16  51 

15  59 

15  07 

36 

40 

3144 

30  24 

29  04 

28  00 

26  40 

25  20 

24  16 

22  56 

2152 

20  48 

19  44 

18  40 

40 

44 

38  24 

36  47 

35  10 

33  53 

32  16 

30  39 

29  21 

27  45 

26  28 

25  10 

23  52 

22  35 

44 

48 

45  41 

43  46 

41  51 

40  19 

38  24 

36  29 

34  57 

33  01 

3129 

29  55 

28  23 

26  51 

48 

52 

53  37 

5122 

49  07 

47  19 

45  04 

42  49 

41  01 

38  45 

36  57 

35  09 

33  21 

3133 

52 

56 

62  12 

59  35 

56  58 

54  53 

52  16 

49  39 

47  33 

44  57 

42  52 

40  46 

38  40 

36  35 

56 

60 

7124 

68  24 

65  24 

63  00 

60  00 

57  00 

54  36 

5136 

49  12 

46  48 

44  24 

42  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

n 

n 

A,h 

1.19 

1.14 

1.09 

1.05 

1.00 

0.95 

0.91 

0.86 

0.82 

0.78 

0.74 

0.70 

A,h 

Log. 

0.075 

0.056 

0.037 

0.021 

0.00 

9.977 

9.959 

9.934 

9.913 

9.892 

9.869 

9.845 

Log. 

55 

90 

43 

19 

72 

04 

50 

81 

09 

23 

10 

Limit 

63 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

86 

Min- 
utes 

Merid- 
ian 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

Latitude  5°  Declination  Contrary  Name. 


31 


Declixations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

5 
23 

// 
22.4 

// 

59 
57 

4 

4  59 
19  58 

n 

18.71 

1 

4 
17 
38 

n 
16.0 

17 
07 
30 

4 

1     II 

3  45 
14  59 
33  42 

14.04 

3 
13 
29 

// 
12.4 

// 

18 
19 
56 

7 

2 
11 
26 

II 
11.2 

// 

59 
57 
56 

2 

2 
10 
24 
43 

II 
10.2 

43 
53 
29 
31 

3 

1 

2 
9 

22 
39 

II 
9.3 

29 
58 
25 
51 

i 

/      // 

2  18 

9  11 

20  39 

36  45 

57  24 

II 
8.61 

1     II 

2  07 

8  31 

19  11 

34  05 

53  16 

II 
7.99 

/      // 

159 

7  57 

17  52 

3144 

49  36 

II 
7.44 

1     II 

151 

7  26 
16  44 
29  44 
46  28 

6.97 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

1.351 
02 

1.272 
07 

1.205 
20 

1.147 
37 

1.095 

87 

1.049 
99 

1.008 
60 

0.970 
35 

0.935 
00 

0.902 
55 

0.871 
57 

0.843 
23 

Log. 

Limit 

7 

8 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81°      80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      II 

/     // 

1      II 

1     II 

1      II 

1      II 

1     II 

1      II 

1     II 

/      // 

1     II 

'      " 

Min. 

4 

145 

139 

1  33 

128 

124 

1  19 

1  16 

1  13 

1  10 

107 

103 

1  02 

4 

8 

6  59 

6  35 

6  13 

5  53 

5  36 

5  19 

5  05 

4  51 

4  38 

4  27 

4  15 

4  06 

8 

12 

15  42 

14  48 

13  59 

13  15 

12  36 

11  59 

11  26 

10  55 

10  26 

10  00 

9  35 

9  13 

12 

16 

27  54 

26  20 

24  53 

23  33 

22  24 

21  17 

20  18 

19  25 

18  34 

17  48 

17  01 

16  23 

16 

20 

43  36 

4108 

38  52'  36  48 

35  00 

33  16 

31  44 

30  20 

29  00 

27  48 

26  36 

25  36 

20 

24 

62  47 

59  14 

55  58!  53  00 

50  24 

47  54 

45  42 

43  41 

4146 

40  02 

38  18 

36  52 

24 

28 

80  37 

76  11 

72  08 

68  36 

65  11 

62  10 

59  27 

56  50 

54  29 

52  09 

50  10 

28 

32 

81  14 

77  39 

74  14 

71  10 

68  06 

65  32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

6.54 

6.17 

5.83 

5.52 

5.25 

4.99 

4.76 

4.55 

4.35 

4.17 

3.99 

3.84 

A,h 

Log. 

0.815 

0.790 

0.765 

0.741 

0.720 

0.698 

0.677 

0.658 

0.638 

0.620 

0.600 

0.584 

Log. 

58 

29 

67 

94 

16 

10 

61 

01 

49 

14 

97 

33 

Limit 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

Min- 
utes 

Merid- 
ian 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

Alti- 
tudes 

32 


Latitude  5°  Decimation  Contrary  Name* 


Declination's. 


Hour 
AngleH 

24° 

25° 

26° 

27°  1   28°  1   29° 

30° 

31° 

32° 

33° 

34° 

35° 

/      // 

0  39 
2  40 
5  59 
10  37 
16  36 
23  54 
32  33 
42  30 
53  47 
66  24 
80  20 
95  37 

II 
2.49 
0.396 
20 

Hour 

Angles 

Mill. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1     II 

0  59 
3  56 
8  51 
15  45 
24  36 
35  26 
48  13 
62  58 
79  43 

II 
3.69 

1 

0 
3 

8 
15 
23 
34 
46 
60 
76 

II 
3.5 

// 

57 
47 
31 
09 
40 
05 
23 
35 
41 

5 

1     II 

0  54 

3  39 

8  11 

14  33 

22  44 

32  44 

44  34 

58  12 

73  39 

90  56 

II 
3.41 

1 

0 
3 

7 
14 
21 
31 
43 
56 
71 
87 

II 
3.2 

// 

52 
31 
54 
02 
56 
35 
00 
09 
04 
44 

9 

'\ 

7 
13 
21 
30 
41 
54 
68 
84 

II 
3.1 

51 
23 
36 
32 
08 
26 
25 
06 
29 
32 

7 

1 

0 
3 

7 
13 
20 
29 
39 
52 
66 
81 

II 
3.0 

n 

49 
16 
21 
03 
24 
23 
59 
13 
06 
36 

6 

1 

0 
3 

7 
12 
19 
28 
38 
50 
63 
78 

II 
2.9 

// 

47 
09 
05 
35 
40 
19 
33 
21 
43 
40 

5 

/      II 

0  46 
3  02 
6  50 
12  10 
19  00 
27  22 
37  14 
48  38 
61  34 
76  00 

II 
2.85 

0  44 
2  57 
6  38 
11  46 
18  24 
26  30 
36  04 
47  06 
59  37 
73  36 

II 
2.76 

I  II 

0  43 
2  50 
6  23 

II  21 
17  44 
25  33 
34  45 
45  23 
57  28 
70  56 
85  50 

II 
2.66 

0  41 

2  45 

6  12 

1100 

17  12 
24  46 
33  43 
44  02 
55  44 
68  48 
83  15 

II 
2.58 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.567 
03 

0.550 
23 

0.532 

75 

0.517 
20 

0.501 
06 

0.485 
72 

0.469 

82 

0.454 

84 

0.440 
91 

0.424 
88 

0.411 
62 

Log. 

Limit 

32 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

41 

M  in- 
utes 

Merid- 
ian 

61° 

60° 

59° 

58°       57°  1 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

Alti- 
tudes 

Declinations  . 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

1     II 

1      II 

1      II 

1      II 

1      II 

r        II 

1     II 

1      II 

1      II 

Min. 

Min. 

4 

0  38 

0  37 

0  36 

0  35 

0  34 

0  33 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

4 

8 

2  35 

2  29 

2  25 

2  20 

2  15 

2  11 

2  07 

2  02 

159 

156 

152 

148 

8 

12 

5  47 

5  35 

5  26 

5  15 

5  05 

4  55 

4  47 

4  37 

4  28 

4  20 

4  12 

4  03 

12 

16 

10  17 

9  57 

9  38 

9  21 

9  03 

8  45 

8  29 

8  11 

7  56 

7  44 

7  28 

7  13 

16 

20 

16  04 

15  32 

15  04 

14  36 

14  08 

13  40 

13  16 

12  48 

12  24 

12  04 

11  40 

11  16 

20 

24 

23  08 

22  22 

2142 

21  02 

20  22 

19  41 

19  06 

18  26 

17  52 

17  23 

16  48 

16  14 

24 

28 

3130 

30  27 

29  32 

28  37 

27  42 

26  47 

26  01 

25  06 

24  18 

23  39 

22  52 

22  05 

28 

32 

4108 

39  46 

38  34 

37  22 

36  10 

34  59 

33  58 

32  46 

3144 

30  53 

29  52 

28  50 

32 

36 

52  03 

50  20 

48  49 

47  19 

45  48 

44  17 

42  59 

41  28 

40  11 

39  06 

37  48 

36  31 

36 

40 

64  16 

62  08 

60  16 

58  24 

56  32 

54  40 

53  04 

51  12 

49  36 

48  16 

46  40 

45  04 

40 

44 

77  45 

75  11 

72  55 

70  40 

68  25 

66  09 

64  12 

6157 

60  01 

58  24 

56  28 

54  32 

44 

48 

92  33 

89  28 

86  47 

84  05 

81  24 

78  43 

76  25 

73  44 

7125 

69  30 

67  10 

64  53 

48 

52 

105  00 

10151 

98  41 

95  32 

92  23 

89  41 

86  32 

83  49 

8134 

78  52 

76  09 

52 

56 

104  01 

100  21 

97  13 

94  36 

9128 

88  20 

56 

60 

11136 

108  36 

105  00 

10124 

60 

'/ 

II 

II 

II 

II 

II 

// 

// 

" 

II 

II 

II 

A,h 

2.41 
0.382 

2.33 

2.26 

2.19 

2.12 

2.05 
0.311 

1.99 

1.92 

1.86 

1.81 

1.75 

1.69 

A,h 

Log. 

0.367 

0.354 

0.340 

0.326 

0.298 

0.283|  0.269 

0.257 

0.243 

0.227 

Log. 

02 

36 

11 

44 

34 

75 

85 

30        51 

68 

04 

89 

Limit 

41 

42 

43 

44 

44 

45 

46 

47 

48 

49 

50 

51 

Min- 
utes 

Merid- 
ian 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42°      41° 

40° 

39° 

38° 

Alti- 
tudes 

Latitude  5°  Declination  Contrary  Name* 


33 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

1     II 

/  II 

1     II 

1     II 

1     II 

/   n 

/  II 

/  // 

/  // 

1     II 

/  * 

1          H 

Mill. 

Min. 

4 

0  27 

0  25 

0  24 

0  23 

0  22 

0  22 

0  22 

0  20 

0  20 

0  19 

0  19 

0  18 

4 

8 

1  45 

142 

138 

135 

133 

129 

1  26 

1  23 

1  20 

1  17 

1  14 

1  11 

8 

12 

3  56 

3  49 

3  40 

3  34 

3  28 

3  20 

3  13 

3  06 

3  00 

2  54 

2  47 

2  41 

12 

16 

7  00 

6  47 

6  32 

6  18 

6  08 

5  56 

5  43 

5  30 

5  20 

5  10 

4  57 

4  47 

16 

20 

10  56 

10  36 

10  12 

9  52 

9  36 

9  16 

8  56 

8  36 

8  20 

8  04 

744 

7  28 

20 

24 

15  45 

15  16 

14  41 

14  12 

13  49 

13  21 

12  52 

12  23 

12  00 

11  37 

1109 

10  46 

24 

28 

2125 

20  47 

20  00 

19  21 

18  49 

18  10 

17  30 

16  52 

16  20 

15  49 

15  09 

14  38 

28 

32 

27  59 

27  08 

26  07 

25  16 

24  35 

23  43 

22  52 

22  01 

21  20 

20  39 

19  47 

19  06 

32 

36 

35  26 

34  21 

33  03 

3158 

3106 

30  02 

28  57 

27  52 

27  00 

26  08 

25  04 

24  12 

36 

40 

43  44 

42  24 

40  48 

39  28 

38  24 

37  04 

35  44 

34  24 

33  20 

32  16 

30  56 

29  52 

40 

44 

52  55 

51  18 

49  22 

47  25 

46  27 

44  51 

43  14 

4137 

40  20 

39  02 

37  26 

36  09 

44 

48 

62  58 

6103 

58  45 

56  50 

55  18 

53  22 

5127 

49  32 

48  00 

46  28 

44  32 

43  00 

48 

52 

73  54 

7139 

68  57 

66  42 

64  54 

62  38 

60  23 

58  08 

56  20 

54  32 

52  16 

50  28 

52 

56 

85  43 

83  06 

79  58 

77  21 

75  15 

72  39 

70  02 

67  25 

65  20 

63  14 

60  38 

58  33 

56 

60 

98  24 

95  24 

9148 

88  48 

86  24 

83  24 

80  24 

77  24 

75  00 

72  36 

69  36 

67  12 

60 

II 

II 

II 

II 

II 

II 

II 

n 

II 

II 

II 

II 

A,h 

1.64 

1.59 

1.53 

1.48 

1.44 

1.39 

1.34 

1.29 

1.25 

1.21 

1.16 

1.12 

Ajh 

Log. 

0.214 

0.201 

0.184 

0.170 

0.158 

0.143 

0.127 

0.110 

0.096 

0.082 

0.064 

0.049 

Log. 

84 

40 

69 

26 

36 

01 

10 

59 

91 

79 

46 

22 

Limit 

52 

53 

55 

57 

58 

59 

61 

63 

64 

66 

68 

70 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Horn- 
Angles 

Min. 

1       II 

1     II 

/   // 

1      II 

1      II 

1      II 

/  II 

1     II 

/  II 

1     II 

1     II 

1     II 

Min. 

4 

0  17 

0  17 

0  16 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

Oil 

Oil 

Oil 

4 

8 

109 

107 

104 

101 

0  58 

0  56 

0  54 

0  51 

0  50 

0  47 

0  44 

0  41 

8 

12 

2  36 

2  30 

2  24 

2  19 

2  13 

2  07 

2  01 

155 

151 

145 

139 

133 

12 

16 

4  36 

4  26 

4  16 

4  05 

3  55 

3  45 

3  35 

3  25 

3  17 

3  07 

2  57 

2  47 

16 

20 

7  12 

6  56 

6  40 

6  24 

6  08 

5  52 

5  36 

5  20 

5  08 

4  52 

4  36 

4  20 

20 

24 

10  22 

9  59 

9  36 

9  13 

8  50 

8  27 

8  04 

7  41 

7  23 

7  00 

6  38 

6  15 

24 

28 

14  07 

13  35 

13  04 

12  33 

12  02 

1130 

10  58 

10  27 

10  04 

9  33 

9  01 

8  29 

28 

32 

18  26 

17  45 

17  04 

16  23 

15  42 

15  01 

14  20 

13  39 

13  09 

12  28 

1146 

1105 

32 

36 

23  20 

22  28 

2136 

20  44 

19  52 

19  01 

18  09 

17  17 

16  38 

15  46 

14  55 

14  03 

36 

40 

28  48 

27  44 

26  40 

25  36 

24  32 

23  28 

22  24 

2120 

20  32 

19  28 

18  24 

17  20 

40 

44 

34  51 

33  33 

32  16 

30  58 

29  41 

28  24 

27  06 

25  49 

24  51 

23  33 

22  16 

20  59 

44 

48 

4128 

39  56 

38  24 

36  52 

35  20 

33  47 

32  15 

30  43 

29  32 

28  00 

26  29 

24  57 

48 

52 

48  40 

46  52 

45  04 

43  16 

41  28 

39  39 

37  51 

36  03 

34  42 

32  54 

3105 

29  17 

52 

56 

56  27 

54  21 

52  16 

50  10 

48  05 

46  00 

43  54 

4149 

40  15 

38  09 

36  04 

33  59 

56 

60 

64  48 

62  24 

60  00 

57  36 

55  12 

52  48 

50  24 

48  00 

46  12 

43  48 

4124 

39  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.08 

1.04 

1.00 

0.96 

0.92 

0.88 

0.84 

0.80 

0.77 

0.73 

0.69 

0.65 
9.812 

A,h 

Log. 

0.033 

0.017 

0.00 

9.982 

9.963 

9.944 

9.924 

9.903 

9.886 

9.863 

9.838 

Log. 

42 

03 

27 

79 

48 

28 

09 

49 

32 

85 

91 

Limit 

71 

73 

74 

75 

77 

79 

81 

83 

85 

87 

89 

91 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

34 


Latitude  6°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Mill. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

r 

4 
19 

H 

18.6 

// 

59 
55 

8 

1      II 

5  58 
23  54 

II 
22.40 

1     II 

/     // 

1 
II 

II 

/       n 

II 

It 

/       n 

II 

/ 

H 

/ 

II 
II 

1 

II 

II 

1     II 

5  51 
23  27 

II 
21.99 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.271 
38 

1.350 
25 

1.342 
23 

Log. 

Limit 

8 

7 

6 

5 

3 

2 

0 

1 

3 

5 

7 

8 

Min- 
utes 

Merid- 
ian 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89°      88° 

87° 

86°      85° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

L2° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min.     ' 

II 

/     // 

/      // 

/      // 

/      // 

1     II 

/      // 

/      // 

1     II 

1      II 

r       II 

/      // 

Min. 

4 

4  52 

4  10 

3  38 

3  13 

2  53 

2  36 

2  22 

2  11 

2  01 

153 

145 

1  39 

4 

8        1 

9  30 

16  39 

14  31 

12  52 

1132 

10  27 

9  31 

8  46 

8  05 

7  31 

7  01 

6  33 

8 

12 

37  27 

32  39 

28  57 

25  56 

23  30 

2126 

19  42 

18  12 

16  54 

15  46    14  45 

12 

16 

5127 

46  08 

4146 

38  06 

35  02 

32  20 

30  02 

28  02 

26  15 

16 

20 

54  44 

50  32 

46  56 

43  48 

41  00 

20 

24 

63  04 

59  03 

24 

28 

80  21 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

II 

II 

II 

II 

II 

II 

II 

n 

n 

II 

II 

A,h    IS 

.27 

15.61 

13.61 

12.06 

10.81 

9.79 

8.93 

8.21 

7.58 

7.04 

6.57 

6.15 

A,h 

Log.      •" 

.261 

1.193 

1.133 

1.081 

1.033 

0.990 

0.950 

0.914 

0.879 

0.847 

0.817 

0.788 

Log. 

74 

40 

86 

35 

83 

78 

85 

34 

67 

57 

57 

88 

Limit 

9 

10 

11 

13 

14 

15 

16 

17 

18 

19 

20 

21 

Min- 
utes 

Merid- 
ian 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

.  73° 

Alti- 
tudes 

Latitude  6°  Decimation  bame  Name. 
Declinations. 


35 


Hour 
Angles 


Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


24°   25= 


1  32 
6  10 
13  51 
24  37 
38  28 
55  23 
75  24 


Log. 


Limit 


Merid- 
ian 


5.77 


1  27 
5  49 
13  04 
23  12 
36  16 
52  13 
71  05 


26° 


27° 


0.761 
18 


22 


72° 


5.44 


0.735 
60 


23 


1  22 
5  28 
12  18 
2154 
34  12 
49  15 
67  02 


5.13 


0.710 
12 


1  18 
5  11 
11  40 
20  44 
32  24 
46  40 
63  30 
82  56 


28° 


1  14 
4  54 
11  02 
19  38 
30  40 
44  10 
60  06 
78  30 


4.86 


24 


71°   70° 


0.686 
64 


25 


69° 


29° 


1  10 
4  40 
10  29 
18  39 
29  08 
41  57 
57  06 
74  34 


30° 


31° 


4.60 


0.662 
76 


26 


68° 


4.37 


0.640 

48 


27 


67° 


107 
4  26 
9  59 
17  45 
27  44 
39  57 
54  21 
70  59 


1  03 
4  13 
9  31 
16  53 
26  24 
38  01 
51  45 
67  35 


4.16 


0.619 
09 


28 


66° 


3.96 


0.597 
70 


29 


65° 


32° 

t     II 

1  00 
4  02 
9  05 
16  07 
25  12 
36  17 
49  24 
64  31 


33° 


0  58 
3  51 
8  39 
15  25 
24  04 
34  40| 
47  10 
61  36| 
77  59 


34° 


3.78 


0.577 
49 


30 


64° 


3.61 


0.557 
51 


31   32 


0  55 
3  41 
8  17 
14  43 
23  00 
33  07 
45  05 
58  53 
74  31 
92  00 


35° 


3.45 


0.537 

82 


63°   62° 


0  53 
3  31 
7  55 
14  05 
22  00 
31  41 
43  07 
56  19 
71  17 
88  00 


3.30 


0.518 
51 


34 


61° 


12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 
Log. 


Min- 
utes 


Alti- 
tudes 


Declin.vtions. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1       II 

1      II 

/      II 

1      II 

1     II 

1      II 

/      II 

/      // 

1     II 

1     II 

1     II 

1     II 

Min. 

4 

0  51 

0  48 

0  46 

0  44 

0  43 

0  41 

0  39 

0  38 

0  36 

0  35 

0  34 

0  32 

4 

8 

3  22 

3  14 

3  05 

2  59 

2  51 

2  45 

2  39 

2  32 

2  26 

2  20 

2  15 

2  10 

8 

12 

7  35 

7  16 

6  58 

6  42 

6  26 

6  10 

5  56 

5  41 

5  29 

5  15 

5  03 

4  52 

12 

16 

13  29 

12  56 

12  22 

1154 

1126 

10  58 

10  32 

10  07 

9  43 

9  21 

9  01 

8  40 

16 

20 

2104 

20  12 

19  20 

18  36 

17  52 

17  08 

16  28 

15  48 

15  12 

14  36 

14  04 

13  32 

20 

24 

30  21 

29  05 

27  50 

26  47 

25  44 

24  40 

23  42 

22  45 

2153 

2102 

20  16 

19  29 

24 

28 

41  17 

39  36 

37  54 

36  28 

35  01 

33  35 

32  17 

30  58 

29  48 

28  37 

27  34 

26  32 

28 

32 

53  55 

51  43 

49  30 

47  37 

45  44 

43  52 

42  10 

40  27 

38  55 

37  22 

36  00 

34  39 

32 

36 

68  16 

65  27 

62  38 

60  16 

57  54 

55  31 

53  21 

51  12 

49  15 

47  19 

45  35 

43  51 

36 

40 

84  16 

80  48 

77  20 

74  24 

7128 

68  32 

65  52 

63  12 

60  48 

58  24 

56  16 

54  08 

40 

44 

86  29 

82  56 

79  42 

76  39 

73  34 

70  40 

68  05 

65  30 

44 

48 

94  51 

9100 

87  33 

84  05 

8101 

77  57 

48 

52 

106  48 

102  45 

98  41 

95  05 

91  29 

52 

56 

56 

60 

60 

II 

n 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

A,h 

3.16 

3.03 

2.90 

2.79 

2.68 

2.57 

2.47 

2.37 

2.28 

2.19 

2.11 

2.03 

A,h 

Log. 

0.499 

0.481 

0.462 

0.445 

0.428 

0.409 

0.392 

0.374 

0.357 

0.340 

0.324 

0.307 

69 

44 

40 

60 

13 

93 

70 

75 

93 

44 

28 

50 

Log. 

Limit 

35 

36 

37 

38 

39 

40 

41 

42 

43 

43 

44 

45 

Min- 
utes 

Merid- 
ian 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

36 


Latitude  6°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 


48°      49° 


0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

101  51 


1.95 


0.290 
03 


46 


48° 


0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

98  15 

112  48 

n 

1.88 


50° 


0.274 
16 


47 


47° 


0  29 

156 

4  20 

7  44 

12  04 

17  23 

23  39 

30  53 

39  06 

48  16 

58  24 

69  30 

81  34 

94  36 

108  36 

n 

1.81 


51° 


0.257 
68 


48 


46° 


0  28 

152 

4  11 

7  25 

11  36 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

104  24 

n 

1.74 


52° 


0.240 
55 


49 


45° 


0  27 

147 

4  00 

7  08 

11  08 

16  02 

2149 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

n 

1.67 


53° 


0.222 

72 


51 


44° 


0  26 

1  42 
3  51 
6  53 

10  44 
15  28 
21  02 
27  28 
34  47 
42  56 
51  57 
61  49 
72  33 
84  09 
96  36 

1.61 


54°      55°      56 


0.206 
83 


53 


43° 


0  25 

1  39 
3  42 
6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

0.187 

52 


54 


42° 


0  23 

1  35 
3  34 
6  18 
9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 


0.170 
26 


55 


41° 


0  22 

1  32 
3  24 
6  06 
9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

0.155 

34 


57° 


56 


40° 


0  22 

1  28 
3  17 
5  51 
9  08 

13  09 
17  54 
23  23 
29  36 
36  32 
44  13 
52  36 
61  44 
71  37 
82  12 

1.37 


58° 


0.136 
72 


57 


39° 


0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 
II 

1.31 


59° 


0.117 
27 


59 


38° 


0  20 

1  21 
3  02 
5  22 
8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
II 

1.26 


Hour 
Angles 


0.100 
37 


61 


37° 


Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Min- 
utes 


Alti- 
tudes 


Deci>inations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

I       II 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

1      II 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

II 

1.16 

1      II 

0  18 

1  11 

2  39 

4  45 

7  24 

10  40 

14  30 

18  56 

23  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 
II 

1.11 

1     II 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
II 

1.06 

1     II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 

1     II 

0  15 

1  01 

2  19 
4  05 
6  24 
9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 
II 

0.96 

t      II 
0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 
15  42 
19  52 
24  32 
29  41 
35  20 
41  28 
48  05 

55  12 

II 

0.92 

I  II 
0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

II  22 

14  51 

18  48 

23  12 

2805 

33  24 

39  12 

45  29 

52  12 
II 

0.87 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 
14  10 
17  56 
22  08 
26  47 
3152 
37  24 
43  23 
49  48 

0.83 

1     II 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 

II 

0.79 

0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12-^8 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 
II 

0.74 

/      // 

OU 

0  44 

1  39 

2  57 
4  36 
6  38 
9  01 

1146 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

4124 
II 

0.69 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.082 
79 

0.064 
46 

0.045 
32 

0.025 
31 

0.004 
32 

9.982 
27 

9.963 
79 

9.939 
52 

9.919 
08 

9.897 
63 

9.869 
23 

9.838 
85 

Log. 

Limit 

63 

65 

67 

69 

71 

73 

75 

77 

79 

81 

83 

85 

Min- 
utes 

Merid- 
ian 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

Alti- 
tudes 

Latitude  6°  Declination  Contrary  Name. 


37 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 
/            II 

145 
7  00 
15  45 
27  59 
43  44 
62  59 

n 

6.56 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

4  59 
19  55 

n 

18.68 

4 
17 
38 

II 
16.0 

16 
04 

27 

2 

1 

3 
14 
33 

II 
14.0 

44 
57 
39 

2 

1        n 

3  19 
13  19 
29  56 
53  12 

II 
12.47 

2 
11 
26 
47 

II 
11.2 

// 

59 
57 
56 
52 

2 

1 

2 

10 
24 
43 

II 
10.2 

n 

43 
53 
29 
31 

O 

2 
10 
22 
40 

II 
9.3 

// 

30 
01 
32 
04 

9 

/     II 

2  18 

9  11 

20  41 

36  47 

57  28 

II 
8.62 

1     II 

2  07 

8  31 

19  11 

34  05 

53  16 

II 
7.99 

/     // 

1  59 

7  57 

17  53 

31  47 

49  40 

II 
7.45 

/       // 

151 

7  26 

16  46 

29  46 

46  32 

n 

6.98 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.271 
38 

1.204 
66 

1.146 

75 

1.095 

87 

1.049 
99 

1.008 
60 

0.972 
67 

0.935 
51 

0.902 
55 

0.872 
16 

0.843 
86 

0.816 
90 

Log. 

Limit 

8 

9 

10 

11 

12 

14 

15 

16 

17 

18 

19 

20 

Min- 
utes 

Merid- 
ian 

84° 

83' 

) 

82< 

3 

81° 

80 

3 

79 

3 

78 

D 

77 

D 

76 

3 

75 

3 

74 

3 

73° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

1     II 

1      II 

1     II 

/      // 

/      // 

1     II 

1     II 

1      II 

1      II 

/      // 

/      // 

Min. 

4 

1  39 

134 

129 

124 

120 

1  16 

1  13 

1  10 

107 

1  04 

102 

0  59 

4 

8 

6  35 

6  14 

5  55 

5  37 

5  21 

5  06 

4  53 

4  40 

4  28 

4  17 

4  07 

3  58 

8 

12 

14  50 

14  01 

13  18 

12  38 

12  01 

11  29 

10  58 

10  29 

10  03 

9  39 

9  16 

8  54 

12 

16 

26  22 

24  55 

23  38 

22  26 

21  23 

20  23 

19  30 

18  39 

17  53 

17  09 

16  28 

15  50 

16 

20 

41  12 

38  56 

36  56 

35  04 

33  24 

3152 

30  28 

29  08 

27  56 

26  48 

25  44 

24  44 

20 

24 

59  20 

56  04 

53  11 

50  30 

48  06 

45  53 

43  52 

4157 

40  14 

38  36 

37  04 

35  37 

24 

28 

80  45 

76  18 

72  23 

68  44 

65  28 

62  26 

59  43 

57  06 

54  45 

52  32 

50  26 

48  29 

28 

32 

81  35 

78  00 

74  34 

7130 

68  36 

65  52 

63  19 

32 

36 

80  08 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

n 

II 

// 

II 

II 

A,h 

6.18 

5.84 

5.54 

5.26 

5.01 

4.78 

4.57 

4.37 

4.19 

4.02 

3.86 

3.71 

A,h 

Log. 

0.790 

0.766 

0.743 

0.720 

0.699 

0.679 

0.659 

0.040 

0.622 

0.604 

0.586 

0.569 

Log. 

99 

41 

51 

99 

84 

43 

92 

48 

21 

23 

59 

37 

Limit 

21 

22 

23 

24 

24 

25 

26 

27 

28 

29 

30 

31 

Min- 
utes 

Merid- 
ian 

72° 

71 

0 

70 

o 

69° 

68 

0 

67 

0 

66 

0 

65 

0 

64 

0 

63 

0 

62 

0 

61° 

Alti- 
tudes 

38 


Latitude  6°  Decimation  Contrary  Name. 


Declination* 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35= 

Hour 
Angles 

Min. 

'   " 

t        n 

'  " 

/  // 

/  // 

I     II 

1     II 

/  // 

1     II 

/   // 

1     II 

/   // 

Min. 

4 

0  57 

0  55 

0  53 

0  51 

0  49 

0  47 

0  46 

0  44 

0  43 

0  42 

0  40 

0  39 

4 

8 

3  49 

3  41 

3  32 

3  24 

3  17 

3  10 

3  04 

2  58 

2  52 

2  46 

2  41 

2  37 

8 

12 

8  34 

8  16 

7  56 

7  39 

7  24 

7  10 

6  55 

6  41 

6  27 

6  14 

6  03 

5  52 

12 

16 

15  14 

14  40 

14  08 

13  37 

13  08 

12  42 

12  17 

11  51 

11  29 

1106 

10  45 

10  24 

16 

20 

23  48 

22  56 

22  04 

21  16 

20  32 

19  52 

19  12 

18  32 

17  56 

17  20 

16  48 

16  16 

20 

24 

34  16 

33  01 

31  47 

30  38 

29  34 

28  36 

27  39 

26  41 

25  50 

24  58 

24  12 

23  25 

24 

28 

46  39 

44  57 

43  15 

4141 

40  15 

38  57 

37  38 

36  20 

35  09 

33  58 

32  56 

31  53 

28 

32 

60  56 

58  43 

56  29 

54  26 

52  34 

50  52 

49  09 

47  27 

45  54 

44  22 

43  00 

41  39 

32 

36 

77  07 

74  18 

7130 

68  55 

66  32 

64  22 

62  13 

60  03 

58  07 

56  10 

54  26 

52  42 

36 

40 

9144 

88  16 

85  04 

82  08 

79  28 

76  48 

74  08 

7144 

69  20 

67  12 

65  04 

40 

44 

86  48 

83  54 

81  19 

78  43 

44 

48 

93  42 

48 

52 

52 

56 

56 

60 

60 

/■/ 

It 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.57 

3.44 

3.31 

3.19 

3.08 

2.98 

2.88 

2.78 

2.69 

2.60 

2.52 

2.44 

A,h 

Log. 

0.552 

0.536 

0.519 

0.503 

0.488 

0.474 

0.459 

0.444 

0.429 

0.414 

0.401 

0.387 

Log. 

67 

56 

83 

79 

55 

22 
37 

39 

04 

75 

97 

40 

39 

Limit 

32 

33 

34 

35 

36 

38 

38 

39 

40 

41 

42 

Min- 
utes 

Merid- 
ian 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   // 

0  38 

2  31 

5  40 

10  04 

15  44 

22  40 

30  50 

40  16 

50  59 

62  56 

76  09 

90  37 

106  21 

// 
2.36 

/  II 

0  36 

2  27 

5  30 

9  46 

15  16 

21  59 

29  56 

39  05 

49  28 

61  04 

73  53 

87  56 

103  12 

II 
2.29 

1     II 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

71  38 

85  15 

100  03 

II 
2.22 

/   // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

/  // 

0  33 

2  13 

5  00 

8  52 

13  52 

19  58 

27  11 

35  30 

44  56 

55  28 

67  07 

79  52 

93  44 

II 
2.08 

1      II 

0  32 

2  09 

4  49 

8  35 

13  24 

19  18 

26  16 

34  18 

43  25 

53  36 

64  51 

77  11 

90  35 

105  03 

// 
2.01 

1      II 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

101  55 

II 
1.95 

1      II 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 
II 

1.89 

1     II 

0  29 

1  57 
4  23 
7  49 

12  12 
17  34 
23  55 
31  13 
39  32 
48  48 
59  03 
70  16 
82  28 
95  39 

109  48 
II 

1.83 

0  28 

1  54 
4  17 
7  35 

11  52 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 
II 

1.78 

I  II 

0  27 
150 
4  08 
7  20 

II  28 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 
II 

1.72 

I  II 

0  27 

1  47 
4  00 
7  08 

II  08 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 
// 

1.67 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.372 
91 

0.359 
84 

0.346 
35 

0.332 
44 

0.318 
06 

0.303 
20 

0.290 
03 

0.276 
46 

0.262 
45 

0.250 
42 

0.235 
53 

0.222 
72 

Log. 

Limit 

42 

43 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

Min- 
utes 

Merid- 
ian 

48°  i  47°  1  46°  i  45° 

44° 

43°  !  42° 

41° 

40° 

39° 

38° 

Q70   Alti- 
"* '   tudes 

Latitude  6°  Declination  Contrary  Name. 
Declinations. 


39 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

,   // 

/  II 

1     II 

1      II 

1      II 

/  // 

1     II 

1     II 

t     II 

1     II 

1     II 

t     II 

Min. 

4 

0  26 

0  25 

0  24 

0  23 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

0  19 

0  18 

4 

8 

143 

1  40 

1  36 

1  34 

131 

128 

124 

122 

120 

1  16 

1  13 

1  11 

8 

12 

3  53 

3  45 

3  37 

3  31 

3  25 

3  17 

3  10 

3  05 

2  59 

2  51 

2  45 

2  39 

12 

16 

6  55 

6  39 

6  27 

6  13 

6  03 

5  51 

5  38 

5  27 

5  17 

5  05 

4  55 

4  45 

16 

20 

10  48 

10  24 

10  04 

9  44 

9  28 

9  08 

8  48 

8  32 

8  16 

7  56 

7  40 

7  24 

20 

24 

15  34 

14  59 

14  30 

14  01 

13  38 

13  09 

12  41 

12  17 

1154 

1126 

1103 

10  40 

24 

28 

21  10 

20  23 

19  44 

19  05 

18  34 

17  54 

17  15 

16  44 

16  12 

15  33 

15  01 

14  30 

28 

32 

27  38 

26  37 

25  46 

24  55 

24  14 

23  23 

22  31 

2151 

21  10 

20  18 

19  37 

18  56 

32 

36 

35  00 

33  42 

32  37 

31  32 

30  40 

29  36 

28  31 

27  39 

26  47 

25  43 

24  51 

23  59 

36 

40 

43  12 

4136 

40  16 

38  56 

37  52 

36  32 

35  12 

34  08 

33  04 

3144 

30  40 

29  36 

40 

44 

52  17 

50  20 

48  43 

47  06 

45  49 

44  13 

42  36 

41  18 

40  00 

38  24 

37  07 

35  49 

44 

48 

62  12 

59  54 

57  59 

56  04 

54  32 

52  36 

50  41 

49  09 

47  37 

45  41 

44  09 

42  37 

48 

52 

73  00 

70  18 

68  03 

65  48 

64  00 

61  44 

59  29 

57  41 

55  53 

53  37 

51  49 

50  01 

52 

56 

84  41 

8132 

78  55 

76  18 

74  13 

71  37 

69  00 

66  54 

64  48 

62  12 

60  07 

58  01 

56 

60 

97  12 

93  36 

90  36 

87  36 

85  12 

82  12 

79  12 

76  48 

74  24 

7124 

69  00 

66  36 

60 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.62 

1.56 

1.51 

1.46 

1.42 

1.37 

1.32 

1.28 

1.24 

1.19 

1.15 

1.11 

A,h 

Log. 

0.209 

0.193 

0.178 

0.164 

0.152 

0.136 

0.120 

0.107 

0.093 

0.075 

0.060 

0.045 

Log. 

52 

12 

98 

35 

29 

72 

57 

21 

42 

55 

70 

32 

Limit 

53 

55 

56 

57 

58 

60 

62 

64 

65 

67 

69 

71 

Min- 
utes 

Merid- 
ian 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1     II 

/  II 

1      II 

/  II 

1      II 

1      II 

1      II 

1      It 

1      II 

1     II 

/  // 

1      II 

Min. 

4 

0  17 

0  16 

0  15 

0  15 

0  14 

0  14 

0  13 

0  13 

0  12 

Oil 

Oil 

Oil 

4 

8 

108 

106 

103 

101 

0  58 

0  55 

0  53 

0  51 

0  49 

0  46 

0  44 

0  42 

8 

12 

2  34 

2  28 

2  23 

2  17 

2  11 

2  05 

159 

155 

150 

144 

1  39 

1  35 

12 

16 

4  34 

4  24 

4  13 

4  03 

3  53 

3  43 

3  33 

3  25 

3  14 

3  04 

2  57 

2  49 

16 

20 

7  08 

6  52 

6  36 

6  20 

6  04 

5  48 

5  32 

5  20 

5  04 

4  48 

4  36 

4  24 

20 

24 

10  16 

9  53 

9  30 

9  07 

8  44 

8  21 

7  58 

7  41 

7  18 

6  55 

6  38 

6  21 

24 

28 

13  59 

13  28 

12  57 

12  25 

1154 

11  22 

10  51 

10  27 

9  56 

9  25 

9  01 

8  37 

28 

32 

18  16 

17  35 

16  54 

16  13 

15  32 

14  51 

14  10 

13  39 

12  58 

12  17 

1146 

11  15 

32 

36 

23  07 

22  15 

2123 

20  31 

19  39 

18  48 

17  56 

17  17 

16  25 

15  33 

14  55 

14  16 

36 

40 

28  32 

27  28 

26  24 

25  20 

24  16 

23  12 

22  08 

2120 

20  16 

19  12 

18  24 

17  36 

40 

44 

34  32 

33  14 

3156 

30  39 

29  21 

28  05 

26  47 

25  49 

24  31 

23  14 

22  16 

21  18 

44 

48 

4105 

39  33 

38  01 

36  29 

34  57 

33  24 

3152 

30  43 

29  09 

27  37 

26  29 

25  20 

48 

52 

48  13 

46  25 

44  37 

42  49 

4101 

39  12 

37  24 

36  03 

34  15 

32  27 

31  05 

29  44 

52 

56 

55  56 

53  50 

51  44 

49  39 

47  33 

45  29 

43  23 

41  49 

39  43 

37  38 

36  04 

34  30 

56 

60 

64  12 

61  48 

59  24 

57  00 

54  36 

52  12 

49  48 

48  00 

45  36 

43  12 

4124 

39  36 

60 

II 

II 

II 

II 

II 

II 

II 

II 

If 

II 

II 

II 

Ajh 

1.07 

1.03 

0.99 

0.95 

0.91 

0.87 

0.83 

0.80 

0.76 

0.72 

0.69 

0.66 

A,h 

Log. 

0.029 

0.012 

9.995 

9.977 

9.959 

9.939 

9.919 

9.903 

9.880 

9.857 

9.838 

9.819 

Log. 

38 

84 

64 

72 

04 

52 

08 

09 

81 

33 

85 

54 

Limit 

72 

74 

75 

76 

77 

79 

81 

83 

85 

87 

90 

93 

:Min- 
utes 

Merid- 
ian 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

Alti- 
tudes 

40 


Latitude  7°  Decimation  Same  Name. 


DlXLI.N 

A!l()\ 

Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

T 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min.      ' 

II 

1     II 

/        n 

/     // 

1     II 

/      // 

/     // 

1 

//    /     II 

/     // 

;       // 

/     II 

Min. 

4 

4  16 

4  59 

5  58 

4 

8        1 

7  03 

19  53 

23  50 

8 

12        3 

8  23 

12 

16 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

11 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h    15 

.99 

18.64 

22.35 

A,h 

1 
Log. 

.203 
85 

1.270 
45 

1.349 

28 

Log. 

Limit 

9 

8 

7 

5 

4 

3 

1 

0 

1 

3 

5 

7 

Min- 
utes 

Merid-      i 
ian          * 

53° 

84° 

85° 

86° 

87° 

88° 

89° 

90< 

"      89° 

88° 

87° 

86° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      II 

1     II 

/      II 

1     II 

/      // 

/      // 

/      // 

1     II 

1       n 

/      // 

/        n 

/      II 

Min. 

4 

5  50 

4  51 

4  08 

3  37 

3  12 

2  51 

2  35 

2  22 

2  10 

2  00 

151 

1  44 

4 

8 

23  20 

19  23 

16  33 

14  26 

12  47 

1127 

10  22 

9  27 

8  41 

8  01 

7  26 

6  57 

8 

12 

37  15 

32  28 

28  45 

25  45 

23  18 

21  16 

19  32 

18  03 

16  46 

15  37 

12 

16 

45  47 

4126 

37  48 

34  44 

32  05 

29  46 

27  47 

16 

20 

54  16 

50  08 

46  32 

43  24 

20 

24 

62  30 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

ff 

II 

II 

II 

II 

II 

II 

II 

II 

II 

» 

II 

A,h 

21.87 

18.17 

15.52 

13.53 

11.98 

10.73 

9.71 

8.86 

8.14 

7.52 

6.98 

6.51 

A,h 

Log. 

1.339 

1.259 

1.190 

1.131 

1.078 

1.030 

0.987 

0.947 

0.910 

0.876 

0.843 

0.813 

Log. 

85 

35 

89 

30 

46 

60 

22 

43 

62 

22 

86 

58 

Limit 

9 

10 

11 

12 

13 

14 

15 

16 

18 

19 

20 

21 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

Latitude  7°  Declination  Same  Name* 


41 


Declinations. 


Hour      f 
Angles     ^ 

}4° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min.      ' 

// 

/      II 

/      II 

1      II 

/      // 

1      II 

/      *■ 

1      II 

1      " 

/      // 

/      // 

/      // 

Min. 

4 

1  37 

1  31 

126 

121 

1  17 

1  13 

109 

106 

102 

0  59 

0  57 

0  54 

4 

8 

6  30 

6  06 

5  44 

5  25 

5  07 

4  51 

4  36 

4  23 

4  10 

4  00 

3  48 

3  38 

8 

12        1 

4  37 

13  44 

12  55 

12  12 

11  31 

10  55 

10  22 

9  51 

9  23 

8  57 

8  33 

8  10 

12 

16        2 

5  59 

24  24 

22  57 

21  40 

20  39 

19  25 

18  26 

17  33 

16  41 

15  55 

15  11 

14  30 

16 

.   20        4 

0  36 

38  08 

35  52 

33  52 

32  00 

30  20 

28  48 

27  24 

26  04 

24  52 

23  44 

22  40 

20 

24       5 

8  28 

54  55 

51  39 

48  46 

46  05 

43  41 

41  29 

39  28 

37  32 

35  48 

34  11 

32  38 

24 

28       7 

9  35 

74  45 

70  18 

66  23 

62  43 

59  27 

56  27 

53  42 

5106 

48  45 

46  31 

44  26 

28 

32 

8155 

77  39 

73  43 

70  08 

66  44 

63  40 

60  45 

58  02 

32 

36 

76  54 

73  26 

36 

40 

90  40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h      6 

.09 

5.72 

5.38 

5.08 

4.80 

4.55 

4.32 

4.11 

3.91 

3.73 

3.56 

3.40 

A,h 

Log.      0 

.784 

0.757 

0.730 

0.705 

0.681 

0.658 

0.635 

0.613 

0.592 

0.571 

0.551 

0.531 

Log. 

62 

40 

78 

86 

24 

01 

48 

84 

18 

71 

45 

48 

Limit 

22 

22 

23 

24 

25 

26 

28 

29 

30 

31 

32 

33 

Min- 
utes 

Merid-      r 
iau 

?3° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

1       II 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

/      // 

/      II 

1      II 

r       II 

1      II 

1     II 

1      II 

1      II 

1      II 

1      II 

1     II 

Min. 

4 

0  52 

0  50 

0  47 

0  46 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

■    0  35 

0  33 

4 

8 

3  28 

3  19 

3  10 

3  03 

2  56 

2  48 

2  42 

2  35 

2  29 

2  24 

2  17 

2  13 

8 

12 

7  48 

7  27 

7  10 

6  52 

6  35 

6  18 

6  04 

5  49 

5  35 

5  23 

5  09 

4  58 

12 

16 

13  52 

13  17 

12  42 

12  12 

1141 

11  14 

10  48 

10  19 

9  57 

9  33 

9  11 

8  50 

16 

20 

21  40 

20  44 

19  52 

19  04 

18  16 

17  32 

16  52 

16  08 

15  32 

14  56 

14  20 

13  48 

20 

24 

31  12 

29  52 

28  36 

27  28 

26  18 

25  15 

24  17 

23  14 

22  22 

2130 

20  39 

19  52 

24 

28 

42  28 

40  38 

38  57 

37  22 

35  48 

34  22 

33  04 

31  38 

30  27 

29  16 

28  05 

27  03 

28 

32 

55  28 

53  04 

50  52 

48  48 

46  46 

44  53 

43  11 

41  18 

39  46 

38  14 

36  41 

35  20 

32 

36 

70  12 

67  11 

64  22 

61  47 

59  11 

56  49 

54  39 

52  16 

50  20 

48  23 

46  27 

44  43 

36 

40 

86  40 

82  56 

79  28 

76  16 

73  04 

70  08 

67  28 

64  32 

62  08 

59  44 

57  20 

55  12 

40 

44 

88  24 

84  52 

8138 

78  05 

75  11 

72  16 

69  23 

66  48 

44 

48 

92  56 

89  28 

86  01 

82  33 

79  29 

48 

52 

105  00 

100  57 

96  53 

93  17 

52 

56 

56 

60 

60 

'/ 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.25 

3.11 

2.98 

2.86 

2.74 

2.63 

2.53 

2.42 

2.33 

2.24 

2.15 

2.07 

Ajh 

Log. 

0.511 

0.492 

0.474 

0.456 

0.437 

0.419 

0.403 

0.383 

0.367 

0.350 

0.332 

0.315 

Log. 

88 

76 

22 

37 

75 

96 

12 

82 

36 

25 

44 

97 

Limit 

34 

35 

36 

37 

38 

39 

40 

41 

42 

42 

43 

44 

Min- 
utes 

Merid- 
ian 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

Alti- 
tudes 

42 


Latitude  T  Decimation  Same  Name. 


Jkcli.matio.n 

>^. 

Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

CQO  ,  Hour 
^^      1  Angles 

Miu. 

1       n 

1      II 

1     II 

1      II 

/  II 

1     II 

/   // 

/   // 

/   // 

1      II 

/   // 

/   // 

Min. 

4 

0  31 

0  30 

0  30 

0  28 

0  27 

0  26 

0  25 

0  24 

0  22 

0  22 

0  21 

0  20 

4 

8 

2  07 

2  02 

1  58 

1  54 

1  49 

1  44 

1  41 

1  36 

1  33 

1  29 

1  25 

121 

8 

12 

4  47 

4  35 

4  25 

4  16 

4  05 

3  54 

3  46 

3  36 

3  28 

3  20 

3  11 

3  03 

12 

16 

8  29 

8  09 

7  51 

7  33 

7  15 

6  58 

6  42 

6  24 

6  08 

5  56 

5  41 

5  25   16 

20 

13  16 

12  44 

12  16 

11  48 

11  20 

10  52 

10  28 

10  00 

9  36 

9  16 

8  52 

8  28;  20 

24 

19  06 

18  20 

17  40 

16  59 

16  19 

15  39 

15  04 

14  24 

13  49 

13  21 

12  46 

12  111  24 

28  . 

26  01 

24  58 

24  02 

23  08 

22  13 

21  18 

20  31 

19  36 

18  49 

18  10 

17  23 

16  36  28 

32 

33  58 

32  36 

31  24 

30  13 

29  01 

27  49 

26  48 

25  36 

24  35 

23  43 

22  42 

21  4l!  32 

36 

42  59 

41  15 

39  45 

38  14 

36  43 

35  13 

33  55 

32  24 

31  06 

30  02 

28  44 

27  26|  36 

40 

53  04 

50  56 

49  04 

47  12 

45  20 

43  28 

4152 

40  00 

38  24 

37  04 

35  28 

33  52 

40 

44 

64  12 

61  37 

59  22 

57  07 

54  51 

52  36 

50  40 

48  24 

46  27 

44  51 

42  55 

40  59 

44 

48 

76  25 

73  21 

70  39 

67  56 

65  15 

62  35 

60  17 

57  36 

55  18 

53  22 

51  04 

48  46 1  48 

52 

89  41 

86  05 

82  55 

79  46 

76  37 

73  27 

70  45 

67  36 

64  54 

62  38 

59  56 

57  14  52 

56 

104  01 

99  49 

96  10 

92  31 

88  51 

85  12 

82  04 

78  24 

75  15 

72  39 

69  31 

66  23  56 

60 

119  24 

114  36 

110  24 

106  12 

102  00 

97  48 

94  12 

90  00 

86  24 

83  24 

79  48 

76  12  60 

II 

1/ 

II 

II 

II 

II 

// 

II 

II 

II 

" 

II 

Aih 

1.99 

1.91 

1.84 

1.77 

1.70 

1.63 

1.57 

1.50 

1.44 

1.39 

1.33 

1.27 

A,h 

Log. 

0.298 

0.281 

0.264 

0.247 

0.230 

0.212 

0.195 

0.176 

0.158 

0.143 

0.123 

0.103 

Log. 

85 

03 

82 

97 

45 

19 

90 

09 

36 

01 

85 

80 

Limit 

45 

46 

47 

48 

50 

52 

53 

54 

55 

56 

58 

60 

Min- 
utes 

Merid- 
ian 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Qoo   Alti- 
"^"   tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

.1.22 

I  II 

0  19 

1  15 

2  48 
5  00 
7  48 

II  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

II 

1.17 

1     II 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 
II 

1.12 

1     II 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 

II 

1.07 

1     II 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
II 

1.02 

/  // 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

II 

0.97 

/  // 
0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 
15  42 
19  52 
24  32 
29  41 
35  20 
41  28 
48  05 
55  12 
II 

0.92 

/  II 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

II 

0.87 

/  II 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 

II 

0.79 

1      II 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
II 

0.75 

1     II 

Oil 

0  45 

1  42 

3  02 

4  44 
6  49 
9  17 

12  07 

15  20 

18  56 

22  54 

27  14 

32  00 

37  06 

42  36 
II 

0.71 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.086 
36 

0.068 
19 

0.049 
22 

0.029 
38 

0.008 
60 

9.986 
77 

9.963 
79 

9.939 
52 

9.919 
08 

9.897 
63 

9.875 
06 

9.851 
26 

Log. 

Limit 

62 

64 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

Latitude  7°  Declination  Gintrafy  Name. 


43 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

4 
17 
38 

n 

15.9 

16 
03 
23 

9 

/        n 

3  44 
14  56 
33  36 

n 

14.00 

3 
13 
29 

n 

12.4 

// 

19 
17 
53 

5 

t 

2 
11 
26 

n 

11.2 

n 

59 
57 
54 

1 

1 

2 
10 
24 
43 

II 
10.1 

43 
52 
27 
29 

9 

1 

2 
9 

22 
39 

II 
9.3 

// 

29 
58 
25 
51 

4 

1 

2 

9 

20 
36 
57 

II 
8.6 

// 

18 
11 
41 
47 
28 

2 

1 

2 

8 
19 
34 
53 

n 

8.0 

// 

08 
32 
12 
08 
20 

0 

/      II 

159 

7  58 
17  55 
31  49 
49  44 

II 
7.46 

/      II 

151 

7  26 

16  46 

29  46 

46  32 

. 

n 

6.98 

/     // 

145 
7  00 
15  45 
27  59 
43  44 
62  59 

It 
6.56 

/     // 

139 
6  36 
14  51 
26  25 
41  16 
59  26 
80  53 

II 
6.19 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.203 
85 

1.146 
13 

1.095 
17 

1.049 
61 

1.008 
17 

0.970 
35 

0.935 
51 

0.903 
09 

0.872 
74 

0.843 
86 

0.816 
90 

0.791 
69 

Log. 

Limit 

9         11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

Min- 
utes 

Merid- 
ian    1 

83°      82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22°  1   23° 

Hour 

Angles 

Min. 

t       n 

/        n 

/      II 

1      II 

'      " 

1      II 

1     II 

1     II 

/      // 

1     II 

1     II 

1     II 

Min. 

4 

134 

129 

124 

120 

1  16 

1  13 

1  10 

107 

104 

1  02 

0  59 

0  57 

4 

8 

6  15 

5  55 

5  38 

5  22 

5  07 

4  53 

4  41 

4  29 

4  18 

4  08 

4  00 

3  50 

8 

12 

14  04 

13  19 

12  41 

12  04 

11  30 

11  00 

10  32 

10  05 

9  40 

9  19 

8  57 

8  37 

12 

16 

25  00 

23  41 

22  31 

21  28 

20  26 

19  32 

18  44 

17  55 

17  12 

16  33 

15  55 

15  19 

16 

20 

39  04 

37  00 

35  12 

33  32 

31  56 

30  32 

29  16 

28  00 

26  52 

25  52 

24  52 

23  56 

20 

24 

56  16 

53  17 

50  41 

48  17 

45  59 

43  58 

42  09 

40  19 

38  41 

37  15 

35  48 

34  28 

24 

28 

76  34 

72  31 

69  00 

65  44 

62  34 

59  51 

57  22 

54  53 

52  40 

50  42 

48  45 

46  55 

28 

32 

81  45 

78  10 

74  55 

71  41 

68  47 

66  13 

63  40 

61  16 

32 

36 

77  33 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

" 

II 

II 

II 

II 

II 

II 

// 

II 

A,h 

5.86 

5.55 

5.28 

5.03 

4.79 

4.58 

4.39 

4.20 

4.03 

3.88 

3.73 

3.59 

A,h 

Log. 

0.767 

0.744 

0.722 

0.701 

0.680 

0.660 

0.642 

0.623 

0.605 

0.588 

0.571 

0.555 

90 

29 

63 

57 

34 

87 

46 

25 

31 

83 

71 

09 

Log. 

Limit 

22 

23 

24 

24 

25 

26 

27 

28 

29 

30 

31 

32 

Min- 
utes 

Merid- 
ian 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

Alti- 
tudes 

44 


Latitude.  7°  Declination  Contrary  Name, 
Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

I  II 

0  43 
2  54 
6  30 

II  34 
18  04 
26  01 
35  25 
46  15 
58  32 
72  16 
87  26 

II 
2.71 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 
2 
3 
4 
5 
7 
9 

0. 
3^ 

8 

4' 

3( 

3 

5 

9 

4 

2 

!.4 

H 

55 
12 
19 
15 
34 
13 
13 
33 
14 
16 

6 

f     II 

0  53 
3  33 
7  59 
14  13 
22  12 
31  58 
43  31 
56  50 
7156 
88  48 

II 
3.33 

1     II 

0  51 
3  26 
7  44 
13  44 
21  28 
30  55 
42  05 
54  57 
69  33 
85  52 

II 
3.22 

0  50 
3  19 
7  27 
13  17 
20  44 
29  52 
40  38 
53  04 
67  11 
82  56 

II 
3.11 

1 

0^ 

3 

7 

12^ 
20  ( 
28' 
39 
51 
64 
80 

II 
3.0 

II 

18 
2 
2 
18 
30 
18 
12 
12 
18 
DO 

0 

1 

0^ 
3( 
6. 

12  5 

19! 

27. 

37 

49 

62 

77 

II 
2.9 

II 

16 
35 
58 
22 
JO 
50 
54 
JO 
38 
20 

0 

I  II 

0  45 
2  59 
6  43 

II  57 
18  40 
26  53 
36  35 
47  47 
60  29 
74  40 

II 
2.80 

/      II 

0  42 

2  48 

6  18 

11  14 

17  32 

25  15 

34  22 

44  53 

56  49 

70  08 

84  52 

II 
2.63 

1     II 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  11 
43  21 
54  52 
67  44 
81  57 

II 
2.54 

1      II 

0  39 
2  38 
5  55 
10  29 
16  24 
23  37 
32  09 
41  59 
53  08 
65  36 
79  22 
94  28 

II 
2.46 

1     II 

0  38 

2  33 

5  44 

10  12 

15  56 

22  57 

31  14 

40  47 

51  38 

63  44 

77  07 

91  46 

107  42 

II 
2.39 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A.,h 

Log. 

0.539 
08 

0.522 

44 

0.507 
86 

0.492 
76 

0.477 
12 

0.462 
40 

0.447 
16 

0.432 
97 

0.419 
96 

0.404 
83 

0.390 
94 

0.378 
40 

Log. 

Limit 

33 

34 

35 

36 

37 

38 

38 

39 

40 

41 

42 

42 

Min- 
utes 

Merid- 
ian 

59° 

58° 

57° 

56°' 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

Declinations. 


Hour 
Angle."! 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

"Hour 
Angles 

Min.  ■ 

1      II 

/      // 

1     II 

/      II 

/      // 

1      II 

/      // 

1     II 

/      // 

/      // 

/      // 

/      // 

Min, 

4 

0  37 

0  36 

0  35 

0  34 

0  33 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

4 

8 

2  28 

2  24 

2  19 

2  15 

2  11 

2  05 

2  02 

159 

1  55 

152 

149 

1  45 

8 

12 

5  32 

5  23 

5  12 

5  03 

4  54 

4  44 

4  37 

4  28 

4  19 

4  12 

4  05 

3  56 

12 

16 

9  52 

9  33 

9  16 

9  01 

8  42 

8  24 

8  11 

7  56 

7  41 

7  28 

7  15 

7  00 

16 

20 

15  24 

14  56 

14  28 

14  04 

13  36 

13  08 

12  48 

12  24 

12  00 

11  40 

11  20 

10  56 

20 

24 

22  11 

2130 

20  50 

20  16 

19  35 

18  54 

18  26 

17  52 

17  17 

16  48 

16  19 

15  45 

24 

28 

30  11 

29  16 

28  21 

27  34 

26  39 

25  45 

25  06 

24  18 

23  31 

22  52 

22  13 

21  25 

28 

32 

39  25 

38  14 

37  02 

36  00 

34  49 

33  38 

32  46 

31  44 

30  43 

29  52 

29  01 

27  59 

32 

36 

49  54 

48  23 

46  53 

45  35 

44  04 

42  33 

4128 

40  11 

38  53 

37  48 

36  43 

35  26 

36 

40 

6136 

59  44 

57  52 

56  16 

54  24 

52  32 

51  12 

49  36 

48  00 

46  40 

45  20 

43  44 

40 

44 

74  32 

72  16 

70  02 

68  05 

65  49 

63  34 

61  57 

60  01 

58  05 

56  28 

54  51 

52  55 

44 

48 

88  42 

86  01 

83  19 

8101 

78  20 

75  39 

73  44 

71  25 

69  07 

67  10 

65  15 

62  58 

48 

52 

104  06 

100  57 

97  47 

95  05 

9156 

88  47 

86  32 

83  49 

81  07 

78  52 

76  37 

73  54 

52 

56 

102  57 

100  21 

97  13 

94  05 

91  28 

88  51 

85  43 

56 

60 

111  36 

108  00 

105  00 

102  00 

98  24 

60 

// 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

A,h 

2.31 

2.24 

2.17 

2.11 

2.04 

1.97 

1.92 

1.86 

1.80 

1.75 

1.70 

1.64 
0.214 

Ajh 

Log. 

0.363 

0.350 

0.336 

0.324 

0.309 

0.294 

0.283 

0.269 

0.255 

0.243 

0.230 

Log. 

61 

25 

46 

28 

63 

47 

30 

51 

27 

04 

45 

84 

Limit 

43 

44 

45 

46 

46 

47 

48 

49 

50 

51 

52 

53 

Min- 
utes 

Merid- 
ian 

47°  1   46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

Alti- 
tudes 

Latitude  7°  Declinatioa  Contrary  Name. 


45 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t      It 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

61  03 

7139 

83  06 

95  24 

1.59 

1        n 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 

n 

1.54 

1     II 

0  23 

1  36 
3  35 
6  21 
9  56 

14  18 

19  29 

25  26 

32  11 

39  44 

48  04 

57  13 

67  09 

77  52 

89  24 
II 

1.49 

1     II 

0  22 

133 

3  28 

6  08 

9  36 

13  49 

18  49 

24  35 

3106 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 

II 

1.44 

t      II 

0  22 
130 
3  23 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

1     II 

0  22 
126 
3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

8100 
II 

1.35 

t     II 

0  21 

1  23 
3  08 
5  36 

8  44 
12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

1.31 

1      II 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
II 

1.26 

1     II 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

I  II 

0  19 

1  15 

2  50 
5  02 
7  52 

II  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 
70  48 

II 

1.18 

1     II 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
5122 
59  35 
68  24 
II 

1.14 

1     II 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
II 

1.10 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Liog. 

0.201 
40 

0.187 
52 

0.173 
19 

0.158 
36 

0.146 
13 

0.130 
33 

0.117 

27 

0.100 
37 

0.086 
36 

0.071 

88 

0.056 
90 

0.041 
39 

Log. 

Limit 

54 

56 

57 

58 

59 

61 

63 

65 

66 

68 

70 

72 

Min- 
utes 

Merid- 
ian 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60°   61° 

62°   63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

/   // 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

II 

1.02 

1     II 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 
II 

0.98 

1      II 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

n 

0.94 

I  II 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

II  46 

15  22 

19  26 

24  00 

29  02 

34  34 

40  34 

47  02 

54  00 
II 

0.90 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 
5136 

It 

0.86 

1     II 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 
14  10 
17  56 
22  08 
26  47 
3152 
37  24 
43  23 

49  48 
It 

0.83 

1      It 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
2120 
25  49 
30  43 
36  03 
4149 
48  00 
It 

0.80 

1      It 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 
It 

0.76 

1     II 

0  11 
0  46 
144 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 

43  12 
11 

0.72 

I  II 

0  11 

0  44 

1  39 

2  57 
4  36 
6  38 
9  01 

II  46 
14  55 
18  24 
22  16 
26  29 
3105 
36  04 
4124 

It 

0.69 

I  II 

Oil 
0  42 
135 
2  49 
4  24 
6  21 
8  37 

II  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 

39  36 
It 

0.66 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.025 
31 

0.008 
60 

9.991 
23 

9.973 
13 

9.954 
24 

9.934 
50 

9.919 
08 

9.903 
09 

83 

9.880 
81 

9.857 
33 

9.838 
85 

9.819 
54 

Log. 

Limit 

73 

75 

76 

77 

78 

80 

82 

85 

87 

90 

93 

Min- 
iites 

Merid- 
ian 

23° 

22° 

21° 

20° 

19° 

18° 

17°  i  16° 

15° 

14° 

13° 

12° 

Alti- 
tudes 

46 


Latitude  8°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0°        1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

1       II     1       n 

/     * 

1       n 

/        ri 

1     II    1 

II     I       HI 

II 

1     II 

/       n 

1       n 

Min. 

4 

3  43     4  15 

4  57 

5  56 

4 

8 

14  54    17  01 

19  50 

23  46 

8 

12 

33  32    38  17 

12 

16 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

II 

n 

II 

1 

1 

n 

II 

1 

f 

II 

n 

II 

// 

A,h 

13.97 

15.95 

18.59 

22.28 

A,h 

Log. 

1.145 
20 

1.202 
76 

1.269 
28 

8 

1.347 
92 

Log. 

Limit 

11 

9 

7 

5 

4 

3 

1 

0 

1 

4 

5 

Min- 
utes 

Merid- 
ian 

82° 

83° 

84° 

85° 

86° 

87° 

38 

°      89° 

90° 

89° 

88° 

87° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13°      14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

t     II 

/           // 

1     II 

1      II 

t     II 

1     II 

1     II 

/      // 

/      // 

1      II 

/      II 

Min. 

4 

5  48 

4  49 

4  06 

3  35 

3  10 

2  51 

2  34 

2  20 

2  09 

159 

150 

4 

8 

23  12 

19  15 

16  27 

14  20 

12  41 

1121 

10  17 

9  23 

8  37 

7  57 

7  22 

8 

12 

36  59 

32  14 

28  32 

25  33 

23  08 

21  06 

19  22 

17  53 

16  37 

12 

16 

45  27 

4108 

37  30 

34  26 

3147 

29  31 

16 

20 

53  48 

49  40 

46  08 

20 

24 

66  26 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

T 

II 

II 

n 

It 

II 

II 

II 

II 

II 

II 

II 

A,h 

21.74 

18.05 

15.41 

13.43 

11.89 

10.65 

9.64 

8.79 

8.07 

7.45 

6.92 

A,h 

Log. 

1.337 

1.256 

1.187 

1.128 

1.075 

1.027 

0.984 

0.943 

0.906 

0.872 

0.840 

Log. 

26 

48 

80 

08 

18 

35 

08 

99 

87 

16 

11 

Limit 

7 

8 

9 

11 

12 

13 

14 

15 

17 

18 

19 

20 

Min- 
utes 

Merid- 
ian 

8 

3° 

85 

3 

84 

3 

83 

0 

82 

3 

51 

3 

80 

0 

79 

0 

78 

0 

77° 

76 

0 

75 

3 

Alti- 
tudes 

Latitude  8°  Declination  Same  Name. 


47 


Declinations. 


Hour       , 
Angles     ' 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min.      ' 

If 

/      // 

/      II 

/      // 

/      // 

1      II 

1      II 

t     II 

r       II 

/      // 

1     II 

/      II 

Min. 

4 

143 

136 

131 

125 

120 

1  16 

1  12 

108 

105 

102 

0  59 

0  56 

4 

8 

6  53 

6  26 

6  02 

5  40 

5  21 

5  04 

4  48 

4  34 

4  19 

4  07 

3  55 

3  45 

8 

12       1 

5  28 

14  28 

13  35 

12  46 

12  03 

11  24 

10  48 

10  15 

9  43 

9  16 

8  50 

8  25 

12 

16       2 

7  28 

25  44 

24  09 

22  42 

21  25 

20  16 

19  12 

18  13 

17  17 

16  28 

15  42 

14  59 

16 

20       4 

2  56 

40  12 

37  44 

35  28 

33  28 

3140 

30  00 

28  28 

27  00 

25  44 

24  32 

23  24 

20 

24       6 

1  49 

57  54 

54  21 

5105 

48  12 

45  36 

43  12 

40  39 

38  53 

37  04 

35  20 

33  42 

24 

28       8 

4  09 

78  48 

73  57 

69  31 

65  36 

62  02 

58  48 

55  48 

52  55 

50  26 

48  05 

45  52 

28 

32 

8104 

76  48 

72  53 

69  07 

65  52 

62  48 

59  54 

32 

36 

79  30 

75  49 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

A,h      € 

.44 

6.03 

5.66 

5.32 

5.02 

4.75 

4.50 

4.27 

4.05 

3.86 

3.68 

3.51 

Ajh 

Log. 

.808 

0.780 

0.752 

0.725 

0.700 

0.676 

0.653 

0.630 

0.607 

0.586 

0.565 

0.545 

Log. 

89 

32 

82 

91 

70 

69 

21 

43 

46 

59 

85 

31 

Limit 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

/       II 

1     II 

1      II 

/      // 

1     II 

/      // 

/      // 

/     // 

/     // 

r       II 

1     II 

1     II 

Min. 

4 

0  54 

0  51 

0  49 

0  46 

0  45 

0  43 

0  41 

0  39 

0  38 

0  36 

0  35 

0  34 

4 

8 

3  34 

3  25 

3  16 

3  07 

3  00 

2  52 

2  45 

2  39 

2  32 

2  26 

2  20 

2  15 

8 

12 

8  02 

7  41 

7  21 

7  02 

6  44 

6  27 

6  12 

5  58 

5  43 

5  29 

5  15 

5  03 

12 

16 

14  18 

13  39 

13  03 

12  30 

12  00 

11  29 

11  00 

10  34 

10  09 

9  43 

9  21 

9  01 

16 

20 

22  20 

21  20 

20  24 

19  32 

18  44 

17  56 

17  12 

16  32 

15  52 

15  12 

14  31 

14  04 

20 

24 

32  10 

30  43 

29  23 

28  07 

26  59 

25  50 

24  46 

23  48 

22  51 

2153 

21  02 

20  16 

24 

28 

43  46 

4149 

39  59 

38  18 

36  43 

35  09 

33  43 

32  25 

3106 

29  48 

28  37 

27  34 

28 

32 

57  10 

54  37 

52  13 

50  01 

47  57 

45  54 

44  02 

42  20 

40  37 

38  55 

37  22 

36  00 

32 

36 

72  22 

69  07 

66  06 

63  17 

60  42 

58  07 

55  44 

53  34 

5125 

49  15 

47  19 

45  35 

36 

40 

89  20 

85  20 

81  36 

78  08 

74  56 

7144 

68  48 

66  08 

63  28 

60  48 

58  24 

56  16 

40 

44 

86  48 

83  15 

80  01 

76  48 

73  34 

70  40 

68  05 

44 

48 

95  14 

91  23 

87  33 

84  05 

81  01 

48 

52 

107  15 

102  45 

98  41 

95  05 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.35 

3.20 

3.06 

2.93 

2.81 

2.69 

2.58 

2.48 

2.38 

2.28 

2.19 

2.11 

A,h 

Log. 

0.525 

0.505 

0.485 

0.466 

0.448 

0.429 

0.411 

0.394 

0.376 

0.357 

0.340 

0.324 

Log. 

04 

15 

72 

87 

71 

75 

62 

45 

58 

93 

44 

28 

Limit 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

48 


Latitude  8°  Declination  Same  Name. 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56^   57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

1       II 

0  32 
2  09 
4  51 

8  37 
13  28 
19  24 
26  24 
34  28 
43  38 
53  52 
65  11 
77  34 
91  02 
105  35 

II 
2.02 

1     II 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

4154 

51  44 

62  35 

74  30 

87  26 

10123 

II 
1.94 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

3155 

40  24 

49  52 

60  21 

71  48 

84  16 

97  45 

112  12 
II 

1.87 

/   // 

0  28 

1  55 

4  18 

7  38 

11  56 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 
II 

1.79 

/  // 

0  27 

1  50 
4  08 
7  20 

1128 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

7731 

89  54 

103  12 
II 

1.72 

1      II 

0  27 

145 

3  57 

7  03 

1100 

15  51 

2133 

28  09 

35  39 

44  00 

53  15 

63  21 

74  21 

86  15 

99  00 
II 

1.65 

1     II 

0  25 
142 
3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

6103 

71  39 

83  06 

95  24 
II 

1.59 

0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 
II 

1.52 

1      II 

0  23 

1  34 
3  31 
6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
II 

1.46 

/   // 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

1     II 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

51  50 

60  50 

70  34 

8100 
II 

1.35 

/  // 

0  20 

1  23 
3  06 
5  30 
8  36 

12  23 
16  52 
22  01 
27  52 
34  24 
41  37 
49  32 
58  08 
67  25 

77  24 
II 

1.29 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

J^og. 

0.305 
35 

0.287 
80 

0.271 

84 

0.252 

85 

0.235 
53 

0.217 

■  48 

0.201 
40 

0.181 
^4 

0.164 
35 

0.146 
13 

0.130 
33 

0.110 
59 

Log. 

Limit 

45 

46 

47 

48 

49 

50 

52 

53 

55 

56 

58 

59 

Min- 
utes 

Merid- 
ian 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

1  -  II 

0  19 

1  19 

2  57 
"5  15 

8  12 

1148 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

/  // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

1     II 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 
14  07 
18  26 
23  20 
28  48 
34  51 
4128 
48  40 
56  27 
64  48 
II 

1.08 

1     II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

3&33 

46  25 

53  50 

6148 
II 

1.03 

/  // 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

31  37 

37  38 

44  10 

51  13 

58  48 

0.98 

/  // 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 
55  48 

n 

0.93 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

1901 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

/  // 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

1     II 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
41  49 

48  00 

II 

0.80 

/  // 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
II 

0.75 

/  II 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

11  57 

15  07 

18  40 

22  35 

26  51 

31  33 

26  35 

42  00 
II 

0.70 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.089 
91 

62 

0.071 
88 

0.053 
08 

0.033 
42 

0.012 
84 

9.991 
23 

9.968 
48 

9.944 
48 

9.924 
28 

9.903 
09 

9.875 
06 

9.845 
10 

Log. 

Limit 

64 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33°   32° 

31° 

30° 

29° 

28° 

27° 

Alti- 
tudes 

Latitude  8°  Declination  Contrary  Name. 

Declinations. 


49 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

3 
14 
33 

II 
13.9 

43 
54 
32 

7 

1 

3 

13 
29 

II 
12.4 

19 
16 
50 

3 

1 

2 
11 
26 

II 
11.1 

II 

59 
56 
51 

5 

2  43 
10  51 
24  26 
43  26 

II 
10.18 

1 

2 

9 
22 
39 

f 
9.3 

II 

29 
57 
23 
49 

3 

2 

9 
20 
36 
57 

II 
8.6 

18 
11 
39 
45 
24 

1 

1 

2 

8 

19 

34 

53 

II 
7.9 

07 
31 
11 
05 
16 

3 

1 

1 
7 

17 
31 
49 

II 
7.4 

59 

58 
55 
49 
44 

3 

151 

7  27 
16  47 
29  49 
46  36 

II 
6.99 

r       II 

145 
7  01 
15  46 
28  02 
43  48 
63  04 

II 
-6.57 

139 
6  37 
14  53 
26  27 
41  20 
59  31 
81  01 

II 
6.20 

/      // 

134 
6  15 
14  04 
25  00 
39  04 
56.16 
76  34 

II 
5.86 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.145 
20 

1.094 
47 

1.048 
83 

1.007 

75 

0.969 

88 

0.935 
00 

0.902 
55 

0.872 
74 

0.844 

48 

0.817 
57 

0.792 
39 

0.767 
90 

Log. 

Limit 

10 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Min- 
utes 

Merid- 
ian 

82° 

8P 

80° 

79° 

78° 

77°      76° 

75° 

74° 

73° 

72° 

71° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

'      II 

1      II 

1      II 

/      II 

1      II 

1      II 

1      II 

1      II 

1      II 

/      II 

t      II 

/      // 

Min. 

4 

1  29 

124 

121 

1  17 

1  14 

1  10 

107 

1  05 

102 

100 

0  58 

0  55 

.      4 

8 

5  56 

5  39 

5  23 

5  08 

4  54 

4  42 

4  30 

4  19 

4  09 

4  00 

3  51 

3  43 

8 

12 

13  21 

12  42 

12  06 

11  32 

1102 

10  34 

10  08 

9  43 

9  20 

•   8  59 

8  39 

8  22 

12 

16 

23  43 

22  34 

2130 

20  32 

19  38 

18  46 

18  00 

17  17 

16  36 

15  57    15  25 

14  50 

16 

20 

37  04 

35  16 

33  36 

32  04 

30  40 

29  20 

28  08 

27  00 

25  56 

24  56    24  04 

-23  12 

20 

24 

53  23 

50  47 

48  23 

46  11 

44  10 

42  14 

40  31 

38  53 

37  21 

35  54 

34  40 

33  24 

24 

28 

72  39 

69  08 

65  51 

62  51 

60  06 

57  30 

55  09 

52  55 

50  50 

48  52 

47  10 

45  29 

28 

32 

82  05 

78  30 

75  06 

72  01 

69  07 

66  23 

63  50 

6136 

59  24 

32 

36 

77  59 

75  10 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

5.56 

5.29 

5.04 

4.81 

4.60 

4.40 

4.22 

4.05 

3.89 

3.74 

3.61 

3.48 

A,h 

Log. 

0.745 

0.723 

0.702 

0.682 

0.662 

0.643 

0.625 

0.607 

0.589 

0.572 

0.557 

0.541 

Log. 

07 

46 

43 

15 

76 

45 

31 

46 

95 

87 

51 

58 

Limit 

23 

24 

25 

26 

26 

27 

28 

29 

30 

31 

32 

33 

Min- 
utes 

Merid- 
ian 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60°      59°l,til- 

60 


Latitude  S°  Declination  Contrary  Name* 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

>        ir 

/      // 

1     II 

1     II 

1     It 

1      II 

1     II 

/     II 

1     II 

/     // 

/     II 

/      // 

Min. 

4 

0  54 

0  52 

0  50 

0  48 

0  46 

0  45 

0  44 

0  43 

0  41 

0  39 

0  38 

0  38 

4 

8 

3  34 

3  28 

3  20 

3  13 

3  06 

3  01 

2  56 

2  49 

2  45 

2  40 

2  35 

2  30 

8 

12 

8  02 

7  47 

7  30 

7  15 

7  01 

6  47 

6  35 

6  21 

6  10 

5  59 

5  47 

5  37 

12 

16 

14  18 

13  49 

13  22 

12  53 

12  27 

12  05 

11  41 

11  19 

10  58 

10  37 

10  17 

9  59 

16 

20 

22  20 

21  36 

20  52 

20  08 

19  28 

18  52 

18  16 

17  40 

17  08 

16  36 

16  04 

15  36 

20 

24 

32  10 

31  06 

30  03 

29  00 

28  02 

27  10 

26  18 

25  27 

24  40 

23  54 

23  08 

22  28 

24 

28 

43  46 

42  20 

40  54 

39  28 

38  10 

36  59 

35  48 

34  37 

33  35 

32  33 

3130 

30  34 

28 

32 

57  10 

55  18 

53  25 

51  32 

49  50 

48  18 

46  46 

45  13 

43  52 

42  30 

41  08 

39  56 

32 

36 

72  22 

69  59 

67  37 

65  14 

63  04 

6108 

59  11 

57  15 

55  31 

53  47 

52  03 

50  33 

36 

40 

89  20 

86  24 

83  28 

80  32 

77  52 

75  28 

73  04 

70  40 

68  32 

66  24 

64  16 

62  24 

40 

44 

88  24 

85  31 

82  56 

80  20 

77  45 

75  30 

44 

48 

95  37 

92  33 

89  51 

48 

52 

105  27 

52 

56 

56 

60 

60 

II 

'1 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

A,h 

3.35 

3.24 

3.13 

3.02 

2.92 

2.83 

2.74 

2.65 

2.57 

2.49 

2.41 

2.34 

A,h 

Log. 

0.525 

0.510 

0.495 

0.480 

0.465 

0.451 

0.437 

0.423 

0.409 

0.396 

0.382 

0.369 

Log. 

04 

55 

54 

01 

38 

79 

75 

25 

93 

20 

02 

22 

Limit 

34 

35 

36 

37 

38 

38 

39 

40 

41 

42 

43 

43 

Min- 
utes 

Merid- 
ian 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

1      II 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
II 

1.62 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      II 

0  36 

2  25 

5  26 

9  38 

15  04 

2142 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

10157 

II 
2.26 

1     II 

0  35 

2  21 
5  17 
9  23 
14  40 
2107 
28  45 
37  33 
47  31 
58  40 
70  59 
84  29 
99  09 

II 
2.20 

1     II 

0  34 

2  16 

5  06 

9  06 

14  12 

20  27 

27  50 

36  21 

46  01 

56  48 

68  44 

8146 

95  59 

II 
2.13 

>     II 

0  33 
2  13 

4  58 
8  50 
13  48 
19  52 
27  03 
35  20 
44  43 
55  12 
66  48 
79  29 
93  17 
108  12 

II 
2.07 

/      // 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

104  32 

II 
2.00 

1      II 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

5144 

62  35 

74  30 

87  26 

10123 

II 
1.94 

1      II 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 

II 

1.89 

/     // 

0  29 
157 
4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
II 

1.83 

1      II 

0  28 

1  54 
4  16 
7  33 

1148 
16  59 
23  08 
30  13 
38  14 
47  12 
57  07 
67  56 
79  46 
92  31 
106  12 
II 

1.77 

1       n 

0  27 

150 

4  08 

7  20 

1128 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 
II 

1.72 

/     II 

0  27 

147 

4  00 

7  08 

1108 

16  02 

2149 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

II 

1.67 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56" 

60 

A,h 

Log. 

0.354 
11 

0.342 

42 

0.328 
38 

0.315 
97 

0.301 
03 

0.287 
80 

0.276 
46 

0.262 
45 

0.247 
97 

0.235 
53 

0.222 
72 

0.209 
52 

Log. 

Limit 

44 

45 

46 

46 

47 

48 

49 

50 

51 

52 

53 

54 

Min- 
utes 

Merid- 
ian 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38=^ 

37° 

36° 

35° 

Alti- 
tudes 

Latitude  8^  Declination  Contrary  Name. 


51 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53°  1  54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

r       n 

0  25 

141 
3  46 
6  42 
10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 
94  12 

n 

1.57 

1       n 

0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 
It 

1.52 

1      II 

0  23 

134 

3  32 

6  16 

9  48 

14  06 

19  13 

25  06 

3145 

39  12 

47  26 

56  27 

66  15 

76  50 

88  12 
It 

1.47 

1      It 

0  22 
131 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
It 

1.42 

1     It 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
It 

1.38 

/  II 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

51  27 

60  23 

70  02 

80  24 
It 

1.34 

1      II 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 
II 

1.29 

/  It 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 

16  20 

2120 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
II 

1.25 

/  It 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 
72  36 
II 

1.21 

I  It 

0  19 

1  15 

2  48 
5  00 
7  48 

II  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/  II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
It 

1.13 

0  17 

1  10 

2  37 

4  39 
7  16 
10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 
65  24 
It 

1.09 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.195 
90 

0.181 

84 

0.167 
32 

0.152 
29 

0.139 

88 

0.127 
10 

0.110 
59 

0.096 
91 

0.082 
79 

0.068 
19 

0.053 
08 

0.037 
43 

Log. 

Limit 

55 

57   58 

59 

60 

62 

64 

66 

67 

69 

71 

73 

Min- 
utes 

Merid- 
ian 

34° 

33°   32° 

31° 

30° 

29°  i  28° 

27°   26° 

25° 

24° 

23° 

Alti- 
tudes 

Declin.^tion 

^. 

Hour 
Angles 

60° 

6P 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/  II 

'  " 

1     It 

1      II 

1      II 

/  II 

1      II 

1      It 

/   // 

/   // 

'   " 

/  // 

Min. 

4 

0  17 

0  16 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

Oil 

Oil 

4 

8 

107 

1  04 

102 

0  59 

0  57 

0  55 

0  52 

0  50 

0  48 

0  45 

0  43 

0  41 

8 

12 

2  31 

2  25 

2  20 

2  14 

2  10 

2  04 

1  58 

152 

148 

142 

137 

133 

12 

16 

4  29 

4  19 

4  08 

3  58 

3  50 

3  40 

3  30 

3  19 

3  12 

3  02 

2  54 

2  47 

16 

20 

7  00 

6  44 

6  28 

6  12 

6  00 

5  44 

5  28 

5  12 

5  00 

4  44 

4  32 

4  20 

20 

24 

10  05 

9  42 

9  18 

8  55 

8  38 

8  16 

7  53 

7  29 

7  12 

6  49 

6  32 

6  15 

24 

28 

13  43 

13  12 

12  41 

12  10 

11  46 

11  14 

10  43 

10  12 

9  48 

9  17 

8  53 

8  29 

28 

32 

17  55 

17  14 

16  34 

15  53 

15  22 

14  40 

13  59 

13  19 

12  48 

12  07 

1136 

11  05 

32 

36 

22  41 

2149 

20  57 

20  05 

19  26 

18  35 

17  43 

16  51 

16  12 

15  20 

14  42 

14  03 

36 

40 

28  00 

26  56 

25  52 

24  48 

24  00 

22  56 

21  52 

20  48 

20  00 

18  56 

18  08 

17  20 

40 

44 

33  53 

32  35 

31  18 

30  00 

29  02 

27  45 

26  28 

25  10 

24  12 

22  54 

2157 

20  59 

44 

48 

40  19 

38  47 

37  15 

35  43 

34  34 

33  01 

31  29 

29  55 

28  46 

27  14 

26  06 

24  57 

48 

52 

47  19 

45  31 

43  43 

4155 

40  34 

38  45 

36  57 

35  09 

33  48 

32  00 

30  38 

29  17 

52 

56 

54  53 

52  47 

50  42 

48  36 

47  02 

44  57 

42  52 

40  46 

39  12 

37  06 

35  33 

33  59 

56 

60 

63  00 

60  36 

58  12 

55  48 

54  00 

5136 

49  12 

46  48 

45  00 

42  36 

40  48 

39  00 

60 

II 

II 

It 

It 

// 

It 

It 

It 

It 

It 

It 

II 

A,h 

1.05 

1.01 

0.97 

0.93 

0.90 

0.86 

0.82 

0.78 

0.75 

0.71 

0.68 

0.65 

A,h 

Log. 

0.021 

0.004 

9.986 

9.968 

9.954 

9.934 

9.913 

9.892 

9.875 

9.851 

9.832 

9.812 

Log. 

19 

32 

77 

48 

24 

50 

81 

09 

06 

26 

51 

91 

Limit 

74 

75 

76 

77 

78 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

Alti- 
tudes 

62 


Latitude  9°  Decimation  Same  Name. 


Dkclinations. 


Hour 
Angles 

0°          1° 

2° 

3° 

4°        5° 

6° 

7° 

8° 

9° 

10° 

IP 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

1        n 

3  18 
13  14 
29  46 

II 
12.40 

/      // 

3  43 
14  51 
33  26 

II 
13.93 

1 

4 

16 
38 

II 
15.9 

14 
57 
10 

3 

4 
19 

II 
18.5 

57 
46 

3 

1 

5 
23 

II 
22.2 

II 

55 
41 

3 

1     II 

1     II 

1 

// 

/ 

II 

/      II 

1     II 
II 

1     II 
II 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

1.093 
42 

1.143 
95 

1.201 
40 

1.267 

88 

1.346 
35 

Log. 

Limit 

12 

10 

9 

8 

7 

6 

5 

3 

1 

0 

2 

4 

Min- 
utes 

Merid- 
ian 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Miu. 

1       II 

1     II 

1      II 

'      " 

/      // 

/      II 

/      II 

/      // 

/      // 

1     II 

1      II 

/      II 

Min. 

4 

5  45 

4  46 

4  05 

3  34 

3  08 

2  49 

2  33 

2  19 

2  07 

158 

4 

8 

23  02 

19  06 

16  19 

14  13 

12  35 

11  16 

10  11 

9  18 

8  31 

7  52 

8 

12 

36  43 

3159 

28  18 

25  21 

22  55 

20  54 

19  11 

17  43 

12 

16 

45  03 

40  45 

37  10 

34  05 

31  29 

16 

20 

58  04 

53  16 

49  12 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

21.59 

17.92 

15.30 

13.33 

11.79 

10.56 

9.55 

8.71 

7.99 

7.38 

A,h 

Log. 

1.334 

1.253 

1.184 

1.124 

1.071 

1.023 

0.980 

0.940 

0.902 

0.868 

Log. 

25 

34 

69 

83 

51 

66 

00 

02 

55 

06 

Limit 

6 

7 

8 

9 

11 

12 

13 

14 

16 

17 

18 

19 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

Alti- 
tudes 

Latitude  9°  Declination  Same  Name. 


53 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

> 

1 

7 

16 
29 
45 
65 

II 
6.8 

// 

50 
18 
26 
14 
40 
46 

5 

142 
6  48 
15  19 
27  13 
42  32 
61  15 
83  23 

II 
6.38 

1 
6 
14 
25 
39 
57 
77 

II 
5.9 

35 
21 
19 
25 
44 
13 
53 

5 

1 

1 
5 
13 
23 
37 
53 
73 

II 
5.5 

29 
58 
25 
51 
16 
40 
01 

9 

/ 

1 

5 
12 
22 
35 
50 
68 

II 
5.2 

II 

24 
37 
38 
26 
04 
30 
44 

6 

1 

1 
5 
11 
21 
33 
47 
64 

4.9 

// 

19 

17 
55 
09 
04 
37 
49 

5 

I  II 

1  15 
5  00 

II  15 
20  01 
31  16 
45  02 
61  17 
80  00 

II 
4.69 

1      II 

1  11 

4  45 
10  40 
18  56 
29  36 
42  37 
58  01 
75  47 

II 
4.44 

1     II 

107 

4  30 
10  06 
17  58 
28  04 
40  25 
55  01 
7151 

II 
4.21 

/      // 

1  04 
4  16 
9  36 
17  04 
26  40 
38  24 
52  16 
68  16 

II 
4.00 

1      II 

101 
4  03 
9  07 
16  13 
25  20 
36  29 
49  39 
64  51 

II 
3.80 

1      II 

0  58 
3  51 

8  41 
15  27 
24  08 
34  46 
47  18 
61  46 
78  12 

II 
3.62 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

Log. 

0.835 
69 

0.804 
82 

0.775 
25 

0.747 
41 

0.720 
99 

0.695 
48 

0.671 
17 

0.647 
38 

0.624 
28 

0.602 
06 

0.579 

78 

0.558 
71 

Log. 

Limit 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

32 

Min- 
utes 

Merid- 
ian 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

470      Hour 
Angles 

Min. 

/       II 

1      II 

/      // 

1      II 

1     It 

/      // 

/      // 

1     II 

'      // 

/      // 

/      // 

/       // 

Min. 

4 

0  55 

0  53 

0  51 

0  48 

0  46 

0  44 

0  43 

0  41 

0  38 

0  37 

0  36 

0  35 

4 

8 

3  42 

3  31 

3  21 

3  13 

3  04 

2  57 

2  49 

2  43 

2  36 

2  29 

2  24 

2  17 

8 

12 

8  19 

7  55 

7  33 

7  13 

6  55 

6  38 

6  21 

6  06 

5  50 

5  35 

5  23 

5  09 

12 

16 

14  45 

14  05 

13  27 

12  51 

12  17 

1146 

11  19 

10  50 

10  22 

9  57 

9  33 

9  11 

16 

20 

23  04 

22  00 

2100 

20  04 

19  12 

18  24 

17  40 

16  56 

16  12 

15  32 

14  56 

14  20 

20 

24 

33  13 

31  41 

30  15 

28  54 

27  39 

26  30 

25  27 

24  23 

23  19 

22  22 

21  30 

20  39 

24 

28 

45  13 

43  07 

4109 

39  20 

37  38 

36  04 

34  37 

33  11 

3146 

30  27 

29  16 

28  05 

28 

32 

59  03 

56  19 

53  45 

51  22 

49  09 

47  06 

45  13 

43  21 

41  29 

39  46 

38  14 

36  41 

32 

36 

74  44 

71  17 

68  03 

65  01 

62  13 

59  37 

57  15 

54  52 

52  29 

50  20 

48  23 

46  27 

36 

40 

92  16 

88  00 

84  00 

80  16 

76  48 

73  36 

70  40 

67  44 

64  48 

62  08 

59  44 

57  20 

40 

44 

85  31 

8157 

78  24 

75  11 

72  16 

69  23 

44 

48 

93  19 

89  28 

86  01 

82  33 

48 

52 

105  00 

100  57 

96  53 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.46 

3.30 

3.15 

3.01 

2.88 

2.76 

2.65 

2.54 

2.43 

2.33 

2.24 

2.15 

A,h 

Log. 

0.539 

0.518 

0.498 

0.478 

0.459 

0.440 

0.423 

0.404 

0.385 

0.367 

0.350 

0.332 

Log. 

08 

51 

31 

57 

39 

91 

25 

83 

61 

36 

25 

44 

Limit 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

42 

43 

Min- 
utes 

Merid- 
ian 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

Alti- 
tudes 

54 


Latitude  9°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 

/        n 

0  33 

0  31 

1      It 
0  30 

1       n 

0  29 

1     II 
0  28 

0  27 

1      II 
0  26 

1     II 
0  25 

1     II 
0  23 

/      // 
0  22 

1  II 
0  22 

/  II 
0  21 

Min. 
4 

8 

2  12 

2  06 

2  01 

1  56 

152 

147 

1  42 

139 

1  35 

131 

1  27 

123 

8 

12 

4  57 

4  46 

4  34 

4  22 

4  12 

4  02 

3  51 

3  43 

3  34 

3  25 

3  16 

3  07 

12 

16 

8  47 

8  26 

8  06 

7  46 

7  28 

7  10 

6  53 

6  37 

6  18 

6  03 

5  48 

5  33 

16 

20 

13  44 

13  12 

12  40 

12  08 

11  401   11  12 

10  44 

10  20 

9  52 

9  28 

9  04 

8  40 

20 

24 

19  47 

19  00 

18  14 

17  29 

16  48    16  08 

15  28 

14  53 

14  12 

13  38 

13  04 

12  29 

24 

28 

26  55 

25  53 

24  50 

23  47 

22  52 

2157 

21  02 

20  15 

19  21 

18  34 

17  46 

16  59 

28 

32 

35  09 

33  48 

32  26 

3103 

29  52 

28  40 

27  28 

26  27 

25  16 

24  14 

23  12 

22  11 

32 

36 

44  30 

42  46 

4102 

39  19 

37  48 

36  18 

34  47 

33  29 

3158 

30  40 

29  23 

28  05 

36 

40 

54  56 

52  48 

50  40 

48  32 

46  40 

44  48 

42  56 

41  20 

39  28 

37  52 

36  16 

34  40 

40 

44 

66  28 

63  53 

61  18 

58  44 

56  28 

54  13 

5157 

50  01 

47  45 

45  49 

43  53 

4157 

44 

48 

79  06 

76  02 

72  58 

69  53 

67  lO!  64  30 

61  49 

59  31 

56  50 

54  32 

52  13 

49  55 

48 

52 

92  50 

89  14 

85  38 

82  01 

78  52!  75  42 

72  33 

69  51 

66  42 

64  00 

61  17 

58  35 

52 

56 

107  41 

103  29 

99  18 

95  08 

91  28|  87  49 

84  09 

8101 

77  21 

74  13 

71  05 

67  57 

56 

60 

114  00 

109  12 

105  00 

100  48 

96  36 

93  00 
II 

88  48 
II 

85  12 
II 

8136 
II 

78  00 
II 

60 

Ajh 

2.06 

1.98 

1.90 

1.82 

1.75 

1.68 

1.61 

1.55 

1.48 

1.42 

1.36 

1.30 

A,h 

0.313 

0.296 

0.278 

0.260 

0.243 

0.225 

0.206 

0.190 

0.170 

0.152 

0.133 

0.113 

Log. 

Log. 

87 

67 

75 

07 
48 

04 

31 

83 

33 

26 

29 

54 

94 

Limit 

44 

45 

46 

49 

51 

52 

53 

54 

55 

57 

59 

Min- 
utes 

Merid- 
ian 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41- 

40° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

1      II 

1     II 

/      // 

/      // 

/      // 

1      II 

/      // 

1     II 

1      II 

/      II 

1      II 

Min. 

4 

0  20 

0  19 

0  19 

0  17 

0  17 

0  15 

0  15 

0  14 

0  14      0  13 

0  12 

0  11 

4 

8 

1  20 

1  16 

1  13 

1  10 

107 

103 

100 

0  57 

0  54 

0  51 

0  49 

0  46 

8 

12 

3  00 

2  51 

2  44 

2  37 

2  30 

2  23 

2  16 

2  08 

2  02 

1  55 

150 

1  44 

12 

16 

5  20 

5  05 

4  52 

4  39 

4  26 

4  13 

4  00 

3  48 

3  38 

3  25 

3  14 

3  04 

16 

20 

8  20 

7  56 

7  36 

7  16 

6  56 

6  36 

6  16 

5  56 

5  40 

5  20 

5  04 

4  48 

20 

24 

12  00 

1126 

10  57 

10  28 

9  59 

9  30 

9  01 

8  33 

8  10 

7  41 

7  18 

6  55 

24 

28 

16  20 

15  33 

14  53 

14  15 

13  35 

12  57 

12  17 

1138 

1106 

10  27 

9  56 

9  25 

28 

32 

21  20 

20  18 

19  27 

18  36 

17  45 

16  54 

16  03 

15  11 

14  30 

13  39 

12  58 

12  17 

32 

36 

27  00 

25  43 

24  38 

23  33 

22  28 

21  23 

20  18 

19  14 

18  22 

17  17 

16  25 

15  33 

36 

40 

33  20 

3144 

30  24 

29  04 

27  44 

26  24 

25  04 

23  44 

22  40 

2120 

20  16 

19  12 

40 

44 

40  20 

38  24 

36  47 

35  10 

33  33 

31  56 

30  19 

28  43 

27  26 

25  49 

24  31 

23  14 

44 

48 

48  00 

45  41 

43  46 

41  51 

39  56 

38  01 

36  06 

34  10 

32  38 

30  43 

29  09 

27  37 

48 

52 

56  20 

53  37 

51  22 

49  07 

46  52 

44  37 

42  22 

40  06 

38  18 

36  03 

34  15 

32  27 

52 

56 

65  20 

62  12 

59  35 

56  58 

54  21 

51  44 

49  07 

46  31 

44  26 

4149 

39  43 

37  38 

56 

60 

75  00 

7124 

68  24 

65  24 

62  24 
II 

59  24 
II 

56  24 
II 

53  24 
II 

5100 
// 

48  00 
II 

45  36 
II 

43  12 

II 

60 

A,h 

1.25 

1.19 

1.14 

1.09 

1.04 

0.99 

0.94 

0.89 

0.85 

0.80 

0.76 

0.72 

A,h 

0.096 

0.075 

0.056 

0.037 

0.017 

9.995 

9.973 

9.949 

9.929 

9.903 

9.880 

9.857 

Log. 

Log. 

91 

55 

90 

43 

03 

64 

13 

39 

42 

09 

81 

33 

Limit 

61 

63 

65 

67 

69 

71 

73 

75 

77 

79 

81 

83 

Min- 
utes 

Merid- 
ian 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

Alti- 
tudes 

Latitude  9°  Decimation  Contrary  Name. 


55 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/        n 

3  18 
13  14 
29  46 

II 
12.40 

/      // 

2  59 
1155 
26  48 

II 
11.17 

1 

2 
10 
24 
43 

II 
10.1 

43 
50 
23 
21 

6 

2 

9 

2^ 
39 

II 
9.3 

11 
29 

56 
20 
44 

1 

/          H 

2  18 

9  10 

20  38 

36  42 

57  20 

II 
8.60 

/      II 

2  07 

8  31 

19  11 

34  05 

53  16 

II 
7.99 

1       n 

159 

7  57 

17  53 

3147 

49  40 

II 
7.45 

/      // 

151 

7  26 

16  46 

29  46 

46  32 

II 
6.98 

1      II 

145 
7  01 
15  46 
28  02 
43  48 
63  04 

II 
6.57 

1     II 

139 

6  37 
14  53 
26  27 
4120 
59  31 
81  01 

II 
6.20 

/      // 

134 
6  16 
14  05 
25  03 
39  08 
56  21 
76  42 

II 
5.87 

/      II 

129 
5  57 
13  22 
23  46 
37  08 
53  28 
72  47 

II 
5.57 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

1.093 
42 

1.048 
05 

1.006 
89 

0.968 
95 

0.934 
50 

0.902 
55 

0.872 
16 

0.843 
86 

0.817 
57 

0.792 
39 

0.768 
64 

0.745 
86 

Log. 

Limit 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

Min- 
utes 

Merid- 
ian 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      II 

/      // 

r       II 

1      II 

1     II 

1      II 

1       n 

1     II 

1     II 

/      // 

/      // 

/      II 

Min. 

4 

124 

121 

1  17 

1  14 

1  10 

107 

105 

102 

100 

0  58 

0  55 

0  54 

4 

8 

5  39 

5  23 

5  08 

4  55 

4  43 

4  31 

4  20 

4  10 

4  01 

3  51 

3  44 

3  36 

8 

12 

12  42 

12  06 

1134 

1103 

10  35 

10  09 

9  45 

9  23 

9  02 

8  41 

8  23 

8  05 

12 

16 

22  34 

21  30 

20  34 

19  41 

18  49 

18  03 

17  19 

16  41 

16  02 

15  27 

14  53 

14  23 

16 

20 

35  16 

33  36 

32  08 

30  44 

29  24 

28  12 

27  04 

26  04 

25  04 

24  08 

23  16 

22  28 

20 

24 

50  47 

48  23 

46  17 

44  16 

42  20 

40  36 

38  59 

37  32 

36  06 

34  46 

33  30 

32  21 

24 

28 

69  08 

65  51 

62  59 

60  14 

57  38 

55  17 

53  03 

5106 

49  08 

47  18 

45  37 

44  02 

28 

32 

82  15 

78  40 

75  16 

72  12 

69  17 

66  44 

64  10 

6146 

59  34 

57  31 

32 

36 

78  12 

75  23 

72  48 

36 

40 

89  52 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

n 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

5.29 

5.04 

4.82 

4.61 

4.41 

4.23 

4.06 

3.91 

3.76 

3.62 

3.49 

3.37 

Aih 

Log. 

0.723 

0.702 

0.683 

0.663 

0.644 

0.626 

0.608 

0.592 

0.575 

0.558 

0.542 

0.527 

Log. 

46 

43 

05 

70 

44 

34 

53 

18 

19 

71 

83 

63 

Limit 

24 

25 

26 

26 

27 

28 

29 

30 

31 

32 

33 

34 

Min- 
utes 

Merid- 
ian 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

66 


Latitude  9°  Declination  Contrary  Name. 

Declinations. 


Hour 
Angle? 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/      // 

/      // 

/      II 

1     II 

1      II 

'     // 

/      // 

/     // 

/      // 

Min. 

4 

0  52 

0  51 

0  49 

0  47 

0  46 

0  44 

0  43 

0  41 

0  40 

0  38 

0  38 

0  36 

4 

8 

3  28 

3  21 

3  15 

3  08 

3  02 

2  57 

2  51 

2  46 

2  41 

2  36 

2  31 

2  27 

8 

12 

7  48 

7  32 

7  18 

7  04 

6  50 

6  38 

6  24 

6  13 

6  01 

5  50 

5  40 

5  30 

12 

16 

13  52 

13  24 

12  58 

12  32 

12  10 

11  46 

11  24 

11  03 

10  43 

10  22 

10  04 

9  46 

16 

20 

2140 

20  56 

20  16 

19  36 

19  00 

18  24 

17  48 

17  16 

16  44 

16  12 

15  44 

15  16 

20 

24 

31  12 

30  09 

29  11 

28  13 

27  22 

26  30 

25  38 

24  52 

24  06 

23  19 

22  40 

21  59      24 

28 

42  28 

4101 

39  43 

38  25 

37  14 

36  04 

34  53 

33  51 

32  48 

31  46 

30  50 

29  56     28 

32 

55  28 

53  35 

5153 

50  11 

48  38 

47  06 

45  34 

44  12 

42  50 

41  29 

40  16 

39  05      32 

36 

70  12 

67  50 

65  40 

63  30 

6134 

59  37 

57  41 

55  57 

54  13 

52  29 

50  59 

49  281     36 

40 

86  40 

83  44 

8104 

78  24 

76  00 

73  36 

71  12 

69  04 

66  56 

64  48 

62  56 

61  04I     40 

44 

86  10 

83  34 

80  59 

78  24 

76  09 

73  53'     44 

48 

96  23 

93  19 

90  37 

87  56     48 

52 

106  21  103  12i     52 

56 

56 

60 

. . . 

60 

H 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

'/ 

A  h 

3.25 

3.14 

3.04 

2.94 

2.85 

2.76 

2.67 

2.59 

2.51 

2.43 

2.36 

2.29      A,li 

Log. 

0.511 

0.496 

0.482 

0.468 

0.454 

0.440 

0.426 

0.413 

0.399 

0.385 

0.372 

0.359    , 

88 

93 

87 

35 

84 

91 

51 

30 

67 

61 

91 

84 

Limit 

35 

35 

36 

37 

38 

39 

40 

40 

41 

42 

43 

44 

Min- 
utes 

Merid- 
ian 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

dfio    '    4.70    i  Hour 
*°         *'      [Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

7138 

85  15 

100  03 

n 

2.22 

/      II 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

1      II 

0  33 

2  14 

5  01 

8  55 

13  56 

20  04 

27  19 

35  40 

45  09 

55  44 

67  26 

80  15 

94  11 

II 
2.09 

/      II 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

91  29 

106  06 

II 
2.03 

1      II 

0  31 

2  05 

4  44 

8  24 

13  08 

18  54 

25  45 

33  38 

42  33 

52  32 

63  34 

75  39 

88  47 

102  57 

II 
1.97 

1      II 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

61  37 

73  21 

86  05 

99  49 

114  36 
II 

1.91 

1     II 

0  30 

158 

4  26 

7  54 

12  20 

17  46 

24  10 

31  34 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

111  00 
II 

1.85 

1      II 

0  29 

155 

4  19 

7  41 

12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

8107 

94  05 

108  00 
II 

1.80 

/      // 

0  28 

152 

4  12 

7  28 

11  40 

16  48 

22  52 

29  52 

37  48 

46  40 

56  28 

67  10 

78  52 

91  28 

105  00 
II 

1.75 

1      If 

0  27 

149 

4  05 

7  15 

1120 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
II 

1.70 

0  27 
•1  45 
3  56 
7  00 
10  56 
15  45 
21  25| 
27  59 
35  261 
43  44 
52  55 
62  58 
73  54 
85  43 

98  24 
// 

1.64 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
51  38 
6126 
72  06 
83  38 

96  00 
// 

1.60 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.346 
35 

0.332 
44 

0.320 
15 

0.307 
50 

0.294 

47 

0.281 
03 

0.267 
17 

0.255 
27 

0.243 
04 

0.230 

45 

0.214 

84 

0.204!    ^ 

12    ^'^^- 

Limit 

45        46 

47 

48 

48 

49 

50 

51 

52 

53 

54 

KC       Miu- 
^^        utes 

Merid- 
ian 

45° 

1   44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

i    Alti- 
tudes 

Latitude  9°  Declination  Contrary  Name. 
Declinations. 


67 


Hour  I  .Qo 
Angles  ^^ 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59°  u""V'' 

[Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

/   // 

0  25 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

81  01 

93  00 
II 

1.55 

1      II 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 

n 

1.50 

/   // 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
It 

1.45 

1     II 
0  22 

130 

3  23 

6  01 

9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 
II 

1.41 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
II 

1.37 

1      II 

0  21 

1  24 
3  10 
5  38 
8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
II 

1.32 

1     II 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

I  II 

0  20 
120 
2  59 
5  17 
8  16 

II  54 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
II 

1.24 

I  II 

0  19 

1  17 

2  53 
5  07 
8  00 

II  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

1.20 

/   // 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 

15  09 

19  47 

25  04 

30  56 

37  26 

44  32 

52  16 

60  38 

69  36 
II 

1.16 

1     II 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 
II 

1.12 

1       II 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 

II 

1.08 

Min. 
4 
8 

12 
16 
20 
24 
28- 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.190 
33 

0.176 
09 

0.161 
37 

0.149 
22 

0.136 

72 

0.120 

57 

0.107 
21 

0.093 
42 

0.079 
18 

0.064 
46 

0.049 
22 

0.033 
42 

Log. 

Limit 

56 

58 

59 

60 

61 

63 

65 

67 

68 

70 

72 

74 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

60°  1  61° 

Min. 

/  II  \  1     II 

4 

0  17  0  16 

8 

107 

104 

12 

2  30 

2  24 

16 

4  26 

4  16 

20 

6  56 

6  40 

24 

9  59 

9  36 

28 

13  35 

13  04 

32 

17  45 

17  04 

36 

22  28 

21  36 

40 

27  44 

26  40 

41 

33  33 

32  16 

48 

39  56 

38  24 

52 

46  52 

45  04 

56 

54  21 

52  16 

60 

62  24 

60  00 

// 

II 

A,h 

1.04 

1.00 

Log. 


Limit 


Merid- 
ian 


0.017    0.00 
03     ... 


75 


76 


21°      20° 


62° 

I      II 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 
II 

0.96 


9.982 
27 


63° 

1     II 

0  14 

0  59 

2  14 

3  58 

64°      65= 


6  12 

8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

41  55 

48  36 

55  48 
II 

0.93 


77 


19° 


9.968 
48 


78 


18° 


0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 


9.949 
39 


0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

51  00 
II 

0.85 


66° 


9.929 
42 


79       80 


0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29| 

36  57 

42  52 

49  12 
II 

0.82 


67°      68= 


9.913 
81 


82 


17= 


16°  I    15= 


0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 


9.892 
09 


84 


14° 


0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 


69° 


0.74     0.71 


9.869 
23 


0  11 
0  45 
142 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  06 
42  36 


70° 


86 


13= 


9.851 
26 


88 


12° 


Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

21  57 

26  06 

30  38 

35  33 

40  48 
II 

0.68 


71° 


9.832 
51 


90 


11= 


0  11 

0  41 

1  33 

2  47 
4  20 
6  15 
8  29 

11  05 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 
II 

0.65 


Hour 
Angles 


9.812 
91 


92 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Min- 
utes 


10= 


Alti- 
tudes 


58 


Latitude  10°  Declination  Same  Name. 
Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9°       10° 

11°  1 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1        u 

2  59 
1153 
26  44 

n 

11.14 

/     // 

3  18 
13  11 
29  40 

n 

12.36 

1     II 

3  42 
14  49 
33  20 

II 
13.89 

1     II 

4  14 
16  54 
38  01 

II 
15.84 

4  55 
19  41 

II 
18.45 

/       n 

5  54 
23  34 

II 
22.10 

II 

/       n 

II 

/     II 
II 

/     II 
II 

1     II 
II 

II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.046 
89 

1.092 
02 

1.142 
70 

1.199 
76 

9 

1.266 
00 

1.344 
39 

Log. 

Limit 

13 

11 

10 

8 

7 

6 

5    . 

3 

1 

0 

2 

Min- 
utes 

Merid- 
ian 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90°  1   89° 

Alti- 
tudes 

Declin.\tions» 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

1      II 

/      // 

1     II 

/      // 

/      II 

/      // 

1      II 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

5  43 

4  44 

4  03 

3  31 

3  07 

2  47 

2  31 

2  18 

2  06 

4 

8 

22  52 

18  58 

16  11 

14  06 

12  28 

11  10 

10  06 

9  11 

8  26 

8 

12 

42  41 

36  24 

3142 

28  03 

25  07 

22  43 

20  41 

18  58 

12 

16 

44  37 

40  21 

36  47 

33  45 

16 

20 

57  28 

52  44 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

n 

II 

II 

II 

n 

If 

n 

A,h 

21.43 

17.78 

15.17 

13.21 

11.69 

10.46 

9.46 

8.62 

7.91 

A,h 

1.331 

1.249 

1.180 

1.120 

1.067 

1.019 

0.975 

0.935 

0.898 

Log. 

Log. 

02 

93 

99 

90 

81 

53 

89 

51 

18 

Limit 

4 

6 

7 

8 

10 

11 

12 

13 

15 

16 

17 

18 

Min- 
utes 

Merid- 
ian 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78 

o 

77° 

Alti- 
tudes 

Latitude  iO°  Declination  Same  Name. 


59 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

7 
17 
31 

48 

n 

7.3 

// 

57 
47 
31 
09 
40 

0 

1 

1 

7 
16 
28 
45 
64 

n 

6.7 

49 
14 
15 
53 

08 
59 

7 

t     II 

141 
6  44 
15  08 
26  56 
42  04 
60  35 
82  27 

II 
6.31 

1      II 

1  34 
6  17 
14  08 
25  08 
39  16 
56  33 
76  58 

II 
5.89 

1 

1 
2 
3 

5 
7 

S 

1 
5 
3 
3 
6 
3 
2 

n 

.5 

// 

28 
54 
16 
36 
52 
05 
16 

3 

1 

1 

2 
3 
4 

6 

S 

II 

123 
5  32 
2  27 
2  09 
4  36 
9  50 
7  49 

II 
.19 

1 

1 
5 
11 
20 
32 
47 
64 
83 

4.9 

// 

18 
13 
46 
54 
40 
02 
02 
38 

0 

1     II 

1  14 
4  56 
1106 
19  46 
30  52 
44  27 
60  30 
79  01 

II 
4.63 

1     II 

1  10 
4  40 
10  31 
18  41 
29  12 
42  03 
57  14 
74  45 

II 
4.38 

1      II 

107 
4  25 
9  57 
17  43 
27  40 
39  51 
54  13 
70  49 

II 
4.15 

1      II 

103 
4  12 
9  28 
16  48 
26  16 
37  49 
5129 
67  15 

II 
3.94 

1      II 

100 
4  00 
9  00 
16  00 
25  00 
36  00 
49  00 
64  00 

II 
3.75 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.863 
32 

0.830 
59 

0.800 
03 

0.770 
12 

0.742 
73 

0.715 
17 

0.690 
20 

0.665 

58 

0.641 
.47 

0.618 
05 

0.595 
50 

0.574 
03 

Log. 

Limit 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

31 

Min- 
utes 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

Alti- 
tudes 

DECLINATIONS 

Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1     II 

1     II 

1      II 

1     II 

1      II 

1      II 

1      II 

1     II 

1     II 

/      // 

1      II 

1     II 

Min. 

4 

0  57 

0  54 

0  52 

0  50 

0  47 

0  45 

0  43 

0  42 

0  39 

0  38 

0  36 

0  35 

4 

8 

3  49 

3  38 

3  28 

3  18 

3  09 

3  01 

2  54 

2  46 

2  40 

2  32 

2  27 

2  20 

8 

12 

8  34 

8  10 

7  48 

7  26 

7  07 

6  47 

6  30 

6  14 

5  59 

5  43 

5  30 

5  15 

12 

16 

15  14 

14  30 

13  52 

13  14 

12  37 

12  05 

11  34 

11  06 

10  37 

10  09 

9  46 

9  21 

16 

20 

23  48 

22  40 

21  40 

20  40 

19  44 

18  52 

18  04 

17  20 

16  36 

15  52 

15  16 

14  36 

20 

24 

34  16 

32  38 

31  12 

29  46 

28  25 

27  10 

26  01 

24  58 

23  54 

22  51 

21  59 

21  02 

24 

28 

46  39 

44  26 

42  28 

40  30 

38  41 

36  59 

35  25 

33  58 

32  33 

31  06 

29  56 

28  37 

28 

32 

60  56 

58  02 

55  28 

52  54 

50  31 

48  18 

46  15 

44  22 

42  30 

40  37 

39  05 

37  22 

32 

36 

77  07 

73  26 

70  12 

66  58 

63  56 

61  08 

58  32 

56  10 

53  47 

51  25 

49  28 

47  19 

36 

40 

90  40 

86  40 

82  40 

78  56 

75  28 

72  16 

69  20 

66  24 

63  28 

61  04 

58  24 

40 

44 

87  26 

83  54 

80  20 

76  48 

73  53 

70  40 

44 

48 

99  50 

95  37 

91  23 

87  56 

84  05 

48 

52 

107  15 

103  12 

98  41 

52 

56 

56 

60 

60 

" 

II 

" 

II 

// 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.57 

3.40 

3.25 

3.10 

2.96 

2.83 

2.71 

2.60 

2.49 

2.38 

2.29 

2.19 

Ajh 

Log. 

0.552 

0.531 

0.511 

0.491 

0.471 

0.451 

0.432 

0.414 

0.396 

0.376 

0.359 

0.340 

Log. 

67 

48 

88 

36 

29 

79 

97 

97 

20 

58 

84 

44 

Limit 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

Min- 
utes 

Merid- 
ian 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

Alti- 
tudes 

60 


Latitude  10°  Declination  Same  Name. 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/  // 

1     II 

1     II 

/  // 

/   // 

1      II 

1     II 

1      II 

1     II 

1     II 

1      II 

1     II 

Min. 

4 

0  34 

0  32 

0  30 

0  30 

0  28 

0  27 

0  27 

0  25 

0  24 

0  22 

0  22 

0  21 

4 

8 

2  14 

2  09 

2  03 

158 

154 

1  50 

1  45 

141 

1  36 

1  33 

128 

124 

8 

12 

5  02 

4  51 

4  38 

4  26 

4  17 

4  06 

3  56 

3  46 

3  36 

3  28 

3  19 

3  10 

12 

16 

8  58 

8  37 

8  14 

7  54 

7  35 

7  18 

7  00 

6  42 

6  24 

6  08 

5  53 

5  38 

16 

20 

14  00 

13  28 

12  52 

12  20 

11  52 

11  24 

10  56 

10  28 

10  00 

9  36 

9  12 

8  48 

20 

24 

20  10 

19  24 

18  31 

17  46 

17  05 

16  25 

15  45 

15  04 

14  24 

13  49 

13  15 

12  41 

24 

28 

27  26 

26  24 

25  14 

24  10 

23  16 

22  21 

21  25 

20  31 

19  36 

18  49 

18  02 

17  15 

28 

32 

35  50 

34  28 

32  57 

3134 

30  23 

29  11 

27  59 

26  48 

25  36 

24  35 

23  33 

22  31 

32 

36 

45  22 

43  38 

4141 

39  58 

38  27 

36  56 

35  26 

33  55 

32  24 

31  06 

29  49 

28  31 

36 

40 

56  00 

53  52 

51  28 

49  20 

47  28 

45  36 

43  44 

4152 

40  00 

38  24 

36  48 

35  12 

40 

44 

67  46 

65  11 

62  16 

59  42 

57  26 

55  10 

52  55 

50  40 

48  24 

46  27 

44  32 

42  36 

44 

48 

80  38 

77  34 

74  07 

71  02 

68  19 

65  38 

62  58 

60  17 

57  36 

55  18 

f2  59 

50  41 

48 

52 

94  38 

9102 

86  59 

83  22 

80  13 

77  04 

73  54 

70  45 

67  36 

64  54 

62  11 

59  29 

52 

56 

105  35 

100  52 

96  42 

93  02 

89  22 

85  43 

82  04 

78  24 

75  15 

72  08 

69  00 

56 

60 

111  00 

106  48 

102  36 

98  24 

94  12 

90  00 

86  24 

82  48 

79  12 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.10 

2.02 

1.93 

1.85 

1.78 

1.71 

1.64 

1.57 

1.50 

1.44 

1.38 

1.32 

A,h 

0.322 

0.305 

0.285 

0.267 

0.250 

0.233 

0.214 

0.195 

0.176 

0.158 

0.139 

0.120 

Log. 

Log. 

22 

35 

56 

17 

42 

00 

84 

90 

09 

36 

88 

57 

Limit 

44 

45 

46 

45 

49 

50 

51 

52 

53 

54 

56 

58 

Min- 
utes 

Merid- 
ian 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60°   61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 
16  28 
2120 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 
75  36 

1.26 

1      II 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 
72  36 
II 

1.21 

1     II 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 

69  00 

II 

1.15 

1     II 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
II 

1.10 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 
II 

1.05 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
II 

1.00 

1     II 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
II 

0.95 

1     II 
0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 

15  22 

19  26 

24  00 

29  02 

34  34 

40  34 

47  02 

54  00 
II 

0.90 

I  II 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

II  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

1     II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

31  06 

36  30 

42  20 

48  36 
II 

0.81 

1     II 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 
II 

0.76 

Oil 
0  45 
142 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  06 
42  36 
II 

0.71 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.100 
37 

0.082 
79 

0.060 
70 

0.041 
39 

0.021 
19 

0.00 

9.977 
72 

9.954 
24 

9.929 
42 

9.908 
49 

9.880 
81 

9.851 
26 

Log. 

Limit 

61 

62 

64 

66 

68 

70 

72 

74 

76 

78 

80 

82 

Min- 
utes 

Merid- 
ian 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

Latitude  J0°  Declination  Contrary  Name. 


61 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

40 

5° 

6° 

70 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

> 

2 
11 
26 

It 
11.1 

59 
53 
44 

4 

1 

2 
10 
24 
43 

It 
10.1 

It 

42 
48 
18 
14 

3 

1 

2 

9 

22 

39 

tt 
9.2 

28 
55 
18 
38 

9 

t 
2 
9 

20 
36 
57 

It 
8.5 

It 

17 
09 
36 
36 
12 

B 

2 

8 

19 

34 

53 

// 
7.9 

07 
30 
08 
00 
08 

7 

1 

7 

17 

31 

49 

II 
lA 

// 

59 
57 
52 
44 
36 

4 

1     It 

151 

7  26 
16  46 
29  46 
46  32 

It 
6.98 

1      It 
145 
7  00 
15  45 
27  59 
43  44 
62  59 

It 
6.56 

t     It 

139 
6  37 
14  53 
26  27 
4120 
59  31 
8101 

6.20 

t     It 

134 
6  16 
14  05 
25  03 
39  08 
56  21 
76  42 

II 
5.87 

/      // 

129 
5  57 
13  22 
23  46 
37  08 
53  28 
72  47 

II 
5.57 

/            II 

125 
5  39 
12  43 
22  37 
35  20 
50  53 
69  15 

It 
5.30 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.046 
89 

1.005 
61 

0.968 
02 

0.933 
49 

0.901 
46 

0.871 
57 

0.843 
86 

0.816 
90 

0.792 
39 

0.768 
64 

0.745 
86 

0.734 

28 

Log. 

Limit 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

Min- 
utes 

Merid- 
ian 

80= 

' 

79' 

) 

78' 

77c 

76' 

3 

75' 

5 

740 

73'^ 

72° 

71° 

70 

D 

69° 

Alti- 
'tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

1     It 

/      II 

1     II 

/      // 

/      // 

/      // 

1      It 

/      // 

Min. 

Min. 

4 

121 

1  17 

1  14 

1  10 

108 

105 

1  02 

100 

0  58 

0  56 

0  54 

0  52 

4 

8 

5  23 

5  08 

4  55 

4  43 

4  32 

4  21 

4  10 

4  02 

3  52 

3  45 

3  36 

3  30 

8 

12 

12  07 

1134 

1103 

10  37 

10  11 

9  46 

9  25 

9  03 

8  42 

8  25 

8  07 

7  51 

12 

16 

2133 

20  34 

19  41 

18  51 

18  05 

17  22 

16  43 

16  05 

15  30 

14  59 

14  25 

13  57 

16 

20 

33  40 

32  08 

30  44 

29  28 

28  16 

27  08 

26  08 

25  08 

24  12 

23  24 

22  32 

21  48 

20 

24 

48  29 

46  17 

44  16 

42  26 

40  42 

39  04 

37  38 

36  11 

34  51 

33  42 

32  27 

3123 

24 

28 

65  59 

62  59 

60  14 

57  46 

55  24 

53  11 

51  14 

49  16 

47  26 

45  52 

44  10 

42  44 

28 

32 

82  15 

78  40 

75  26 

72  22 

69  28 

65  54 

64  21 

6157 

59  54 

57  41 

55  49 

32 

36 

78  25 

75  49 

73  01 

70  38 

36 

40 

90  08 

87  12 

40 

44 

. . . 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

It 

It 

It 

ti 

II 

II 

It 

It 

It 

It 

It 

A,h 

5.05 

4.82 

4.61 

4.42 

4.24 

4.07 

3.92 

3.77 

3.63 

3.51 

3.38 

3.27 

A,h 

Log. 

0.703 

0.683 

0.663 

0.645 

0.627 

0.609 

0.593 

0.576 

0.559 

0.545 

0.528 

0.514 

Log. 

29 

05 

70 

42 

37 

59 

29 

34 

91 

31 

92 

55 

Limit 

25 

26 

27 

27 

28 

29 

30 

31 

31 

32 

33 

34 

Min- 
utes 

Merid- 
ian 

68 

D 

67° 

66° 

65 

5 

64 

3 

63' 

3 

62° 

61° 

60° 

59° 

58° 

57° 

Alti- 
tudes 

62 


Latitude  10°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

t       It 

'      " 

1       n 

f     II 

1      II 

1      II 

/      // 

/      // 

/      // 

1     II 

1      II 

1     II 

Min. 

4 

0  51 

0  49 

0  47 

0  46 

0  44 

0  43 

0  42 

0  40 

0  39 

0  38 

0  37 

0  36 

4 

8 

3  22 

3  16 

3  09 

3  03 

2  58 

2  52 

2  47 

2  42 

2  37 

2  32 

2  28 

2  24 

8 

12 

7  35 

7  21 

7  07 

6  52 

6  39 

6  27 

6  15 

6  04 

5  53 

5  43 

5  32 

5  23 

12 

16 

13  29 

13  03 

12  37 

12  12 

1149 

1129 

1109 

10  48 

10  27 

10  09 

9  52 

9  33 

16 

20 

2104 

20  24 

19  44 

19  04 

18  28 

17  56 

17  24 

16  52 

16  20 

15  52 

15  24 

14  56 

20 

24 

30  21 

29  23 

28  25 

27  28 

26  35 

25  50 

25  04 

24  17 

23  31 

22  51 

22  11 

21  30 

24 

28 

41  17 

39  59 

38  41 

37  22 

36  12 

35  09 

34  06 

33  04 

32  01 

3106 

30  11 

29  16 

28 

32 

53  55 

52  13 

50  31 

48  48 

47  17 

45  54 

44  32 

43  11 

4149 

40  37 

39  25 

38  14 

32 

36 

68  16 

66  06 

63  56 

6147 

59  50 

58  07 

56  23 

54  39 

52  55 

5125 

49  54 

48  23 

36 

40 

84  16 

8136 

78  56 

76  16 

73  52 

71  44 

69  36 

67  28 

65  20 

63  28 

6136 

59  44 

40 

44 

86  48 

84  13 

81  38 

79  03 

76  48 

74  32 

72  16 

44 

48 

94  05 

91  23 

88  42 

86  01 

48 

52 

107  15 

104  06 

100  57 

52 

56 

56 

60 

60 

n 

n 

n 

II 

II 

II 

II 

II 

II 

II 

II 

" 

A,h 

3.16 

3.06 

2.96 

2.86 

2.77 

2.69 

2.61 

2.53 

2.45 

2.38 

2.31 

2.24 

A,h 

Log. 

0.499 

0.485 

0.471 

0.456 

0.442 

0.429 

0.416 

0.403 

0.389 

0.376 

0.363 

0.350 

Log. 

69 

72 

29 

37 

48 

75 

64 

12 

17 

58 

61 

25 

liirait 

35 

36 

37 

38 

39 

40 

41 

41 

42 

43 

44 

45 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
3e 
40 
44 
48 
52 
56 
60 

Ajh 

/      II 

0  35 

2  19 

5  12 

9  16 

14  28 

20  50 

28  51 

37  02 

46  53 

57  52 

70  02 

83  19 

97  47 

II 
2.YI 

/      II 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

II 
2.11 

1      II 

0  33 

2  11 

4  55 

8  45 

13  40 

19  41 

26  47 

34  59 

44  17 

54  40 

66  09 

78  43 

92  23 

II 
2.05 

0  31 

2  07 

4  47 

8  29 

13  16 

19  06 

26  01 

33  58 

42  59 

53  04 

64  12 

76  25 

89  41 

104  01 

II 
1.99 

/      // 

0  30 

2  03 

4  38 

8  14 

12  52 

18  31 

25  14 

32  57 

41  41 

51  28 

62  16 

74  07 

86  59 

100  52 

II 
1.93 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

31  55 

40  24 

49  52 

60  21 

71  48 

84  16 

97  45 

112  12 

II 

1.87 

1     II 

0  29 

1  56 
4  22 
7  46 

12  08 

17  29 

23  47 

3103 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 
II 

1.82 

1     II 

0  28 

1  54 
4  16 
7  33 

1148 
16  59 
23  08 
30  13 
38  14 
47  12 
57  07 
67  56 
79  46 
92  31 
106  12 
II 

1.77 

I  II 

0  27 
150 
4  08 
7  20 

II  28 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 
II 

1.72 

/      // 

0  27 

147 

4  00 

7  08 

1108 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12' 
II 

1.67 

1     II 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 

II 

1.62 

1      II 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 

94  12 

II 

1.57 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.336 
46 

0.324 
28 

0.311 
75 

0.298 
85 

0.285 
56 

0.271 
84 

0.260 
07 

0.247 
97 

0.235 
53 

0.222 
72 

0.209 
52 

0.195 
90 

Log. 

Limit 

46 

47 

48 

49 

49 

50 

51 

52 

53 

54 

55 

56 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

Latitude  J0°  Declination  Contrary  Name. 


63 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

1      II 

1      II 

/  II 

1      II 

1      II 

1      II 

1      II 

/   // 

1      II 

1      II 

'   " 

/  II 

Min. 

4 

0  24 

0  23 

0  22 

0  22 

0  22 

0  21 

0  20 

0  19 

0  19 

0  19 

0  18 

0  17 

4 

8 

138 

1  35 

133 

1  29 

126 

123 

1  21 

1  18 

1  15 

1  13 

1  11 

1  08 

8 

12 

3  40 

3  34 

3  28 

3  20 

3  14 

3  08 

3  02 

2  56 

2  50 

2  44 

2  39 

2  34 

12 

16 

6  32 

6  18 

6  08 

5  56 

5  46 

5  36 

5  22 

5  12 

5  02 

4  52 

4  45 

4  34 

16 

20 

10  12 

9  52 

9  36 

9  16 

9  00 

8  44 

8  24 

8  08 

7  52 

7  36 

7  24 

7  08 

20 

24 

14  41 

14  12 

13  49 

13  21 

12  58 

12  35 

12  06 

11  43 

1120 

10  57 

10  40 

10  16 

24 

28 

20  00 

19  21 

18  49 

18  10 

17  38 

17  07 

16  28 

15  57 

15  25 

14  53 

14  30 

13  59 

28 

32 

26  07 

25  16 

24  35 

23  43 

23  02 

22  21 

21  30 

20  49 

20  08 

19  27 

18  56 

18  16 

32 

36 

33  03 

31  58 

3106 

30  02 

29  10 

28  18 

27  13 

26  21 

25  30  24  38 

23  59 

23  07 

36 

40 

40  48 

39  28 

38  24 

37  04 

36  00 

34  56 

33  36 

32  32 

31  28j  30  24 

29  36 

28  32 

40 

44 

49  22 

47  45 

46  27 

44  51 

43  34 

42  16 

40  39 

39  22 

38  05  36  47 

35  49 

34  32 

44 

48 

58  45 

56  50 

55  18 

53  22 

51  50 

50  18 

48  23 

46  51 

45  18  43  46 

42  37 

41  05 

48 

52 

68  57 

66  42 

64  54 

62  38 

60  50 

59  02 

56  47 

54  29 

53  10  51  22 

50  01 

48  13 

52 

56 

79  58 

77  21 

75  15 

72  39 

70  34 

68  28 

65  51 

63  46 

61  41  59  35 

58  01 

55  56 

56 

60 

9148 

88  48 

86  24 

83  24 

8100 

78  36 

75  36 

73  12 

70  48  68  24 

66  36 

64  12 

60 

II 

II 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

A,h 

1.53 

1.48 

1.44 

1.39 

1.35 

1.31 

1.26 

1.22 

1.18 

1.14 

1.11 

1.07 

A,h 

Log. 

0.184 

0.170 

0.158 

0.143 

0.130 

0.117 

0.100 

0.086 

0.071 

0.056 

0.045 

0.029 

Log. 

69 

26 

36 

01 

33 

27 

37 

36 

88 

90 

32 

38 

Limit 

57 

58 

60 

61 

62 

64 

66 

68 

69 

0 

70 

72 

74 

Min- 
utes 

Merid- 
ian 

32° 

31° 

30° 

29°  j  28° 

27° 

26° 

25° 

24°   23° 

22° 

21° 

Alti- 
tudes 

Deci,in.\tions. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

1     II 

0  15 

1  03 

2  23 
4  13 
6  36 
9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

51  44 

59  24 
II 

0.99 

1     II 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
II 

0.95 

/   // 

0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 

15  42 

19  52 

24  32 

29  41 

35  20 

4128 

48  05 

55  12 
II 

0.92 

1     II 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
If 

0.88 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 
50  24 
II 

0.84 

1      II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

/  II 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

0.77 

1     II 

0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 

15  59 

19  44 

23  52 

28  23 

33  21 

38  40 

44  24 
II 

0.74 

1      II 

0  11 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

31  33 

36  35 

42  00 
II 

0.70 

1      II 

0  11 

0  42 

1  36 

2  52 
4  28 
6  26 
8  45 

1126 

14  29 

17  52 

21  38 

25  43 

30  11 

35  02 

40  12 
II 

0.67 

1     II 

Oil 

0  40 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
II 

0.64 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.012 

84 

9.995 
64 

9.977 
72 

9.963 
79 

9.944 
48 

9.924 

28 

9.908 
49 

9.886 
49 

9.869 
23 

9.845 
10 

9.826 
07 

9.806 
18 

Log. 

Limit 

75 

76 

77 

78 

79 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9°  1 

Alti- 
tudes 

64 


Latitude  ii°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 
10 
24 
43 

■  • 
10.1 

n 

42 
46 
14 
06 

0 

1 

2 
11 
26 

II 
11.1 

n 

58 
50 
38 

0 

1       n 

3  17 
13  08 
29  32 

II 
12.31 

3 
14 
33 

II 
13.8 

II 

42 
45 
11 

3 

1       n 

4  12 
16  50 
37  53 

II 
15.78 

4 
19 

II 
18.3 

54 
36 

7 

1 

5 
23 

■  ■ 

II 
21.9 

n 

52 
27 

9 

t       n 
If 

1 

II 

n 

1 

n 

// 

ir 

1     II 
II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.004 
32 

1.045 
32 

1.090 
26 

1.140 

82 

1.198 
11 

1.264 
11 

1.342 
23 

Log. 

Liiuit 

14 

13 

12 

11 

10 

9 

7 

6 

5 

3 

1 

0 

Min- 
utes 

Merid- 
ian 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/      II 

1     II 

1     II 

1      II 

1      II 

1     II 

/     // 

/      // 

1     II 

/       n 

1     It 

Min. 

4 

5  40 

4  43 

4  01 

3  29 

3  05 

2  46 

2  30 

2  16 

4 

8 

22  41 

18  48 

16  03 

13  58 

12  21 

1103 

10  00 

9  06 

8 

12 

36  06 

31  25 

27  48 

24  52 

22  29 

20  28 

12 

16 

44  12 

39  59 

36  24 

16 

20 

56  52 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

II 

II 

// 

II 

'/ 

n 

II 

II 

II 

II 

II 

A,h 

21.26 

17.63 

15.04 

13.09 

11.58 

10.36 

9.37 

8.53 

A,h 

Log. 

1.327 

1.246 

1.177 

1.116 

1.063 

1.015 

0.971 

0.930 

Log. 

56 

25 

25 

94 

71 

36 

74 

95 

Limit 

2 

4 

5 

7 

8 

9 

10 

11 

13 

15 

16 

17 

Min- 
utes 

Merid- 
ian 

I 

19 

3 

88° 

87° 

8 

6° 

85° 

84' 

' 

83< 

> 

82° 

81 

3 

80 

3 

79° 

78° 

Alti- 
tudes' 

Latitude  M°  Declination  Same  Name. 


65 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

f 

2 

8 
18 
33 
52 

n 

7.8 

05 
21 
47 
25 
12 

3 

f 

1 

7 
17 
30 
48 

II 
7.2 

// 

55 
42 
20 

48 
08 

2 

1 

1 
2 
A 
6 

6 

1 
7 
6 
8 
4 
4 

// 
.6 

// 

47 
08 
03 
33 
36 
14 

9 

1 

1 

2 
4 

5 

8 

6 

II 

1  39 
6  39 
4  57 
6  35 
1  32 
9  48 
1  25 

II 
.23 

1 

1 
2 
3 
5 
7 

S 

1 
6 
3 

4 
8 
5 
6 

'/ 

.8 

II 

33 

12 
58 
50 
48 
53 
03 

2 

I 

1 
2 
3 
5 
7 

S 

1 
5 
3 
3 
6 
2 
1 

// 
.4 

II 

27 
50 
07 
17 
24 
25 
21 

6 

1 

1 

2 
3 
4 
6 

1 
5 

2 
1 
4 
9 

7 

// 
.1 

// 

22 
28 
18 
54 
12 
15 
02 

3 

1      II 

1  17 
5  09 
1135 
20  37 
32  12 
46  22 
63  07 
82  26 

II 
4.83 

/      // 

1  13 
4  52 
10  57 
19  27 
30  24 
43  47 
59  35 
77  49 

II 
4.56 

1      II 

109 
4  36 
10  22 
18  26 
28  48 
41  29 
56  27 
73  43 

II 
4.32 

1     II 

105 

4  22 
9  49 
17  27 
27  16 
39  16 
53  27 
69  48 

II 
4.09 

/      II 

1  02 

4  08 
9  19 
16  33 
25  52 
37  15 
50  42 
66  13 

II 
3.88 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.893 
76 

0.858 
54 

0.825 
43 

0.794 
49 

0.764 
92 

0.737 
19 

0.710 
12 

0.683 
95 

0.658 
96 

0.635 

48 

0.611 

72 

0.588 
83 

Log. 

Limit 

18 

19 

20 

21 

22 

23 

24 

26 

27 

28 

29- 

30 

Min- 
utes 

Merid- 
ian 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1      II 

1     II 

/      // 

1      II 

1     II 

1     II 

1      II 

1      II 

1     II 

/      // 

1      II 

1      II 

Min. 

4 

0  59 

0  56 

0  54 

0  51 

0  49 

0  46 

0  44 

0  43 

0  41 

0  39 

0  37 

0  36 

4 

8 

3  56 

3  45 

3  34 

3  24 

3  15 

3  06 

2  58 

2  50 

2  43 

2  37 

2  29 

2  24 

8 

12 

8  51 

8  25 

8  02 

7  39 

7  19 

6  59 

6  41 

6  23 

6  07 

5  52 

5  35 

5  23 

12 

16 

15  45 

14  59 

14  18 

13  37 

13  01 

12  25 

1151 

1121 

10  53 

10  24 

9  57 

9  33 

16 

20 

24  36 

23  24 

22  20 

21  16 

20  20 

19  24 

18  32 

17  44 

17  00 

16  16 

15  32 

14  56 

20 

24 

35  26 

33  42 

32  10 

30  38 

29  17 

27  56 

26  41 

25  33 

24  29 

23  25 

22  22 

21  30 

24 

28 

48  13 

45  52 

43  46 

4141 

39  51 

38  02 

36  20 

34  45 

33  19 

3153 

30  27 

29  16 

28 

32 

62  58 

59  54 

57  10 

54  26 

52  03 

49  40 

47  27 

45  23 

43  31 

41  39 

39  46 

38  14 

32 

36 

79  43 

75  49 

72  22 

68  55 

65  53 

62  51 

60  03 

57  28 

55  05 

52  42 

50  20 

48  23 

36 

40 

89  20 

85  04 

8120 

77  36 

74  08 

70  56 

68  00 

65  04 

62  08 

59  44 

40 

44 

85  50 

82  17 

78  43 

75  11 

72  16 

44 

48 

93  42 

89  28 

86  01 

48 

52 

105  00 

100  57 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.69 

3.51 

3.35 

3.19 

3.05 

2.91 

2.78 

2.66 

2.55 

2.44 

2.33 

2.24 

A,h 

Log. 

0.567 

0.545 

0.525 

0.503 

0.484 

0.463 

0.444 

0.424 

0.406 

0.387 

0.367 

0.350 

Log. 

03 

31 

04 

79 

30 

89 

04 

88 

54 

39 

36 

25 

Limit 

31 

32 

33 

34 

35 

37 

38 

39 

40 

40 

41 

42 

Min- 
utes 

Merid- 
ian 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

Alti- 
tudes 

66 


Latitude  M°  Declination  Same  Name 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/  // 

/  // 

1     II 

1      II 

1      II 

/  // 

I      II 

1     II 

/  // 

1      II 

1     II 

1     II 

Min. 

4 

0  35 

033 

0  31 

0  30 

0  29 

0  27 

0  27 

0  25 

0  24 

0  23 

0  22 

0  22 

4 

8 

2  17 

2  11 

2  05 

2  01 

1  56 

151 

146 

142 

137 

1  34 

130 

1  26 

8 

12 

5  08 

4  55 

4  44 

4  32 

4  20 

4  09 

3  59 

3  49 

3  39 

3  31 

3  22 

3  13 

12 

16 

9  08 

8  45 

8  24 

'  8  04 

7  44 

7  23 

7  05 

6  47 

6  29 

6  13 

5  58 

5  43 

16 

20 

14  16 

13  40 

13  08 

12  36 

12  04 

11  32 

1104 

10  36 

10  08 

9  44 

9  20 

8  56 

20 

24 

20  33 

19  41 

18  54  18  09 

17  23 

16  36 

15  57 

15  16 

14  36 

14  01 

13  26 

12  52 

24 

28 

27  57 

26  47 

25  45  24  42 

23  39 

22  37 

2141 

20  47 

19  52 

19  05 

18  18 

17  30 

28 

32 

36  31 

34  59 

33  38  32  15 

30  53 

29  32 

28  19 

27  08 

25  56 

24  55 

23  54 

22  52 

32 

36 

46  14 

44  17 

42  33  40  50 

39;;o6 

37  22 

35  52 

34  21 

32  50 

31  32 

30  14 

28  57 

36 

40 

57  04 

54  40 

52  32  50  24 

48  16 

46  08 

44  16 

42  24 

40  32 

38  56 

37  20 

35  44 

40 

44 

69  03 

66  09 

63  34 

60  59 

58  24 

55  49 

53  34 

51  18 

49  03 

47  06 

45  10 

43  14 

44 

48 

82  10 

78  43 

75  39 

72  34 

69  30 

66  24 

63  44 

6103 

58  22 

56  04 

53  46 

51  27 

48 

52 

96  26 

92  23 

88  47 

85  10 

8134 

77  58 

74  48 

7139 

68  30 

65  48 

63  06 

60  23 

52 

56 

107  09 

102  57 

98  47 

94  36 

90  25 

86  46 

83  06 

79  27 

76  18 

73  10 

70  02 

56 

60 

113  24 

108  36 

103  48 

99  36 

95  24 

91  12 

87  36 

84  00 

80  24 

60 

It 

II 

// 

// 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

2.14 

2.05 

1.97 

1.89 

1.81 

1.73 

1.66 

1.59 

1.52 

1.46 

1.40 

1.34 

A,h 

Log. 

0.330 

0.311 

0.294 

0.276 

0.257 

0.238 

0.220 

0.201 

0.181 

0.164 

0.146 

0.127 

Log. 

41 

75 

47 

46 

68 

05 

11 

40 

84 

35 

13 

10 

Limit 

43 

44 

45 

47 

48 

50 

51 

52 

53 

54 

56 

58 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

I  II 

0  19 

1  18 

2  56 
5  12 
8  08 

II  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 
73  12 

1.22 

1      II 

0  19 

114 

2  47 

4  57 

7  44 

1109 

15  09 

19  47 

25  04 

30  56 

37  26 

44  32 

52  16 

60  38 

69  36 
II 

1.16 

1     II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 

14  30 

18  56 

23  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 
II 

1.11 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

II 

1.06 

1      II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

21  49 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

II 

1.01 

/   // 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

II 

0.96 

1      II 
0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

II 

0.91 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

5136 
II 

0.86 

/  // 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

1      II 

0  12 

0  50 

1-51 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

0.77 

/   // 

0  11 

0  47 

1  45 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

Min. 

4 

8 
12 
16 
20 
24 
28 

32  ■ 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.107 
21 

0.086 
36 

0.064 
46 

0.045 
32 

0.025 
31 

0.004 
32 

9.982 
27 

9.959 
04 

9.934 
50 

9.908 
49 

9.886 
49 

9.863 
32 

Log. 

Limit 

60 

62 

64 

66 

68 

70 

71 

73 

75 

77 

79 

81 

Min- 
utes 

Merid- 
ian 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

Latitude  11°  Declination  Contrary  Name. 


67 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

2 
10 
24 
43 

n 

10.1 

42 

46 
14 
06 

0 

1 

2 

9 

22 
39 

n 

9.2 

28 
54 
15 
33 

7 

2 

9 

20 
36 
57 

II 
8.5 

// 

17 

08 
33 
31 
04 

6 

2 
8 

19 

33 

53 

II 
7.9 

// 

07 
29 
07 
57 
04 

6 

1 

7 

17 
31 
49 

II 
1A 

II 

58 
56 
50 
42 
32 

3 

/ 

1 

7 

16 
29 
46 

II 
6.9 

II 

51 
26 
44 

44 

28 

7 

1     II 

145 
7  00 
15  45 
27  59 
43  44 
62  59 

" 
6.56 

/     // 

139 
6  36 
14  51 
26  25 
41  16 
59  26 
80  53 

II 
6.19 

/     // 

134 
6  15 
14  04 
25  00 
39  04 
56  16 
76  34 

II 
5.86 

1     II 

129 
5  57 
13  22 
23  46 
37  08 
53  28 
72  47 

If 
5.57 

1      II 

1  25 
5  39 
12  43 
22  37 
35  20 
50  53 
69  15 

II 
5.30 

1      II 

1  21 
5  23 
12  07 
21  33 
33  40 
48  29 
65  59 

II 
5.05 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.004 
32 

0.967 
08 

0.932 
47 

0.900 
91 

0.870 
99 

0.843 
23 

0.816 
90 

0.791 
69 

0.767 
90 

0.745 
86 

0.724 

28 

0.703 
29 

Log. 

Limit 

14 

15 

16 

17 

18        19 

20 

21 

22 

23 

24 

25 

Min- 
utes 

Merid- 
ian 

79° 

78° 

77° 

76° 

75°      74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

1     II 

1     II 

/      // 

/     // 

1     II 

1      II 

1      II 

1     II 

1     II 

1      II 

/      // 

Min. 

4 

1  17 

114 

110 

108 

105 

102 

100 

0  59 

0  56 

0  54 

0  52 

0  51 

4 

8 

5  09 

4  55 

4  44 

4  32 

4  21 

4  11 

4  02 

3  53 

3  45 

3  38 

3  30 

3  23 

8 

12 

1135 

1105 

10  38 

10  12 

9  48 

9  26 

9  05 

8  44 

8  27 

8  10 

7  53 

7  36 

12 

16 

20  37 

19  43 

18  54 

18  08 

17  24 

16  46 

16  07 

15  32 

15  01 

14  30 

13  59 

13  32 

16 

20 

32  12 

30  48 

29  32 

28  20 

27  12 

26  12 

25  12 

24  16 

23  28 

22  40 

21  52 

21  08 

20 

24 

46  22 

44  22 

42  31 

40  48 

39  10 

37  43 

36  17 

34  57 

33  48 

32  38 

31  29 

30  26 

24 

28 

63  07 

60  22 

57  54 

55  32 

53  19 

51  22 

49  24 

47  33 

46  00 

44  26 

42  52 

4125 

28 

32 

82  26 

78  50 

75  37 

72  32 

69  38 

67  05 

64  31 

62  07 

60  04 

58  02 

55  59 

54  06 

32 

36 

... 

78  38 

76  02 

73  26 

70  51 

68  29 

36 

40 

90  40 

87  28 

84  32 

40 

44 

44 

48 

48 

52 

52 

56 

e    .    . 

56 

60 

60 

II 

n 

II 

n 

II 

II 

II 

II 

II 

II 

II 

1/ 

Aih 

4.83 

4.62 

4.43 

4.25 

4.08 

3.93 

3.78 

3.64 

3.52 

3.40 

3.28 

3.17 

Aih 

Log. 

0.683 

0.664 

0.646 

0.628 

0.610 

0.594 

0.577 

0.561 

0.546 

0.531 

0.515 

0.501 

Log. 

95 

64 

40 

39 

66 

39 

49 

10 

54 

48 

87 

06 

Limit 

26 

27 

28 

28 

29 

30 

31 

32 

32 

33 

34 

35 

Min- 
utes 

Merid- 
ian 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

68 


Latitude  n°  Declination  Contrary  Name* 


Dkclinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0 
3 
7 
13 
20 
29 
40 
52 
66 
81 

n 

3.0 

49 
17 
22 
06 
28 
28 
07 
24 
19 
52 

7 

0 
3 
7 
12 
19 
28 
38 
50 
64 
79 

II 
2.S 

47 
10 
08 
40 
48 
30 
49 
42 
09 
12 

7 

0  46 
3  04 
6  55 
12  17 
19  12 
27  39 
37  38 
49  09 
62  13 
76  48 

II 

2.88 

1 

0 
2 
6 
11 
18 
26 
36 
47 
60 
74 

II 

in 

// 

44 
59 
42 
54 
36 
47 
28 
37 
16 
24 

9 

1     II 

0  43 
2  53 
6  29 
1131 
18  00 
25  55 
35  17 
46  05 
58  19 
72  00 
87  07 

II 
2.70 

I  II 

0  42 
2  47 
6  17 

II  11 
17  28 
25  10 
34  14 
44  42 
56  36 
69  52 
84  33 

n 
2.62 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  11 
43  21 
54  52 
67  44 
8157 

II 
2.54 

1     II 

0  39 

2  39 

5  56 

10  32 

16  28 

23  42 

32  17 

42  10 

53  21 

65  52 

79  42 

94  51 

n 

2.47 

0  38 

2  34 

5  46 

10  14 

16  00 

23  02 

31  22 

40  58 

51  50 

64  00 

77  26 

92  10 

108  10 

II 
2.40 

1     II 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

II 
2.33 

1      II 

0  36 

2  25 

5  26 

9  38 

15  04 

2142 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

10151 

II 
2.26 

1     II 

0  35 

2  20 

5  15 

9  21 

14  36 

2102 

28  37 

37  22 

47  19 

58  24 

70  40 

84  05 

98  41 

II 
2.19 

Min, 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.487 
14 

0.472 
76 

0.459 
39 

0.445 
60 

0.431 
36 

0.418 
30 

0.404 
83 

0.392 
70 

0.380 
21 

0.367 
36 

0.354 
11 

0.340 
44 

Log. 

Limit 

36 

37 

38 

39 

40 

41 

42 

42 

43 

44 

45 

46 

Min- 
utes 

Merid- 
ian 

55 

3 

54 

°l 

53° 

52 

= 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1      II 

0  34 

2  16 

5  06 

9  06 

14  12 

20  27 

27  50 

36  21 

46  01 

56  48 

68  44 

81  46 

95  59 

2.13 

1      II 

0  33 

2  13 

4  58 

8  50 

13  48 

19  52 

27  03 

35  20 

44  43 

55  12 

66  48 

79  29 

93  17 

108  12 

II 
2.07 

/      // 

0  32 

2  09 

4  49 

8  35 

13  24 

19  18 

26  16 

34  18 

43  25 

53  36 

64  51 

77  11 

90  35 

105  03 

II 
2.01 

/      // 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

II 
1.96 

/      // 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

4102 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 

II 

1.90 

/      // 

0  30 

1  58 
4  25 
7  51 

12  16 
17  40 
24  02 
3124 
39  45 
49  04 
59  22 
70  39 
82  55 
96  10 
110  24 
II 

1.84 

1     II 

0  28 

155 

4  18 

7  38 

1156 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 

II 

1.79 

/     II 

0  28 

152 

4  11 

7  25 

1136 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

104  24 
II 

1.74 

I  II 

0  27 
148 
4  03 
7  13 

II  16 

16  14 

22  05 

28  50 

36  31 

45  04 

54  32 

64  53 

76  09 

88  20 

10124 
II 

1.69 

/      // 

0  27 

145 

3  56 

7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 

II 

1.64 

/      // 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 
II 

1.60 

1      II 

0  25 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

8101 

93  00 
II 

1.55 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.328 
38 

0.315 
97 

0.303 
20 

0.292 
26 

0.278 
75 

0.264 

82 

0.252 
85 

0.240 
55 

0.227 
89 

0.214 

84 

0.204 
12 

0  190 
33 

Log. 

Limit 

46 

47 

48 

49 

49 

50 

51 

52 

53 

54 

55 

56 

Min- 
utes 

Merid- 
ian 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

Alti- 
tudes 

Latitude  ti°  Decimation  Q)ntrary  Name. 


69 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

f       II 

1     II 

1     II 

/  II 

/  II 

1     II 

1      II 

1     II 

1     II 

1     II 

/  // 

1     II 

Min. 

4 

0  24 

0  23 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

0  19 

0  18 

0  17 

0  17 

4 

8 

1  36 

134 

131 

128 

125 

123 

1  20 

1  17 

1  15 

1  12 

1  10 

1  08 

8 

12 

3  36 

3  31 

3  25 

3  17 

3  11 

3  06 

3  00 

2  54 

2  48 

2  42 

2  37 

2  33 

12 

16 

6  24 

6  13 

6  03 

5  51 

5  41 

5  30 

5  20 

5  10 

5  00 

4  50 

4  39 

4  31 

16 

20 

10  00 

9  44 

9  28 

9  08 

8  52 

8  36 

8  20 

8  04 

7  48 

7  32 

7  16 

7  04 

20 

24 

14  24 

14  01 

13  38 

13  09 

12  46 

12  23 

12  00 

1137 

11  14 

10  51 

10  28 

10  11 

24 

28 

19  36 

19  05 

18  34 

17  54 

17  23 

16  52 

16  20 

15  49 

15  17 

14  46 

14  15 

13  51 

28 

32 

25  36 

24  55 

24  14 

23  23 

22  42 

22  01 

21  20 

20  39 

19  58 

19  17 

18  36 

18  05 

32 

36 

32  24 

31  32 

30  40 

29  36 

28  44 

27  52 

27  00 

26  08 

25  17 

24  25 

23  33 

22  54 

36 

40 

40  00 

38  56 

37  52 

36  32 

35  28 

34  24 

33  20 

32  16 

31  12 

30  08 

29  04 

28  16 

40 

44 

48  24 

47  06 

45  49 

44  13 

42  55 

41  37 

40  20 

39  02 

37  46 

36  28 

35  10 

34  12 

44 

48 

57  36 

56  04 

54  32 

52  36 

5104 

49  32 

48  00 

46  28 

44  55 

43  23 

41  51 

40  42 

48 

52 

67  36 

65  48 

64  00 

61  44 

59  56 

58  08 

56  20 

54  32 

52  43 

55  55 

49  07 

47  46 

52 

56 

78  24 

76  18 

74  13 

71  37 

69  31 

67  25 

65  20 

63  14 

61  10 

59  04 

56  58 

55  24 

56 

60 

90  00 

87  36 

85  12 

82  12 

79  48 

77  24 

75  00 

72  36 

70  12 

67  48 

65  24 

63  36 

60 

II 

II 

II 

n 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.50 

1.46 

1.42 

1.37 

1.33 

1.29 

1.25 

1.21 

1.17 

1.13 

1.09 

1.06 

A,h 

Log. 

0.176 

0.164 

0.152 

0.136 

0.123 

0.110 

0.096 

0.082 

0.068 

0.053 

0.037 

0.025 

Log. 

09 

35 

29 

72 

85 

59 

91 

.  79 

19 

08 

43 

31 

Limit 

57 

59 

61 

62 

64 

65 

67 

69 

70 

71 

72 

74 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1      II 

1      II 

1      II 

1     II 

1      II 

1      II 

1      II 

/   // 

/  II 

1      II 

/  // 

/  // 

Min. 

4 

0  16 

0  15 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

Oil 

Oil 

Oil 

Oil 

4 

8 

105 

102 

101 

0  58 

0  55 

0  54 

0  51 

0  50 

0  47 

0  45 

0  42 

0  40 

8 

12 

2  27 

2  22 

2  17 

2  11 

2  05 

2  01 

1  55 

151 

1  45 

1  41 

136 

132 

12 

16 

4  21 

4  10 

4  03 

3  53 

3  43 

3  35 

3  25 

3  17 

3  07 

2  59 

2  52 

2  44 

16 

20 

6  48 

6  32 

6  20 

6  04 

5  48 

5  36 

5  20 

5  08 

4  52 

4  40 

4  28 

4  16 

20 

24 

9  48 

9  24 

9  07 

8  44 

8  21 

8  04 

7  41 

7  23 

7  00 

6  43 

6  26 

6  09 

24 

28 

13  20 

12  49 

12  25 

1154 

11  22 

10  58 

10  27 

10  04 

9  33 

9  09 

8  45 

8  21 

28 

32 

17  24 

16  44 

16  13 

15  32 

14  51 

14  20 

13  39 

13  09 

12  28 

11  57 

11  26 

10  55 

32 

36 

22  02 

21  10 

20  31 

19  39 

18  48 

18  09 

17  17 

16  38 

15  46 

15  07 

14  29 

13  50 

36 

40 

27  12 

26  08 

25  20 

24  16 

23  12 

22  24 

21  20 

20  32 

19  28 

18  40 

17  52 

17  04 

40 

44 

32  55 

3137 

30  39 

29  21 

28  05 

27  06 

25  49 

24  51 

23  33 

22  35 

21  38 

20  39 

44 

48 

39  10 

37  38 

36  29 

34  57 

33  24 

32  15 

30  43 

29  32 

28  00 

26  51 

25  43 

24  34 

48 

52 

45  58 

44  10 

42  49 

4101 

39  12 

37  51 

36  03 

34  42 

32  54 

3133 

30  11 

28  50 

52 

56 

53  19 

51  13 

49  39 

47  33 

45  29 

43  54 

4149 

40  15 

38  09 

36  35 

35  02 

33  27 

56 

60 

61  12 

58  48 

57  00 

54  36 

52  12 

50  24 

48  00 

46  12 

43  48 

42  00 

40  12 

38  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

n 

II 

II 

II 

A,h 

1.02 

0.98 

0.95 

0.91 

0.87 

0.84 

0.80 

0.77 

0.73 

0.70 

0.67 

0.64 

Ajh 

Log. 

0.008 

9.991 

9.977 

9.959 

9.939 

9.924 

9.903 

9.886 

9.863 

9.845 

9.826 

9.806 

Log. 

60 

23 

72 

04 

.   52 

28 

09 

49 

32 

10 

07 

18 

Limit 

76 

77 

78 

79 

79 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

Alti- 
tudes 

70 


Latitude  J  2°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

P 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t 

2 

9 

22 
39 

II 
9.2 

28 
52 
11 
25 

4 

1 

2 
10 
24 
42 

II 
10.0 

n 

41 
44 
09 
55 

6 

2 
11 
26 

II 
11.0 

// 

57 
47 
31 

5 

3 

13 
29 

II 
12.2 

16 
05 
26 

6 

3_ 
14 
33 

n 

13.7 

iQ 
22 
03 

7 

1 

4 
16 
37 

II 
J5.7 

11 
45 
41 

0 

1 

4 
19 

n 
18.2 

II 
52 
30 

7 

1     II 

5  50 
23  20 

H 

21.87 

n 

// 

II 

// 

1 
II 

// 

1 

n 

// 

Min. 
4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.965 
67 

1.002 
60 

1.043 
36 

1.088 
49 

1.138 
93 

1.195 
90 

1.261 

74 

1.339 
85 

Log. 

Limit 

15 

14 

13 

12 

11 

10 

8 

7 

6 

5 

3 

1 

Min- 
utes 

ISIeiid- 
ian 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

Alti- 
tudes 

Declinations. 


Hour       I 
Angles 

2°       ] 

L3° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min.      ' 
4 

//    1 

II 

/           ft 

1 

// 

/ 

// 

1     II 
5  37 

1     II 
4  39 

1     II 
3  58 

1      II 
3  27 

3  03 

2  44 

1     II 

2  28 

Min. 
4 

8 

22  29 

18  39 

15  53 

13  50 

12  14 

10  56 

9  54 

8 

12 

35  46 

31  08 

27  31 

24  36 

22  15 

12 

16 

43  44 

39  33 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

A,h      . 

II 

'^ 

II 

1 

1 

/ 

II 
21.07 

n 

17.47 

II 
14.90 

II 
12.97 

n 
11.46 

II 
10.25 

9.27 

A,h 

- 

1.323 

1.242 

1.173 

1.112 

1.059 

1.010 

0.967 

Log. 

Log. 

66 

29 

19 

94 

18 

72 

08 

Limit 

0 

2 

4 

5 

7 

8 

9 

10 

12 

14 

15 

16 

Min- 
utes 

Merid-      ( 
ian 

0° 

B9° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

Alti- 
tudes 

Latitude  12°  Declination  Same  Name. 


71 


Declinations. 


Hour      94^0 
Angles     '^* 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34°  1   35° 

Hour 

Angles 

Miu. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A.h 

2 

9. 

20 

36 

56 

n 
8.4 

n 

15 
01 
16 
00 
16 

4 

2 

8 
18 
33 
51 

II 

7.7 

II 

04 

16 
35 
01 
36 

4 

1 

1 

7 

17 

30 

47 

II 
7.1 

// 

55 
37 

08 
28 
36 

4 

1 
7 
15 
28 
44 
63 

II 
6.6 

46 
03 
51 
13 
04 
28 

1 

1 

1 
6 
14 
26 
41 
59 
80 

II 
6.1 

// 

39 
33 

45 
15 
00 
03 
21 

5 

1 

1 
6 
13 
24 
38 
55 
75 

II 
5.7 

II 

32 

08 
48 
32 
20 
12 
08 

5 

1 

1 
5 
12 
22 
35 
51 
70 

II 
5.3 

// 

26 
44 
55 
57 
52 
39 
18 

S 

1     II 

121 

5  24 
12  09 
21  35 
33  44 
48  35 
66  07 

II 
5.06 

I  II 

1  16 
5  05 

II  26 
20  18 
3144 
45  42 
62  10 
81  14 

II 
4.76 

'      II 

1  11 

4  48 
10  47 
19  09 
29  56 
43  05 
58  41 
76  38 

II 
4.49 

/      // 

108 

4  32 
10  12 
18  08 
28  20 
40  48 
55  32 
72  32 

// 
4.25 

1     II 

104 

4  18 

9  40 

17  12 

26  52 

38  41 

52  40 

68  47 

II 
4.03 

Min. 
-   4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.926 
34 

0.888 
74 

0.853 
70 

0.820 
20 

0.788 
88 

0.759 
67 

0.730 

78 

0.704 
15 

0.677 
61 

0.652 
25 

0.628 
39 

0.605 
31 

Log. 

Limit 

17 

18 

19 

20 

21 

22 

23 

25 

26 

27 

28 

29 

Min- 
utes 

Merid- 
ian 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

1       II 
101 

1     II 
0  58 

/     II 
0  55 

1     II 
0  52 

1       n 

0  50 

1  ,  II 
0  47 

1     II 
0  46 

0  43 

1       n 
0  42 

0  39 

/      II 
0  38 

1     II 
0  36 

Min. 
4 

8 

4  05 

3  52 

3  41 

3  31 

3  20 

3  11 

3  02 

2  55 

2  47 

2  40 

2  33 

2  26 

8 

12 

9  10 

8  42 

8  17 

7  54 

7  30 

7  11 

6  50 

6  33 

6  15 

5  59 

5  44 

5  29 

12 

16 

16  18 

15  30 

14  43 

14  02 

13  22 

12  45 

12  10 

1139 

1109 

10  37 

10  12 

9  43 

16 

20 

25  28 

24  12 

23  00 

21  56 

20  52 

19  56 

19  00 

18  12 

17  24 

16  36 

15  56 

15  12 

20 

24 

36  41 

34  51 

33  07 

31  35 

30  03 

28  42 

27  22 

26  12 

25  04 

23  54 

22  57 

2153 

24 

28 

49  55 

47  26 

45  05 

43  00 

40  54 

39  05 

37  14 

35  41 

34  06 

32  33 

31  14 

29  48 

28 

32 

65  11 

6157 

58  53 

56  09 

53  25 

5102 

48  38 

46  36 

44  32 

42  30 

40  47 

38  55 

32 

36 

78  25 

74  31 

7104 

67  37 

64  35 

6134 

58  58 

56  23 

53  47 

51  38 

49  15 

36 

40 

92  00 

87  44 

83  28 

79  44 

76  00 

72  48 

69  36 

66  24 

63  44 

60  48 

40 

44 

88  05 

84  13 

80  20 

77  07 

73  34 

44 

48 

95  37 

9146 

87  33 

48 

52 

107  42 

102  45 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

n 

II 

II 

n 

Z.,h 

3.82 

3.63 

3.45 

3.29 

3.13 

2.99 

2.85 

2.73 

2.61 

2.49 

2.39 

2.28 

A,h 

Log. 

0.582 

0.559 

0.537 

0.517 

0.495 

0.475 

0.454 

0.436 

0.416 

0.396 

0.378 

0.357 

Log. 

06 

91 

82 

20 

54 

67 

84 

16 

•64 

20 

40 

93 

Limit 

30 

31 

32 

33 

34 

35 

36 

37 

38 

40 

41 

42 

Min- 
utes 

Merid- 
ian 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

Alti- 
tudes 

72 


Latitude  J 2°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56°   57° 

58° 

59° 

Hour 

Angles 

Min. 

t     11 

1     II 

/  // 

1      II 

1      II 

1     II 

1     II 

t      II 

1     II 

1     II 

1      II 

t      II 

Min. 

4 

0  35 

0  33 

0  32 

0  30 

0  30 

0  28 

0  27 

0  26 

0  25 

0  23 

0  22 

0  22 

4 

8 

2  20 

2  14 

2  09 

2  02 

1  58 

1  53 

1  48 

1  43 

1  39 

1  35 

130 

1  26 

8 

12 

5  15 

5  01 

4  49 

4  37 

4  25 

4  14 

4  03 

3  53 

3  43 

3  34 

3  23 

3  14 

12 

16 

9  21 

8  55 

8  35 

8  11 

7  51 

7  30 

7  13 

6  55 

6  37 

6  18 

6  01 

5  46 

16 

20 

14  36 

13  56 

13  24 

12  48 

12  16 

11  44 

11  16 

10  48 

10  20 

9  52 

9  24 

9  00 

20 

24 

2102 

20  04 

19  18 

18  26 

17  40 

16  54 

16  14 

15  34 

14  53 

14  12 

13  32 

12  58 

24 

28 

28  37 

27  19 

26  16 

25  06 

24  02 

23  00 

22  05 

21  10 

20  15 

19  21 

18  26 

17  38 

28 

32 

37  22 

35  40 

34  18^  32  46 

31  24 

30  02 

28  50 

27  38 

26  27 

25  16 

24  04 

23  02 

32 

36 

47  19 

45  09 

43  25 

41  28 

39  45 

38  01 

36  51 

35  00 

33  29 

3158 

30  27 

29  10 

36 

40 

58  24 

55  44 

53  36 

51  12 

49  04 

46  56 

45  04 

43  12 

4120 

39  28 

37  36 

36  00 

40 

44 

70  40 

67  26 

64  51 

6157 

59  22 

56  47 

54  32 

52  17 

50  01 

47  45 

45  29 

43  34 

44 

48 

84  05 

80  15 

77  11 

73  44 

70  39 

67  33 

64  53 

62  12 

59  31 

56  50 

54  09 

5150 

48 

52 

98  41 

94  11 

90  35 

86  32 

82  55 

79  19 

76  09 

73  00 

69  51 

66  42 

63  33 

60  50 

52 

56 

105  03 

100  21 

96  10 

9159 

88  20 

84  41 

81  01 

77  21 

73  41 

70  34 

56 

60 

110  24 

105  36 

101  24 

97  12 

93  00 

88  48 

84  36 

8100 

60 

n 

II 

// 

II 

II 

II 

II 

II 

// 

II 

II 

// 

Ajh 

2.19 

2.09 

2.01 

1.92 

1.84 

1.76 

1.69 

1.62 

1.55 

1.48 

1.41 

1.35 

A,h 

Log. 

0.340 

0.320 

0.303 

0.283 

0.264 

0.245 

0.227 

0.209 

0.190 

0.170 

0.149 

0.130 

Log. 

44 

15 

20 

30 

82 

51 

89 

52 

33 

26 

22 

33 

Limit 

43 

44 

45 

46 

47 

49 

50 

51 

52 

53 

55 

57 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
-  52 
56 
60 

A,h 

/   // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

4137 

49  32 

58  08 

67  25 

77  24 
II 

1.29 

I  II 

0  19 

1  19 

2  57 
5  15 
8  12 

II  48 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
n 

1.23 

I  II 

0  19 

1  15 

2  50 
5  02 
7  52 

II  20 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

/   // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
II 

1.07 

1     II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

// 

0.96 

/   // 
0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 

15  32 

19  39 

24  16 

29  21 

34  57 

41  01 

47  33 

54  36 
II 

0.91 

I  II 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

II  22 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  29 

52  12 
II 

0.87 

1     II 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 

13  59 

17  43 

2152 

26  28 

31  29 

36  57 

42  52 

49  12 
II 

0.82 

/  // 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

1      II 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 

15  33 

19  12 

23  14 

27  37 

32  27 

37  38 

43  12 
II 

0.72 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.110 
59 

0.089 
91 

0.071 

88 

0.049 
22 

0.029 
38 

0.004 
32 

9.982 
27 

9.959 
04 

9.939 
52 

9.913 
81 

9.886 
49 

9.857 
33 

Log. 

Limit 

59 

61 

63 

65 

67 

69 

71 

73 

75 

77 

79 

81 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

Latitude  J  2°  Declination  Contrary  Name. 
Declinations. 


Horn- 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 

9 

22 

39 

// 
9.2 

28 
52 
11 
25 

4 

2 

9 

20 

36 

56 

II 
8.5 

II 

17 
07 
30 
26 
56 

4 

1 

2 

8 

19 

33 

52 

II 
7.9 

06 
27 
02 
50 
52 

3 

1 

7 
17 
31 
49 

II 
7.4 

58 
55 
47 
37 
24 

1 

1 
7 
16 
29 
46 
66 

II 
6.9 

51 
24 
41 
39 
20 
43 

5 

1 

1 
6 

15 
27 
43 
62 

II 
6.5 

// 

45 
59 
42 
54 
36 
47 

4 

1 
6 
14 
26 
41 
59 
80 

II 
6.1 

II 

39 
35 
50 
22 
12 
20 
45 

8 

1     II 

134 
6  15 
14  04 
25  00 
39  04 
56  16 
76  34 

II 
5.86 

1  29 
5  56 
13  21 
23  43 
37  04 
53  23 
72  39 

II 
5.56 

/      // 

124 
5  39 
12  42 
22  34 
35  16 
50  47 
69  08 

II 
5.29 

1     II 

1  21 
5  23 
12  07 
21  33 
33  40 
48  29 
65  59 

II 
5.05 

I  II 

1  17 
5  09 

II  35 
20  37 
32  12 
46  22 
63  07 
82  26 

II 
4.83 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
^    56 
60 

A,h 

Log. 

0.965 
67 

0.931 
46 

0.899 
27 

0.869 

82 

0.841 
98 

0.815 

58 

0.790 
99 

0.767 
90 

0.745 
07 

0.723 
46 

0.703 
29 

0.683 
95 

Log. 

Limit 

15        16 

17 

18 

19 

20 

20 

21 

22 

23 

24 

25 

Min- 
utes 

Merid- 
ian 

78°      77° 

76° 

75° 

74° 

73°      72° 

71° 

70° 

69° 

68° 

67° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1     II 

1     II 

1     II 

1     II 

1     II 

1          H 

1     II 

1     II 

/      // 

1      II 

/      // 

/     // 

Min. 

4 

1  14 

1  10 

108 

105 

102 

100 

0  59 

0  56 

0  54 

0  52 

0  51 

0  49 

4 

8 

4  55 

4  44 

4  32 

4  22 

4  11 

4  03 

3  53 

3  46 

3  39 

3  31 

3  23 

3  17 

8 

12 

1105 

10  38 

10  12 

9  49 

9  26 

9  06 

8  45 

8  28 

8  11 

7  54 

7  38 

7  24 

12 

16 

19  43 

18  54 

18  08 

17  27 

16  46 

16  10 

15  35 

15  04 

14  33 

14  02 

13  34 

13  08 

16 

20 

30  48 

29  32 

28  20 

27  16 

26  12 

25  16 

24  20 

23  32 

22  44 

2156 

21  12 

20  32 

20 

24 

44  22 

42  31 

40  48 

39  16 

37  43 

36  23 

35  03 

33  53 

32  44 

31  35 

30  32 

29  34 

24 

28 

60  22 

57  54 

55  32 

53  27 

51  22 

49  32 

47  41 

46  08 

44  34 

43  00 

4133 

40  15 

28 

32 

78  50 

75  37 

72  32 

69  48 

67  05 

64  41 

62  17 

60  15 

58  12 

56  09 

54  16 

52  34 

32 

36 

78  51 

76  15 

73  39 

7104 

68  42 

66  32 

36 

40 

90  56 

87  44 

84  48 

82  08 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

4.62 

4.43 

4.25 

4.09 

3.93 

3.79 

3.65 

3.53 

3.41 

3.29 

3.18 

3.08 

Ajh 

Log. 

0.664 

0.646 

0.628 

0.611 

0.594 

0.578 

0.562 

0.547 

0.532 

0.517 

0.502 

0.488 

Log. 

64 

40 

39 

72 

39 

64 

29 

77 

75 

20 

43        55 

Limit 

26 

27 

28 

29 

30 

31 

32 

33 

33 

34 

35 

36 

Min- 
utes 

Merid- 
ian 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55°     ^"'- 
^^       tudes 

74 


Latitude  J  2°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/   // 

1     II 

1     II 

1     II 

1     II 

/  // 

/  // 

1     II 

/  // 

/  // 

1      II 

1     II 

Min. 

4 

0  47 

0  46 

0  45 

0  43 

0  43 

0  41 

0  39 

0  38 

0  38 

0  36 

0  35 

0  35 

4 

8 

3  11 

3  05 

2  59 

2  54 

2  49 

2  44 

2  40 

2  35 

2  30 

2  26 

2  22 

2  17 

8 

12 

7  11 

6  56 

6  43 

6  32 

6  20 

6  09 

5  59 

5  47 

5  37 

5  29 

5  18 

5  09 

12 

16 

12  45 

12  20 

1157 

1136 

11  16 

10  55 

10  37 

10  17 

9  59 

9  43 

9  26 

9  11 

16 

20 

19  56 

19  16 

18  40 

18  08 

17  36 

17  04 

16  36 

16  04 

15  36 

15  12 

14  44 

14  20 

20 

24 

28  42 

27  45 

26  53 

26  07 

25  21 

24  35 

23  54 

23  08 

22  28 

2153 

21  13 

20  39 

24 

28 

39  05 

37  46 

36  35 

35  33 

34  29 

33  27 

32  33 

31  30 

30  34 

29  48 

28  53 

28  05 

28 

32 

51  02 

49  19 

47  47 

46  25 

45  03 

43  41 

42  30 

4108 

39  56 

38  55 

37  43 

36  41 

32 

36 

64  35 

62  26 

60  29 

58  45 

57  02 

55  18 

53  47 

52  03 

50  33 

49  15 

47  44 

46  27 

36 

40 

79  44 

77  04 

74  40 

72  32 

70  24 

68  16 

66  24 

64  16 

62  24 

60  48 

58  56 

57  20 

40 

44 

87  46 

85  11 

82  36 

80  20 

77  45 

75  30 

73  34 

71  18 

69  23 

44 

48 

95  37 

92  33 

89  51 

87  33 

84  52 

82  33 

48 

52 
56 

105  27 

102  45 

99  36 

96  53 

52 
56 

60 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

60 

Ajh 

2.99 

2.89 

2.80 

2.72 

2.64 

2.56 

2.49 

2.41 

2.34 

2.28 

2.21 
0.344 

2.15 

A,h 

0.475 

0.460 

0.447 

0.434 

0.421 

0.408 

0.396 

0.382 

0.369 

0.357 

0.332 

Log. 

Log. 

67 

90 

16 

57 

60 

24 

20 

02 

22 

93 

39 

44 

Limit 

37 

38 

38 

39 

40 

41 

42 

43 

44 

45 

46 

46 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51°  i  50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

Declinations, 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/   // 

/  II 

1     II 

1      II 

/  II 

/   // 

1      II 

1      II 

/  // 

1      II 

1      II 

1     II 

Min. 

4 

0  33 

0  32 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

0  26 

0  25 

0  24 

4 

8 

2  14 

2  10 

2  06 

2  02 

2  00 

156 

1  53 

150 

147 

143 

1  41 

1  38 

8 

12 

5  01 

4  52 

4  46 

4  37 

4  29 

4  20 

4  14 

4  06 

4  00 

3  53 

3  46 

3  40 

12 

16 

8  55 

8  40 

8  26 

8  11 

7  59 

7  44 

7  30 

7  18 

7  08 

6  55 

6  42 

6  32 

16 

20 

13  56 

13  32 

13  12 

12  48 

12  28 

12  04 

11  44 

11  24 

1108 

10  48 

10  28 

10  12 

20 

24 

20  04 

19  29 

19  00 

18  26 

17  57 

17  23 

16  54 

16  25 

16  02 

15  34 

15  04 

14  41 

24 

28 

27  19 

26  32 

25  53 

25  06 

24  26 

23  39 

23  00 

22  21 

2149 

21  10 

20  31 

20  00 

28 

32 

35  40 

34  39 

33  48 

32  46 

3155 

30  53 

30  02 

29  11 

28  30 

27  38 

26  48 

26  07 

32 

36 

45  09 

43  51 

42  46 

4128 

40  24 

39  06 

38  01 

36  56 

36  05 

35  00 

33  55 

33  03 

36 

40 

55  44 

54  08 

52  48 

51  12 

49  52 

48  16 

46  56 

45  36 

44  32 

43  12 

4152 

40  48 

40 

44 

67  26 

65  30 

63  53 

61  57 

60  21 

58  24 

56  47 

55  10 

53  54 

52  17 

50  40 

49  22 

44 

48 

80  15 

77  57 

76  02 

73  44 

7148 

69  30 

67  33 

65  38 

64  07 

62  12 

60  17 

58  45 

48 

52 

94  11 

9129 

89  14 

86  32 

84  16 

81  34 

79  19 

77  04 

75  15 

73  00 

70  45 

68  57 

52 

56 

103  29 

100  21 

97  45 

94  36 

91  59 

89  22 

87  18 

84  41 

82  04 

79  58 

56 

60 

112  12 

108  36 

105  36 

102  36 

100  12 

97  12 

94  12 

91  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.09 

2.03 

1.98 

1.92 

1.87 

1.81 

1.76 

1.71 

1.67 

1.62 

1.57 

1.53 

A,h 

Log. 

0.320 

0.307 

0.296 

0.283 

0.271 

0.257 

0.245 

0.233 

0.222 

0.209 

0.195 

0.184 

Log. 

15 

50 

67 

30 

84 

68 

51 

00 

72 

52 

90 

69 

Limit 

47 

48 

49 

50 

50 

51 

52 

53 

54 

55 

56 

57 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40° 

39° 

38° 

37° 

.36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

Latitude  J2*^  Declination  Contrary  Name* 


76 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/  // 

1       n 

1       n 

1     II 

/  II 

/  II 

1     II 

/  // 

1      II 

1      II 

/  // 

1     II 

Min. 

4 

0  23 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

0  19 

0  18 

0  17 

0  17 

4 

8 

135 

133 

1  30 

127 

124 

122 

1  20 

1  17 

1  14 

1  11 

109 

107 

8 

12 

3  34 

3  28 

3  22 

3  16 

3  10 

3  05 

2  59 

2  53 

2  47 

2  41 

2  36 

2  31 

12 

16 

6  18 

6  08 

5  58 

5  48 

5  38 

5  27 

5  17 

5  07 

4  57 

4  47 

4  36 

4  29 

16 

20 

9  52 

9  36 

9  20 

9  04 

8  48 

8  32 

8  16 

8  00 

7  44 

7  28 

7  12 

7  00 

20 

24 

14  12 

13  49 

13  36 

13  04 

12  41 

12  17 

1154 

11  31 

1109 

10  46 

10  22 

10  05 

24 

28 

19  21 

18  49 

18  18 

17  46 

17  15 

16  44 

16  12 

15  41 

15  09 

14  38 

14  07 

13  43 

28 

32 

25  16 

24  35 

23  54 

23  12 

22  31 

21  51 

21  10 

20  29 

19  47 

19  06 

18  26 

17  55 

32 

36 

3158 

3106 

30  14 

29  23 

28  31 

27  39 

26  47 

25  55 

25  04 

24  12 

23  20 

22  41 

36 

40 

39  28 

38  24 

37  20 

36  16 

35  12 

34  08 

33  04 

32  00 

30  56 

29  52 

28  48 

28  00 

40 

44 

47  45 

46  27 

45  10 

43  53 

42  36 

41  18 

40  00 

38  43 

37  26 

36  09 

34  51 

33  53 

44 

48 

56  50 

55  18 

53  46 

52  13 

50  41 

49  09 

47  37 

46  05 

44  32 

43  00 

41  28 

40  19 

48 

52 

66  42 

64  54 

63  06 

61  17 

59  29 

57  41 

55  53 

54  05 

52  16 

50  28 

48  40 

47' 19 

52 

56 

77  21 

75  15 

73  10 

7105 

69  00 

66  54 

64  48 

62  43 

60  38 

58  33 

56  27 

54  53 

56 

60 

88  48 

86  24 

84  00 

81  36 

79  12 

76  48 

74  24 

72  00 

69  36 

67  12 

64  48 

63  00 

60 

n 

n 

II 

II 

ir 

II 

II 

II 

II 

II 

11 

II 

A,h 

1.48 

1.44 

1.40 

1.36 

1.32 

1.28 

1.24 

1.20 

1.16 

1.12 

1.08 

1.05 

A,h 

Log. 

0.170 

0.158 

0.146 

0.133 

0.120 

0.107 

0.093 

0.079 

0.064 

0.049 

0.033 

0.021 

Log. 

26 

36 

13 

54 

57 

21 

42 

18 

46 

22 

42 

19 

Limit 

58 

60 

61 

62 

64 

65 

67 

69 

70 

71 

72 

74 

Min- 
utes 

Merid- 
ian 

30° 

29° 

28° 

27° 

26° 

25° 

24^ 

23° 

22° 

21° 

20° 

19° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

1.01 

1      II 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

II 

0.97 

1     II 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

II 

0.94 

I  II 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

II  46 

15  22 

19  26 

24  00 

29  02 

34  34 

40  34 

47  02 

54  00 
II 

0.90 

1      II 

0  14 
0  55 

2  05 

3  43 

5  48 
8  21 
1122 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 
II 

0.87 

/   // 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 

II 

0.83 

1      II 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/  II 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 
II 

0.76 

1      II 

Oil 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 
15  46 
19  28 
23  33 
28  00 
32  54 
38  09 
43  48 

0.73 

I  II 

Oil 
0  44 
139 
2  57 
4  36 
6  38 
9  01 

II  46 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

41  24 
II 

0.69 

/   // 

Oil 

0  42 

1  35 

2  49 
4  24 
6  21 
8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 
II 

0.66 

1      II 

0  10 

0  40 

1  30 

2  42 
4  12 
6  03 
8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
II 

0.63 

Min. 

4 

8 

12 

16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Log. 

0.004 
32 

9.986 

77 

9.973 
13 

9.954 
24 

9.939 
52 

9.919 
08 

9.903 
09 

9.880 
81 

9.863 
32 

9.838 
85 

9.819 
54 

9.799 
34 

Log. 

Limit 

76 

77 

78 

79 

80 

81 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

Alti- 
tudes 

76 


Latitude  13°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

2 

9 

20 
36 
56 

n 

8.5 

16 
04 
24 
16 
40 

[) 

2 

9 

22 
39 

II 
9.2 

II 

27 
49 
05 
15 

0 

1 

2 
10 
24 
42 

II 
10.0 

II 

40 

41 
03 
45 

2 

1 

2 
11 
26 

II 
11.0 

56 
44 
24 

D 

/      II 

3  15 
13  01 
29  17 

II 
12.20 

1     II 

3  39 
14  36 
32  51 

II 
13.69 

1     II 

4  10 
16  39 
37  27 

II 
15.61 

/      II 

4  51 
19  23 

II 
18.17 

1     II 

5  48 
23  12 

II 
21.74 

/ 

// 

II 

1 

// 

II 

1     II 
II 

Min. 

4 

8 
12 
16  . 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.929 
42 

0.963 
79 

1.000 

87 

1.041 
39 

1.086 
36 

1.136 
40 

1.193 
40 

1.259 
35 

1.337 
26 

Log. 

Limit 

16 

15 

14 

13 

12 

11 

10 

8 

7 

6 

4 

3 

Min- 
utes 

Merid- 
ian 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14 

°      15 

o      16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

1     II 

1 

//    1 

//    /      // 

/      II 

/     // 

1     II 

1      II 

/      // 

1      II 

/      // 

Min. 

4 

5  34 

4  37 

3  56 

3  26 

3  02 

242 

4 

8 

22  16 

18  28 

15  44 

13  41 

12  06 

10  49 

8 

12 

35  24 

30  47 

27  13 

24  20 

12 

16 

43  16 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

20.88 

17.31 

14.75 

12.83 

11.34 

10.14 

A,h 

Log. 

1.319 
73 

1.238 
30 

1.168 
79 

1.108 
23 

1.054 
61 

1.006 
04 

Log. 

Limit 

1 

0 

1 

3 

5 

7 

9 

10 

11 

12 

13 

14 

Min- 
utes 

Merid- 
ian 

89°  i   90° 

89< 

'      88< 

>      87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

Alti- 
tudes 

Latitude  J  3°  Declination  Same  Name. 


77 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

2 

9 
21 
39 

II 
9.1( 

II 

27 
46 
59 
D5 

5 

2  13 

8  54 

20  01 

35  35 

55  36 

8.34 

2 

8 
18 
32 
50 

II 
7.6' 

03 
09 
20 
36 
56 

t 

1 

1 

7 
16 
30 
47 

II 
7.0. 

53 
31 

55 
05 
OO 

/ 

1 

6 
15 
27 
43 
62 

II 
6.5> 

// 

44 
58 
40 
52 
32 
41 

J 

/      II 

1  37 
6  29 
14  34 
25  54 
40  28 
58  16 
79  19 

II 
6.07 

1 

1 

6 
13 
24 
37 
54 
74 

II 
5.6' 

31 
03 
36 
12 
48 
26 
05 

r 

/     // 

1  25 
5  40 
12  44 
22  40 
35  24 
50  59 
69  23 

5.31 

I  II 

1  19 
5  18 

II  58 
21  14 
33  12 
47  48 
65  03 

II 
4.98 

/     // 

1  15 
5  00 
11  15 
20  01 
31  16 
45  02 
61  17 
80  02 

II 
4.69 

1  10 

4  44 
10  38 
18  54 
29  32 
42  31 
57  54 
75  37 

II 
4.43 

/      // 

107 
4  27 
10  02 
17  50 
27  52 
40  08 
54  37 
7120 

II 
4.18 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.961 
90 

0.921 
17 

0.883 
09 

0.848 
19 

0.814 
91 

0.783 
19 

0.753 

58 

0.725 
09 

0.697 
23 

0.671 
17 

0.646 
40 

0.621 
18 

Log. 

Limit 

15 

16 

18 

19 

20 

21 

22 

24 

25 

26 

27 

29 

Min- 
utes 

Merid- 
ian 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

1     II 

/     // 

/     /' 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

103 

100 

0  57 

0  54 

0  51 

0  49 

0  46 

0  45 

0  43 

0  41 

0  39 

0  37 

4 

8 

4  13 

4  01 

3  49 

3  37 

3  27 

3  17 

3  07 

2  59 

2  51 

2  43 

2  37 

2  29 

8 

12 

9  31 

9  02 

8  34 

8  08 

7  45 

7  24 

7  02 

6  43 

6  24 

6  07 

5  52 

5  35 

12 

16 

16  53 

16  02 

15  14 

14  28 

13  47 

13  08 

12  30 

1157 

1124 

10  53 

10  24 

9  57 

16 

20 

26  24 

25  04 

23  48 

22  36 

2132 

20  32 

19  32 

18  40 

17  48 

17  00 

16  16 

15  32 

20 

24 

38  01 

36  06 

34  16 

32  33 

31  00 

29  34 

28  07 

26  53 

25  38 

24  29 

23  25 

22  22 

24 

28 

5145 

49  08 

46  39 

44  18 

42  13 

40  15 

38  18 

36  35 

34  53 

33  19 

31  53 

30  27 

28 

32 

67  35 

64  10 

60  56 

57  51 

55  08 

52  34 

50  01 

47  47 

45  34 

43  31 

41  39 

39  46 

32 

36 

77  07 

73  14 

69  46 

66  32 

63  17 

60  29 

57  41 

55  05 

52  40 

50  20 

36 

40 

90  24 

86  08 

82  08 

78  08 

74  40 

71  12 

68  00 

65  04 

62  08 

40 

44 

86  10 

82  17 

78  43 

75  11 

44 

48 

93  42 

89  28 

48 

52 

105  00 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

A,h 

3.96 

3.76 

3.57 

3.39 

3.23 

3.08 

2.93 

2.80 

2.67 

2.55 

2.44 

2.33 

A,h 

Log. 

0.597 

0.575 

0.552 

0.530 

0.509 

0.488 

0.466 

0.447 

0.426 

0.406 

0.387 

0.367 

Log. 

70 

19 

67 

20 

20 

55 

87 

16 

51 

54 

39 

36 

Limit 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

Min- 
utes 

Merid- 
ian   ' 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

78 


Latitude  13°  Declination  Same  Name. 
Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  35 

2  23 

5  21 

9  31 

14  52 

21  24 

29  09 

38  04 

48  10 

59  28 

71  57 

85  38 

100  30 

// 
2.23 

0  34 

2  16 

5  06 

9  06 

14  12 

20  27 

27  50 

36  21 

46  01 

56  48 

68  44 

81  46 

95  59 

2.13 

/     // 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

44  04 

54  24 

65  49 

78  20 

9156 

106  37 

If 
2.04 

/     // 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

II 
1.96 

/     // 

0  30 
2  00 
4  29 

7  59 
12  28 
17  57 
24  26 
3155 
40  24 
49  52 
60  21 
71  48 
84  16 
97  45 

112  12 

II 

1.87 

0  28 

1  55 
4  18 
7  38 

1156 
17  11 
23  24 
30  33 
38  40 
47  44 
57  45 
68  42 
80  40 
93  33 

107  24 

II 

1.79 

/     // 

0  27 

150 

4  06 

7  18 

1124 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 

1.71 

1     II 

0  27 

145 

3  56 

7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
II 

1.64 

/     // 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41  52 

50  40 

60  17 

70  45 

82  04 

94  12 

II 

1.57 

0  24 

1  36 
3  36 
6  24 

10  00 
14  24 
19  36 
25  36 
32  24 
40  00 
48  24 
57  36 
67  36 
78  24 

90  00 

II 

1.50 

0  22 

132 

3  24 

6  06 

9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

6144 

71  37 

82  12 
II 

1.37 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.348 
30 

0.328 
38 

0.309 
63 

0.292 
26 

0.271 
84 

0.252 

85 

0.233 
00 

0.214 
84 

0.195 
90 

0.176 
09 

0.155 
34 

0.136 
72 

Log. 

Limit 

42 

43 

44 

45 

46 

48 

50 

51 

52 

53 

55 

57 

Min- 
utes 

Merid- 
ian 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/     /' 

/     // 

/     // 

/     // 

/     // 

/     /' 

/     // 

/     '/ 

/       n 

Min. 

Min. 

4 

0  21 

0  20 

0  19 

0  18 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

Oil 

4 

8 

123 

120 

1  16 

1  12 

109 

105 

102 

0  58 

0  55 

0  53 

0  50 

0  47 

8 

12 

3  08 

3  00 

2  51 

2  42 

2  36 

2  27 

2  20 

2  13 

2  05 

159 

152 

1  45 

12 

16 

5  36 

5  20 

5  05 

4  50 

4  36 

4  21 

4  08 

3  55 

3  43 

3  33 

3  19 

3  07 

16 

20 

8  44 

8  20 

7  56 

7  32 

7  12 

6  48 

6  28 

6  08 

5  48 

5  32 

5  12 

4  52 

20 

24 

12  35 

12  00 

1126 

10  51 

10  22 

9  48 

9  18 

8  50 

8  21 

7  58 

7  29 

7  00 

24 

28 

17  07 

16  20 

15  33 

14  46 

14  07 

13  20 

12  41 

12  02 

1122 

10  51 

10  12 

9  33 

28 

32 

22  21 

21  20 

20  18 

19  17 

18  26 

17  24 

16  34 

15  42 

14  51 

14  10 

13  19 

12  28 

32 

36 

28  18 

27  00 

25  43 

24  25 

23  20 

22  02 

20  57 

19  52 

18  48 

17  56 

16  51 

15  46 

36 

40 

34  56 

33  20 

3144 

30  08 

28  48 

27  12 

25  52 

24  32 

23  12 

22  08 

20  48 

19  28 

40 

44 

42  16 

40  20 

38  24 

36  28 

34  51 

32  55 

31  18 

29  41 

28  05 

26  47 

25  10 

23  33 

44 

48 

50  18 

48  00 

45  41 

43  23 

4128 

39  10 

37  15 

35  20 

33  24 

3152 

29  55 

28  00 

48 

52 

59  02 

56  20 

53  37 

55  55 

48  40 

45  48 

43  43 

4128 

39  12 

37  24 

35  09 

32  54 

52 

56 

68  28 

65  20 

62  12 

59  04 

56  27 

53  19 

50  42 

48  05 

45  29 

43  23 

40  46 

38  09 

56 

60 

78  36 

75  00 

7124 

67  48 

64  48 

61  12 

58  12 

55  12 

52  12 

49  48 

46  48 

43  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

A,h 

1.31 

1.25 

1.19 

1.13 

1.08 

1.02 

0.97 

0.92 

0.87 

0.83 

0.78 

0.73 

A,h 

Log. 

0.117 

0.096 

0.075 

0.053 

0.033 

0.008 

9.986 

9.963 

9.939 

9.919 

9.892 

9.863 

Log. 

27 

91 

55 

08 

42 

60 

77 

79 

52 

08 

09 

32 

Limit 

59 

60 

62 

64 

66 

68 

70 

72 

74 

76 

78 

80 

Min- 
utes 

Merid- 
ian 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

Alti- 
tudes 

Latitude  13"  Declination  Contrary  Name. 


79 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8°        9° 

10° 

11° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

2 

9 

20 

36 

56 

II 
8.5 

// 

16 
04 
24 
16 
40 

3 

1 
2 
8 
18 
33 
52 

II 
7.9 

06 
26 
58 
45 
44 

I 

1 

1 

7 
17 
31 
49 

II 
7.3< 

58 
53 
44 
32 
16 

1 
7 
16 
29 
46 
66 

6.9 

// 

50 
23 

38 
34 
12 
31 

3 

/      // 

144 
6  58 
15  40 
27  52 
43  32 
62  41 

II 
6.53 

/      // 

1  39 
6  35 
14  48 
26  20 
41  08 
59  14 
80  37 

II 
6.17 

/ 

1 
6 
14 
24 
38 
56 
76 

II 
5.8 

34 
14 
01 
55 
56 
04 
18 

t 

/      // 

1  29 
5  55 
13  19 
23  41 
37  00 
53  17 
72  31 

II 
5.55 

/      // 

124 
5  39 
12  42 
22  34 
35  16 
50  47 
69  08 

II 
5.29 

/      // 

1  21 
5  23 
12  06 
21  30 
33  36 
48  23 
65  51 

II 
5.04 

/      // 

1  17 
5  08 
11  34 
20  34 
32  08 
46  17 
62  59 
82  15 

II 
4.82 

/      // 

114 

4  55 

1105 

19  43 

30  48 
44  22 
60  22 
78  50 

II 
4.62 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.929 
42 

0.898 
18 

0.868 
64 

0.840 
73 

0.814 
91 

0.790 
29 

0.766 
41 

0.744 
29 

0.723 
46 

0.702 
43 

0.683 
05 

0.664 
64 

Log. 

Limit 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

Min- 
utes 

Merid-      770 
ian         '' 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       'I 

/      " 

1     '1 

1     II 

t     II 

1      II 

/      '/ 

1     II 

/      // 

/      // 

r       II 

/      // 

Min. 

4 

1  10 

1  08 

105 

103 

100 

0  59 

0  56 

0  54 

0  53 

0  51 

0  49 

0  48 

4 

8 

4  44 

4  32 

4  22 

4  12 

4  03 

3  54 

3  46 

3  39 

3  31 

3  24 

3  18 

3  12 

8 

12 

10  38 

10  12 

9  49 

9  28 

9  06 

8  47 

8  28 

8  11 

7  55 

7  39 

7  25 

7  12 

12 

16 

18  54 

18  08 

17  27 

16  48 

16  10 

15  37 

15  04 

14  33 

14  05 

13  37 

13  11 

12  48 

16 

20 

29  32 

28  20 

27  16 

26  16 

25  16 

24  24 

23  32 

22  44 

22  02 

21  16 

20  36 

20  00 

20 

24 

42  31 

40  48 

39  16 

37  49 

36  23 

35  09 

33  53 

32  44 

3141 

30  38 

29  40 

28  48 

24 

28 

57  54 

55  32 

53  27 

51  29 

49  32 

47  49 

46  08 

44  34 

43  07 

4141 

40  23 

39  12 

28 

32 

75  37 

72  32 

69  48 

67  15 

64  41 

62  27 

60  15 

58  12 

56  19 

54  26 

52  44 

51  12 

32 

36 

79  04 

76  15 

73  39 

71  17 

68  55 

66  45 

64  48 

36 

40 

90  56 

88  00 

85  04 

82  24 

80  00 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

4.43 

4.25 

4.09 

3.94 

3.79 

3.66 

3.53 

3.41 

3.30 

3.19 

3.09 

3.00 

Ajh 

Log. 

0.646 

0.628 

0.611 

0.595 

0.578 

0.563 

0.547 

0.532 

0.518 

0.503 

0.489 

0.477 

Log. 

40 

39 

72 

50 

64 

48 

77 

75 

51 

79 

96 

12 

Limit 

28 

29 

30 

30 

31 

32 

33 

34 

34 

35 

36 

37 

Min- 
utes 

Merid- 
ian 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

Alti- 
tudes 

80 


Latitude  iZ°  Decimation  Contrary  Name. 
Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

/             // 

/     II 

/     // 

/      /' 

/      " 

/     // 

/     // 

/     // 

Mill. 

Min. 

4 

0  46 

0  45 

0  43 

0  43 

0  41 

0  40 

0  38 

0  38 

0  36 

0  35 

0  35 

0  34 

4 

8 

3  05 

3  00 

2  55 

2  49 

2  45 

2  40 

2  36 

2  31 

2  27     2  23 

2  19 

2  15 

8 

12 

6  58 

6  46 

6  33 

6  21 

6  10 

6  00 

5  50 

5  40 

5  30     5  21 

5  12 

5  03 

12 

16 

12  22 

12  02 

1139 

11  19 

10  58 

10  40 

10  22 

10  04 

9  46 

9  31 

9  16 

9  01 

16 

20 

19  20 

18  48 

18  12 

17  40 

17  08 

16  40 

16  12 

15  44 

15  16 

14  52 

14  28 

14  04 

20 

24 

27  50 

27  05 

26  12 

25  27 

24  40 

24  00 

23  19 

22  40 

21  59 

21  24 

20  50 

20  16 

24 

28 

37  54 

36  51 

35  41 

34  37 

33  35 

32  40 

3146 

30  50 

29  56 

29  09 

28  21 

27  34 

28 

32 

49  30 

48  07 

46  36 

45  13 

43  52 

42  40 

41  29 

40  16 

39  05 

38  04 

37  02 

36  00 

32 

36 

62  38 

60  55 

58  58 

57  15 

55  31 

54  00 

52  29 

50  59 

49  28 

48  10 

46  53 

45  35 

36 

40 

77  20 

75  12 

72  48 

70  40 

68  32 

66  40 

64  48 

62  56 

61  04 

59  28 

57  52 

56  16 

40 

44 

88  05 

85  31 

82  56 

80  40 

78  24 

76  09 

73  53 

7157 

70  02 

68  05 

44 

48 

96  00 

93  19 

90  37 

87  56 

85  38 

83  19 

8101 

48 

52 

106  21 

103  12 

100  30 

97  47 

95  05 

52 

56 

56 

60 

60 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.90 

2.82 

2.73 

2.65 

2.57 

2.50 

2.43 

2.36 

2.29 

2.23 

2.17 

2.11 

A,h 

Log. 

0.462 

0.450 

0.436 

0.423 

0.409 

0.397 

0.385 

0.372 

0.359 

0.348 

0.336 

0.324 

Log. 

40 

25 

16 

25 

93 

94 

61 

91 

84 

30 

46 

28 

Limit 

38 

39 

39 

40 

41 

42 

43 

44 

45 

46 

47 

47 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

/      // 

/     // 

/     // 

/      // 

/     II  \  1     II 

/      // 

/      // 

/      // 

/     // 

/      // 

/     // 

Min. 

4 

0  33 

0  31 

0  31 

0  30 

0  29     0  28 

0  28 

0  27 

0  27 

0  26 

0  25 

0  24 

4 

8 

2  11 

2  07 

2  04 

2  01 

1  57      1  54 

1  52 

148 

1  45 

142 

139 

136 

8 

12 

4  55 

4  47 

4  40 

4  32 

4  23     4  17 

4  11 

4  03 

3  56 

3  50 

3  43 

3  37 

12 

16 

8  45 

8  29 

8  16 

8  04 

7  49     7  35 

7  25 

7  13 

7  00 

6  50 

6  37 

6  27 

16 

20 

13  40 

13  16 

12  56 

12  36 

12  12 

1152 

1136 

11  16 

10  56 

10  40 

10  20 

10  04 

20 

24 

19  41 

19  06 

18  37 

18  09 

17  34 

17  05 

16  42 

16  14 

15  45 

15  22 

14  53 

14  30 

24 

28 

26  47 

26  01 

25  31 

24  42 

23  55 

23  16 

22  44 

22  05 

21  25 

20  54 

20  15 

19  44 

28 

32 

34  59 

33  58 

33  07 

32  15 

31  13 

30  23 

29  42 

28  50 

27  59 

27  18 

26  27 

25  46 

32 

36 

44  17 

42  59 

41  54 

40  50 

39  32 

38  27 

37  35 

36  31 

35  26 

34  34 

33  29 

32  37 

36 

40 

54  40 

53  04 

51  44 

50  24 

48  48 

47  28 

46  24 

45  04 

43  44 

42  40 

41  20 

40  16 

40 

44 

66  09 

64  12 

62  35 

60  59 

59  03 

57  26 

56  08 

54  32 

52  55 

51  38 

50  01 

48  43 

44 

48 

78  43 

76  25 

74  30 

72  34 

70  16 

68  19 

66  47 

64  53 

62  58 

6126 

59  31 

57  59 

48 

52 

92  23 

89  41 

87  26 

85  10 

82  28 

80  13 

78  25 

76  09 

73  54 

72  06 

69  51 

68  03 

52 

56 

107  09 

104  00 

101  23 

98  47 

95  39 

93  02 

90  56 

88  20 

85  43 

83  38 

8101 

78  55 

56 

60 

113  24 

109  48 

106  48 

104  24 

10124 

98  24 

96  00 

93  00 

90  36 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.05 

1.99 

1.94 

1.89 

1.83 

1.78 

1.74 

1.69 

1.64 

1.60 

1.55 

1.51 

A,h 

Log. 

0.311 

0.298 

0.287 

0.276 

0.262 

0.250 

0.240 

0.227 

0.214 

0.204 

0.190 

0.178 

Log. 

75 

85 

80 

46 

45 

42 

55 

89 

84 

12 

33 

98 

Limit 

48 

49 

50 

51 

51 

52 

53 

54 

55 

56 

57 

58 

Min- 
utes 

Merid- 
ian 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

Latitude  J  3°  Declination  Contrary  Name. 


81 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  23 

1  34 
3  31 
6  13 
9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
II 

1.46 

0  22 
131 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
II 

1.42 

I     II 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 

1.38 

1     II 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

51  27 

60  23 

70  02 

80  24 
II 

1.34 

/   // 

0  21 

1  23 
3  07 
5  33 

8  40 
12  29 
16  59 
22  11 
28  05 
34  40 
41  57 
49  55 
58  35 
67  57 

78  00 

II 

1.30 

/  // 

0  20 
121 
3  02 
5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
II 

1.26 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  29 

63  46 

73  12 
II 

1.22 

/  // 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

/  // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 

69  00 

II 

1.15 

/  II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 
II 

1.07 

/  // 

0  17 

1  07 

2  30 
4  26 
6  56 
9  59 

13  35 
17  45 
22  28 
27  44 
33  33 
39  56 
46  52 
54  21 

62  24 

II 

1.04 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.164 
35 

59 

0.152 

29 

0.139 

88 

0.127 
10 

0.113 
94 

0.100 
37 

0.086 
36 

0.071 

88 

0.060 
70 

0.045 
32 

0.029 
38 

0.017 
03 

Log. 

Limit 

61 

62 

63 

64 

66 

68 

70 

71 

72 

73 

75 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/   // 

/   // 

/  // 

/  // 

/  /' 

/  // 

/  // 

/  // 

1     II 

/  // 

/  // 

/  // 

Min. 

4 

0  16 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

Oil 

Oil 

0  10 

4 

8 

104 

101 

0  59 

0  57 

0  55 

0  53 

0  51 

0  49 

0  47 

0  44 

0  42 

0  40 

8 

12 

2  24 

2  19 

2  14 

2  10 

2  04 

159 

154 

150 

145 

139 

135 

130 

12 

16 

4  16 

4  05 

3  58 

3  50 

3  40 

3  33 

3  22 

3  14 

3  07 

2  57 

2  49 

2  42 

16 

20 

6  40 

6  24 

6  12 

6  00 

5  44 

5  32 

5  16 

5  04 

4  52 

4  36 

4  24 

4  12 

20 

24 

9  36 

9  13 

8  55 

,8  38 

8  16 

7  58 

7  35 

7  18 

7  00 

6  38 

6  21 

6  03 

24 

28 

13  04 

12  33 

12  10 

11  46 

11  14 

10  51 

10  20 

9  56 

9  33 

9  01 

8  37 

8  14 

28 

32 

17  04 

16  23 

15  53 

15  22 

14  40 

14  10 

13  29 

12  58 

12  28 

1146 

11  15 

10  45 

32 

36 

21  36 

20  44 

20  05 

19  26 

18  35 

17  56 

17  04 

16  25 

15  46 

14  55 

14  16 

13  37 

36 

40 

26  40 

25  36 

24  48 

24  00 

22  56 

22  08 

2104 

20  16 

19  28 

18  24 

17  36 

16  48 

40 

44 

32  16 

30  58 

30  00 

29  02 

27  45 

26  47 

25  29 

24  31 

23  33 

22  16 

21  18 

20  20 

44 

48 

38  24 

36  52 

35  43 

34  34 

33  01 

3152 

30  18 

29  09 

28  00 

26  29 

25  20 

24  11 

48 

52 

45  04 

43  16 

4155 

40  34 

38  45 

37  24 

35  36 

34  15 

32  54 

31  05 

29  44 

28  23 

52 

56 

52  16 

50  10 

48  36 

47  02 

44  57 

43  23 

41  17 

39  43 

38  09 

36  04 

34  30 

32  56 

56 

60 

60  00 

57  36 

55  48 

54  00 

5136 

49  48 

47  24 

45  36 

43  48 

4124 

39  36 

37  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.00 

0.96 

0.93 

0.90 

0.86 

0.83 

0.79 

0.76 

0.73 

0.69 

0.66 

0.63 

A,h 

Log. 

0.00 

9.982 

9.968 

9.954 

9.934 

9.919 

9.897 

9.880 

9.863 

9.838 

9.819 

9.799 

Log. 

27 

48 

24 

50 

08 

63 

81 

32 

85 

54 

34 

Limit 

77 

78 

79 

79 

80 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

Alti- 
tudes 

82 


Latitude  14°  Declination  Same  Name. 


Declinations. 


Hour 
AngleB 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 

8 
18 
33 
52 

II 

7.8 

// 

06 
24 
55 
37 
32 

8 

2 
9 

20 
36 
56 

It 
8.4 

// 

15 
03 
20 

08 
28 

1 

1 

2 

9 
21 
39 

II 
9.1( 

27 
46 
59 
05 

5 

1 

2 
10 
23 
42 

II 
9.9 

39 
38 
56 
32 

1 

1 

2 
11 
26 
46 

II 
10.9' 

55 
40 
16 
40 

1 

1 

3 

12 

29 

II 
12.1. 

15 

56 
06 

3 
14 
32 

II 
13.6 

38 
31 
39 

I 

4 
16 
37 

II 
15.5- 

08 
33 
15 

J 

18. 

49 
15 

35 

/     // 

5  45 
23  02 

II 
21.59 

II 

// 

/ 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.896 
53 

0.927 

88 

0.961 
90 

0.998 
70 

1.039 
02 

1.083 
86 

1.133 

86 

1.190 
89 

256 

48 

1.334 
25 

Log. 

Limit 

17 

16 

15 

14 

13 

12 

10 

9 

8 

7 

6 

5 

Min- 
utes 

Merid- 
ian 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

Alti- 
tudes 

Declin.\tioxs. 


Hour      1 
Angles     ■" 

2°      13° 

14<^ 

15' 

16' 

17' 

18' 

'      19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min.      ' 

//     /       // 

1 

'/    / 

//    / 

//    1 

//    / 

II    1     II 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

5  31 

4  35 

3  53 

3  23 

2  59 

4 

8 

22  03 

18  16 

15  34 

13  32 

1158 

8 

12 

35  01 

30  27 

26  54 

12 

16 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

.52 

52 

56 

56 

60 

60 

//              // 

" 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

20.67 

17.13 

14.59 

12.69 

11.21 

A,h 

Log. 

1.315 
34 

1.233 
76 

1.164 
06 

1.103 
46 

1.049 
61 

Log. 

Limit 

3          1 

0 

2 

4 

6 

7 

8 

9 

11 

12 

13 

Min- 
utes 

Merid-     , 
ian        ' 

J8°      89 

3 

( 

)0 

'      89* 

'      88 

'      87< 

'      86' 

'      85 

° 

84' 

83' 

82= 

81° 

Alti- 
tudes 

Latitude  14°  Declination  Same  Name* 


83 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
IB 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 
10 
24 
42 

II 
10.0 

40 
41 
D3 
45 

2 

2 

9 
21 
38 

II 
9.0 

// 

25 
39 
43 
37 

5 

1 

2 

8 
19 
35 
54 

II 
8.2 

12 

48 
47 
39 
56 

4 

1 

2 

8 

18 

32 

50 

II 
7.5 

31 
33 
37 
13 
20 

5 

1 

7 

16 
29 
46 
66 

II 
6.9 

51 

24 
41 
39 
20 
43 

5 

1 

1 
6 

15 

27 

42 

61 

84 

II 
6.4 

43 
53 

28 
28 
56 
49 
39 

4 

1 

1 
6 
14 
25 
39 
57 
78 

II 
5.9 

35 
23 
23 
33 
56 
30 
17 

3 

/      // 

129 

5  56 
13  21 
23  43 
37  04 
53  23 
72  39 

II 
5.56 

/     // 

123 
5  35 
12  33 
22  19 
34  52 
50  12 
68  21 

II 
5.23 

/     // 

1  18 
5  14 
1147 
20  57 
32  44 
47  08 
64  10 

II 
4.91 

1  14 
4  55 
11  05 
19  43 
30  48 
44  22 
60  22 
78  50 

II 
4.62 

/      // 

1  10 

4  38 
10  26 
18  34 
29  00 
4146 
56  50 
74  14 

4.35 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

1.000 

87 

0.956 
65 

0.915 
93 

0.877 
95 

0.841 
98 

0.808 
89 

0.777 
43 

0.745 
07 

0.718 
50 

0.691 
08 

0.664 
64 

0.638 
49 

Log. 

Limit 

14 

15 

17 

18 

19 

20 

22 

23 

24 

25 

26 

28 

Min- 
utes 

Merid- 
ian 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

Alti- 
tudes 

Declinations. 


Hour       q, 
Angles     "^" 

5" 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
An'gles 

Min.     ' 

" 

/      // 

/      // 

1      II 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

1     II 

/      // 

Min. 

4          1 

06 

1  02 

0  59 

0  56 

0  53 

0  51 

0  48 

0  46 

0  44 

0  42 

0  40 

0  38 

4 

8         4 

23 

4  09 

3  56 

3  44 

3  33 

3  23 

3  13 

3  04 

2  56 

2  47 

2  40 

2  33 

8 

12         9 

51 

9  20 

8  51 

8  24 

7  59 

7  36 

7  15 

6  53 

6  35 

6  17 

6  00 

5  44 

12 

16       17 

33 

16  36 

15  45 

14  56 

14  13 

13  32 

12  53 

12  15 

11  41 

11  11 

10  40 

10  12 

16 

20       27 

24 

25  56 

24  36 

23  20 

22  12 

21  08 

20  08 

19  08 

18  16 

17  28 

16  40 

15  56 

20 

24       39 

28 

37  21 

35  26 

33  36 

3158 

30  26 

29  00 

27  33 

26  18 

25  10 

24  00 

22  57 

24 

28       53 

42 

50  50 

48  13 

45  44 

43  31 

41  25 

39  28 

37  30 

35  48 

34  14 

32  40 

31  14 

28 

32       70 

08 

66  23 

62  58 

59  44 

56  50 

54  06 

5132 

48  59 

46  46 

44  42 

42  40 

40  47 

32 

36 

79  43 

75  36 

71  56 

68  29 

65  14 

62  00 

59  11 

56  36 

54  00 

51  38 

36 

40 

88  48 

84  32 

80  32 

76  32 

73  04 

69  52 

66  40 

63  44 

40 

44 

88  24 

84  33 

80  40 

77  07 

44 

48 

96  00 

9146 

48 

52 

107  42 

52 

56 

56 

60 

60 

1 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h     4. 

11 

3.89 

3.69 

3.50 

3.33 

3.17 

3.02 

2.87 

2.74 

2.62 

2.50 

2.39 

A,h 

0. 
Log. 

613 

0.589 

0.567 

0.544 

0.522 

0.501 

0.480 

0.457 

0.437 

0.418 

0.397 

0.378 

Log. 

84 

95 

03 

07 

44 

06 

01 

88 

75 

30 

94 

40 

Limit       2 

9 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

Min- 
utes 

Merid-      o 
ian         0 

3° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

Alti- 
tudes 

84 


Latitude  J 4°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  /' 

/  // 

/  // 

/  /' 

/  // 

/  // 

/  // 

/   // 

/  /' 

/  // 

Min. 

4 

0  36 

0  35 

0  33 

0  31 

0  30 

0  29 

0  28 

0  27 

0  25 

0  24 

0  23 

0  22 

4 

8 

2  26 

2  19 

2  13 

2  07 

2  02 

1  56 

152 

1  47 

142 

1  37 

1  33 

129 

8 

12 

5  29 

5  14 

5  00 

4  47 

4  35 

4  22 

411 

4  00 

3  49 

3  39 

3  29 

3  20 

12 

16 

9  43 

9  18 

8  52 

8  29 

8  09 

7  46 

7  25 

7  08 

6  47 

6  29 

6  11 

5  56 

16 

20 

15  12 

14  32 

13  52 

13  16 

12  44 

12  08 

11  36 

1108 

10  36 

10  08 

9  40 

9  16 

20 

24 

21  53 

20  56 

19  58 

19  06 

18  20 

17  29 

16  42 

16  02 

15  16 

14  36 

13  55 

13  21 

24 

28 

29  48 

28  29 

27  11 

26  01 

24  58 

23  47 

22  44 

21  49 

20  47 

19  52 

18  57 

18  10 

28 

32 

38  55 

37  12 

35  30 

33  58 

32  36 

31  03 

29  42 

28  30 

27  08 

25  56 

24  45 

23  43 

32 

36 

49  15 

47  06 

44  56 

42  59 

41  15 

39  19 

37  35 

36  05 

34  21 

32  50 

31  19 

30  02 

36 

40 

60  48 

58  08 

55  28 

53  04 

50  56 

48  32 

46  24 

44  32 

42  24 

40  32 

38  40 

37  04 

40 

44 

73  34 

70  21 

67  07 

64  12 

61  37 

58  44 

56  08 

53  54 

51  18 

49  03 

46  47 

44  51 

44 

48 

87  33 

83  42 

79  52 

76  25 

73  21 

69  53 

66  47 

64  07 

6103 

58  22 

55  41 

53  22 

48 

52 

102  45 

98  14 

93  44 

89  41 

86  05 

82  01 

78  25 

75  15 

71  39 

68  30 

65  21 

62  38 

52 

56 

104  00 

99  49 

95  08 

90  56 

87  18 

83  06 

79  27 

75  37 

72  39 

56 

60 

// 

II 

II 

109  12 
II 

104  24 

100  12 

95  24 
II 

91  12 

II 

87  00 
II 

83  24 

60 

A,h 

2.28 

2.18 

2.08 

1.99 

1.91 

1.82 

1.74 

1.67 

1.59 

1.52 

1.45 

1.39 

A,h 

Log. 

0.357 

0.338 

0.318 

0.298 

0.281 

0.260 

0.240 

0.222 

0.201 

0.181 

0.161 

0.143 

Log. 

93 

46 

06 

85 

03 

07 

55 

72 

40 

84 

37 

01 

Limit 

41 

42 

43 

44 

46 

47 

49 

50 

51 

52 

54 

56 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  // 

/  II 

/  // 

/  /' 

/  // 

/  // 

1     II 

/  // 

/  // 

/  // 

Min. 

4 

0  21 

0  20 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

0  12 

4 

8 

1  24 

121 

1  17 

1  13 

1  10 

1  06 

102 

0  59 

0  56 

0  53 

0  51 

0  48 

8 

12 

3  10 

3  02 

2  53 

2  45 

2  37 

2  28 

2  22 

2  14 

2  07 

1  59 

154 

1  48 

12 

16 

5  38 

5  22 

5  07 

4  55 

4  39 

4  24 

4  10 

3  58 

3  45 

3  33 

3  22 

3  12 

16 

20 

8  48 

8  24 

8  00 

7  40 

7  16 

6  52 

6  32 

6  12 

5  52 

5  32 

5  16 

5  00 

20 

24 

12  41 

12  06 

11  31 

11  03 

10  28 

9  53 

9  24 

8  55 

8  27 

7  58 

7  35 

7  12 

24 

28 

17  15 

16  28 

15  41 

15  01 

14  15 

13  28 

12  49 

12  10 

11  30 

10  51 

10  20 

9  48 

28 

32 

22  31 

21  30 

20  29 

19  37 

18  36 

17  35 

16  44 

15  53 

15  01 

14  10 

13  29 

12  48 

32 

36 

28  31 

27  13 

25  55 

24  51 

23  33 

22  15 

21  10 

20  05 

19  01 

17  56 

17  04 

16  12 

36 

40 

35  12 

33  36 

32  00 

30  40 

29  04 

27  28 

26  08 

24  48 

23  28 

22  08 

2104 

20  00 

40 

44 

42  36 

40  39 

38  43 

37  07 

35  10 

33  14 

3137 

30  00 

28  24 

26  47 

25  29 

24  12 

44 

48 

50  41 

48  23 

46  05 

44  09 

4151 

39  33 

37  38 

35  43 

33  47 

3152 

30  18 

28  46 

48 

52 

59  29 

56  47 

54  05 

51  49 

49  07 

46  25 

44  10 

4155 

39  39 

37  24 

35  36 

33  48 

52 

56 

69  00 

65  51 

62  43 

60  07 

56  58 

53  50 

51  13 

48  36 

46  00 

43  23 

41  17 

39  12 

56 

60 

79  12 

75  36 

72  00 

69  00 

65  24 

6148 

58  48 

55  48 

52  48 

49  48 

47  24 

45  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.32 

1.26 

1.20 

1.15 

1.09 

1.03 

0.98 

0.93 

0.88 

0.83 

0.79 

0.75 

A,h 

1 

0.120 

0.100 

0.079 

0.060 

0.037 

0.012 

9.991 

9.968 

9.944 

9.919 

9.897 

9.875 

Log. 

57 

37 

18 

70 

43 

84 

23 

48 

48 

08 

63 

06 

Limit 

58 

60 

62 

64 

66 

67 

69 

71 

73 

75 

77 

79 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

Latitude  J  4°  Declination  Contrary  Name. 

Declinations,  c     O 


86 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

,        Mill. 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 

8 

18 

33 

52 

It 
7.8 

06 
24 
55 
37 
32 

1 
7 

17 

31 

49 

If 
7.3 

58 
51 
40 
24 
D4 

5 

1  50 
7  22 
16  35 
29  29 
46  04 
66  20 

II 
6.91 

1 
6 

15 

27 

43 

62 

6.5 

// 

44 
57 
37 
47 
24 
30 

1 

1  39 
6  33 
14  45 
26  15 
41  00 
59  03 
80  21 

6.15 

1 
6 

13 

24 

38 

55 

76 

5.8 

33 
13 

59 
53 
52 

58 
11 

3 

/ 

1 
5 
13 
23 
36 
53 
72 

II 
5.5 

n 

29 
55 

18 
38 
56 
11 
23 

4 

/      // 

124 
5  38 
12  41 
22  31 
35  12 
50  41 
69  00 

II 
5.28 

/     // 

1  21 
5  23 
12  06 
21  30 
33  36 
48  23 
65  51 

II 
5.04 

1      II 

1  17 
5  08 
1134 
20  34 
32  08 
46  17 
62  59 
82  15 

II 
4.82 

/      // 

1  14 

4  55 
11  03 
19  41 
30  44 
44  16 
60  14 
78  40 

II 
4.61 

1  10 
4  44 
10  38 
18  54 
29  32 
42  31 
57  54 
75  37 

II 
4.43 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.896 
53 

0.866 

'    88 

0.839 

48 

0.813 

58 

0.788 
88 

0.765 
67 

0.743 
51 

0.722 
63 

0.702 
43 

0.683 
05 

0.663 
70 

0.646 
40 

Log. 

Limit 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

Miii- 
Tites 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

/      // 

/      // 

1     II 

/     // 

/      // 

/      // 

/     // 

/     '/ 

/     // 

/      // 

/     // 

/      // 

Min. 

4 

108 

105 

103 

101 

0  59 

0  57 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

4 

8 

4  32 

4  22 

4  12 

4  03 

3  54 

3  47 

3  39 

3  32 

3  25 

3  18 

3  13 

3  06 

8 

12 

10  12 

9  49 

9  28 

9  07 

8  47 

8  30 

8  13 

7  56 

7  41 

7  26 

7  13 

6  59 

12 

16 

18  08 

17  27 

16  48 

16  13 

15  37 

15  06 

14  35 

14  08 

13  39 

13  14 

12  51 

12  25 

16 

20 

28  20 

27  16 

26  16 

25  20 

24  24 

23  36 

22  48 

22  04 

2120 

20  40 

20  04 

19  24 

20 

24 

40  48 

39  16 

37  49 

36  29 

35  09 

33  59 

32  50 

31  47 

30  43 

29  46 

28  54 

27  56 

24 

28 

55  32 

53  27 

5129 

49  39 

47  49 

46  15 

44  42 

43  15 

4149 

40  30 

39  20 

38  02 

28 

32 

72  32 

69  48 

67  15 

64  51 

62  27 

60  25 

58  22 

56  29 

54  37 

52  54 

5122 

49  40 

32 

36 

79  04 

76  28 

73  52 

71  30 

69  07 

66  58 

65  01 

62  51 

36 

40 

91  12 

88  16 

85  20 

82  40 

80  16 

77  36 

40 

44 

44 

48 

48 

52 

. .  . 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

n 

II 

II 

II 

II 

A,h 

4.25 

4.09 

3.94 

3.80 

3.66 

3.54 

3.42 

3.31 

3.20 

3.10 

3.01 

2.91 

A,h 

Log. 

0.628 

0.611 

0.595 

0.579 

0.563 

0.549 

0.534 

0.519 

0.505 

0.491 

0.478 

0.463 

Log. 

39 

72 

50 

78 

48 

00 

03 

83 

15 

36 

57 

89 

Limit 

29 

30 

31 

31 

32 

33 

34 

35 

35 

36 

37 

38 

Min- 
utes 

Merid- 
ian 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

Alti- 
tudes 

86 


Latitude  14°  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/     // 

/     // 

/     /' 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  45 

0  44 

0  43 

0  41 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  34 

0  33 

4 

8 

3  01 

2  56 

2  50 

2  46 

2  41 

2  37 

2  32 

2  28 

2  24 

2  19 

2  16 

2  13 

8 

12 

6  47 

6  35 

6  23 

6  13 

6  01 

5  52 

5  43 

5  32 

5  24 

5  14 

5  06 

4  58 

12 

16 

12  05 

11  41 

11  21 

1103 

10  43 

10  24 

10  09 

9  52 

9  36 

9  18 

9  06 

8  50 

16 

20 

18  52 

18  16 

17  44 

17  16 

16  44 

16  16 

15  52 

15  24 

15  00 

14  32 

14  12 

13  48 

20 

24 

27  10 

26  18 

25  33 

24  52 

24  06 

23  25 

22  51 

22  11 

21  36 

20  56 

20  27 

19  52 

24 

28 

36  59 

35  48 

34  45 

33  51 

32  48 

3153 

3106 

30  11 

29  24 

28  29 

27  50 

27  03 

28 

32 

48  18 

46  46 

45  23 

44  12 

42  50 

4139 

40  37 

39  25 

38  24 

37  12 

36  21 

35  20 

32 

36 

6108 

59  11 

57  28 

55  57 

54  13 

52  42 

5125 

49  54    48  36 

47  06 

46  01 

44  43 

36 

40 

75  28 

73  04 

70  56 

69  04 

66  56 

65  04 

63  28 

61  36 

60  00 

58  08 

56  48 

55  12 

40 

44 

88  24 

85  50 

83  34 

80  59 

78  43 

76  48 

74  32 

72  36 

70  21 

68  44 

66  48 

44 

48 

96  23 

93  42 

9123 

88  42 

86  24 

83  42 

8146 

79  29 

48 

52 

107  15 

104  06 

10124 

98  14 

95  59 

93  17 

52 

56 

56 

60 

60 

It 

// 

n 

" 

II 

H 

II 

" 

n 

n 

II 

II 

A,h 

2.83 

2.74 

2.66 

2.59 

2.51 

2.44 

2.38 

2.31 

2.25 

2.18 

2.13 

2.07 

Ajh 

Log 

0.451 

0.437 

0.424 

0.413 

0.399 

0.387 

0.376 

0.363 

0.352 

0.338 

0.328 

0.315 

Log. 

79 

75 

88 

20 

67 

39 

58 

61 

18 

46 

38 

97 

Limit 

39 

39 

40 

41 

42 

43 

44 

44 

45 

46 

47 

48 

Min- 
utes 

Merid- 
ian 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44°      45° 

46° 

47° 

Hour 
Angles 

/     // 

/     //    /     // 

Min. 

Min. 

4 

0  32 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

0  26 

0  25 

0  24 

0  23 

4 

8 

2  09 

2  05 

2  02 

1  58 

155 

152 

150 

1  46 

J  43 

1  41 

1  38 

136 

8 

12 

4  49 

4  43 

4  35 

4  26 

4  19 

4  12 

4  06 

3  59 

3  53 

3  46 

3  40 

3  35 

12 

16 

8  35 

8  21 

8  09 

7  54 

7  41 

7  28 

7  18 

7  05 

6  55 

6  42 

6  32 

6  21 

16 

20 

13  24 

13  04 

12  44 

12  20 

12  00 

11  40 

11  24 

11  04 

10  48 

10  28 

10  12 

9  56 

20 

24 

19  18 

18  49 

18  20 

17  46 

17  17 

16  48 

16  25 

15  57 

15  34 

15  04 

14  41 

14  18 

24 

28 

26  16 

25  37 

24  58 

24  10 

23  31 

22  52 

22  21 

21  41 

21  10 

20  31 

20  00 

19  29 

28 

32 

34  18 

33  27 

32  36 

3134 

30  43 

29  52 

29  11 

28  19 

27  38 

26  48 

26  07 

25  26 

32 

36 

43  25 

42  20 

41  15 

39  58 

38  53 

37  48 

36  56 

35  52 

35  00 

33  55 

33  03 

32  11 

36 

40 

53  36 

52  16 

50  56 

49  20 

48  00 

46  40 

45  36 

44  16 

43  12 

4152 

40  48 

39  44 

40 

44 

64  51 

63  14 

6137 

59  42 

58  05 

56  28 

55  10 

53  34 

52  17 

50  40 

49  22 

48  04 

44 

48 

77  11 

75  16 

73  21 

7102 

69  07 

67  10 

65  38 

63  44 

62  12    60  17 

58  45 

57  13 

48 

52 

90  35 

88  20 

86  05 

83  22 

8107 

78  52 

77  04 

74  48 

73  OO;  70  45 

68  57 

67  09 

52 

56 

105  03 

102  26 

99  49 

96  42 

94105 

9128 

89  22 

86  46 

84  41 

82  04 

79  58 

77  52 

56 

60 

114  36 

11100 

108  00 

105  00 

102  36 

99  36 

97  12 

94  12 

9148 

89  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.01 

1.96 

1.91 

1.85 

1.80 

1.75 

1.71 

1.66 

1.62 

1.57 

1.53 

1.49 

A, A 

Log. 

0.303 

0.292 

0.281 

0.267 

0.255 

0.243 

0.233 

0.220 

0.209 

^  0.195 

0.184 

0.173 

Log. 

20 

26 

03 

17 

27 

04 

00 

11 

52 

90 

69 

19 

Limit 

49 

50 

51 

52 

52 

53 

54 

55 

56 

56 

57 

58 

Min- 
utes 

Merid- 
ian 

40° 

39°  1   38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

Latitude  J  4°  Declination  Contrary  Name. 


87 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Anglea 

Min. 

/   // 

1      It 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  It 

/  // 

Min. 

4 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

0  19 

0  18 

0  18 

0  17 

0  16 

4 

8 

1  33 

130 

127 

124 

1  22 

120 

1  17 

1  15 

1  12 

1  10 

108 

106 

8 

12 

3  28 

3  22 

3  16 

3  10 

3  05 

3  00 

2  54 

2  48 

2  42 

2  38 

2  33 

2  28 

12 

16 

6  08 

5  58 

5  48 

5  38 

5  27 

5  20 

5  10 

5  00 

4  50 

4  42 

4  31 

4  24 

16 

20 

9  36 

9  20 

9  04 

8  48 

8  32 

8  20 

8  04 

7  48 

7  32 

7  20 

7  04 

6  52 

20 

24 

13  49 

13  26 

13  04 

12  41 

12  17 

12  00 

1137 

11  14 

10  51 

10  34 

10  11 

9  53 

24 

28 

18  49 

18  18 

17  46 

17  15 

16  44 

16  20 

15  49 

15  17 

14  46 

14  22 

13  51 

13  28 

28 

32 

24  35 

23  54 

23  12 

22  31 

2151 

2120 

20  39 

19  58 

19  17 

18  46 

18  05 

17  35 

32 

36 

3106 

30  14 

29  23 

28  31 

27  39 

27  00 

26  08 

25  17 

24  25 

23  46 

22  54 

22  15 

36 

40 

38  24 

37  20 

36  16 

35  12 

34  08 

33  20 

32  16 

31  12 

30  08 

29  20 

28  16 

27  28 

40 

44 

46  27 

45  10 

43  53 

42  36 

41  18 

40  20 

39  02 

37  46 

36  28 

35  30 

34  12 

33  14 

44 

48 

55  18 

53  46 

52  13 

50  41 

49  09 

48  00 

46  28 

44  55 

43  23 

42  14 

40  42 

39  33 

48 

52 

64  54 

63  06 

61  17 

59  29 

57  41 

56  20 

54  32 

52  43 

55  55 

49  34 

47  46 

46  25 

52 

56 

75  15 

73  10 

7105 

69  00 

66  54 

65  20 

63  14 

61  10 

59  04 

57  30 

55  24 

53  50 

56 

60 

86  24 

84  00 

81  36 

79  12 

76  48 

75  00 

72  36 

70  12 

67  48 

66  00 

63  36 

6148 

60 

ti 

It 

It 

ti 

" 

" 

tt 

I' 

ti 

ti 

" 

11 

A,h 

1.44 

1.40 

1.36 

1.32 

1.28 

1.25 

1.21 

1.17 

1.13 

1.10 

1.06 

1.03 

Ajh 

Log. 

0.158 

0.146 

0.133 

0.120 

0.107 

0.096 

0.082 

0.068 

0.053 

0.041 

0.025 

0.012 

Log. 

36 

13 

54 

57 

21 

91 

79 

19 

08 

39 

31 

84 

Limit 

60 

62 

63 

65 

66 

67 

69 

71 

72 

73 

74 

75 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/  // 

/  It 

1     It 

1     It 

1      It 

/  // 

/  // 

/  // 

/  // 

1     If 

/  It 

/  // 

Min. 

4 

0  15 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

0  12 

0  11 

Oil 

Oil 

0  10 

4 

8 

103 

loi 

0  58 

0  57 

0  54 

0  52 

0  51 

0  48 

0  46 

0  43 

0  41 

0  39 

8 

12 

2  23 

2  19 

2  13 

2  08 

2  02 

158 

154 

148 

1  44 

137 

1  33 

129 

12 

16 

4  13 

4  05 

3  55 

3  48 

3  38 

3  30 

3  22 

3  12 

3  04 

2  54 

2  47 

2  39 

16 

20 

6  36 

6  24 

6  08 

5  56 

5  40 

5  28 

5  16 

5  00 

4  48 

4  32 

4  20 

4  08 

20 

24 

9  30 

9  13 

8  50 

8  33 

8  10 

7  53 

7  35 

7  12 

6  55 

6  32 

6  15 

5  58 

24 

28 

12  57 

12  33 

12  02 

1138 

1106 

10  43 

10  20 

9  48 

9  25 

8  53 

8  29 

8  06 

28 

32 

16  54 

16  23 

15  42 

15  11 

14  30 

13  59 

13  29 

12  48 

12  17 

11  36 

1105  10  34 

32 

36 

2123 

20  44 

19  52 

19  14 

18  22 

17  43 

17  04 

16  12 

15  33 

14  42 

14  03  13  24 

36 

40 

26  24 

25  36 

24  32 

23  44 

22  40 

2152 

2104 

20  00 

19  12 

18  08 

17  20 

16  32 

40 

44 

3156 

30  58 

29  41 

28  43 

27  26 

26  28 

25  29 

24  12 

23  14 

2157 

20  59 

20  01 

44 

48 

38  01 

36  52 

35  20 

34  10 

32  38 

31  29 

30  18 

28  46 

27  37 

26  06 

24  57 

23  48 

48 

52 

44  37 

43  16 

41  28 

40  06 

38  18 

36  57 

35  36 

33  48 

32  27 

30  38 

29  17 

27  56 

52 

56 

5144 

50  10 

48  05 

46  31 

44  26 

42  52 

41  17 

39  12 

37  38 

35  33 

33  59 

32  25 

56 

60 

59  24 

57  36 

55  12 

53  24 

5100 

49  12 

47  24 

45  00 

43  12 

40  48 

39  00 

37  12 

60 

II 

II 

II 

II 

II 

It 

It 

It 

It 

II 

It 

It 

Aih 

0.99 

0.96 

0.92 

0.89 

0.85 

0.82 

0.79 

0.75 

0.72 

0.68 

0.65 

0.62 

A,h 

Log. 

9.995 

9.982 

9.963 

9.949 

9.929 

9.913 

9.897 

9.875 

9.857 

9.832 

9.812 

9.792 

Log. 

64 

27 

79 

39 

42 

81 

63 

06 

33 

51 

91 

39 

Limit 

77 

78 

79 

79 

80 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

Alti- 
tudes 

Latitude  J 5°  Decimation  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

1°        2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

10°      11° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

7 
17 
31 
48 

II 
7.3. 

57 
49 
35 
17 
52 

5 

2 

8 
18 
33 
52 

n 

7.8^ 

06 
22 
49 
27 
16 

I 

1 

2 

9 
20 
35 
56 

II 
8.4. 

14 

00 
14 
58 
12 

J 

/ 

2 

9 
21 
38 

* 
9.1 

26 
43 
51 
53 

1 

2 
10 
23 
42 

9.9 

II 

38 
34 
49 
19 

2 

2 
11 
26 
46 

II 
10.8 

II 

54 
36 
37 
25 

3 

12 

28 

n 

12.0 

n 

13 

52 
57 

5 

/     II 

3  37 
14  26 
32  28 

. 

n 

13.53 

1     II 

4  06 
16  27 
36  59 

II 
15.41 

4  46 
19  06 

n 

17.92 

5  43 
22  52 

n 

21.43 

1 

// 

I) 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.865 
10 

0.894 
32 

0.925 
83 

0.959 
52 

0.996 
51 

1.036 
63 

1.081 
35 

1.131 
30 

1.187 
80 

1.253 
34 

1.331 
02 

Log. 

Limit 

19 

18 

17 

16 

15 

14 

12 

11 

10 

9 

8 

6 

Min- 
utes 

Merid- 
ian    ' 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16°" 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 
II 

// 

n 

// 

1 

II 

II 

// 

1 

II 

// 

n 

// 

II 

It 

n 

1 

5 
21 

II 
20.4 

27 
49 

5 

/ 

4 
18 
40 

■'' 
16.9 

II 

31 
04 
40 

4 

/      // 

3  51 
15  24 
34  38 

II 
14.43 

3 
13 
30 

II 
12.5' 

21 
23 
36 

1 

ISIin. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

1.310 
69 

1.228 
91 

1.159 
27 

1.098 
30 

Log. 

Limit 

5 

3 

1 

0 

2 

4 

6 

7 

8 

10 

11 

12 

Min- 
utes 

Merid- 
ian 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

Qrto       Alti- 
°^       tudes 

Latitude  J 5°  Declination  Same  Name. 


89 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

2 
11 
26 

11.0 

57 
50 
J6 

/ 

2 
10 
23 
42 

11 
9.9 

It 

38 
J3 
16 
14 

3 

/ 

2 

9 
21 
38  ( 

II 
8.9 

22 
31 
26 
36 

3 

1 

2 

8 
19 
34 
54 

8.1 

// 

10 
iO 
30 
12 
12 

3 

1 
1, 

7. 
17. 
31' 
49. 

II 
7.4 

// 

59 
57 
52 
14 
36 

1 

1  . 

7 

16 
29 
45 
65 

6.8 

// 

50 

19 
28 
16 
14 
52 

3 

/     // 

142 
6  46 
15  14 
27  06 
42  20 
60  58 
82  59 

II 
6.35 

1     II 

1  34 
6  17 
14  10 
25  10 
39  20 
56  38 
77  06 

II 
5.90 

/     // 

128 
5  52 
13  12 
23  28 
36  40 
52  48 
71  52 

II 
5.50 

/     // 

123 
5  29 
12  21 
21  59 
34  20 
49  27 
67  17 

II 
5.15 

1  17 
5  09 
11  35 
20  37 
32  12 
46  22 
63  07 
82  26 

II 
4.83 

/      // 

1  13 
4  51 
10  54 
19  22 
30  16 
43  35 
59  19 
77  29 

4.54 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.044 
54 

0.995 
64 

0.950 
85 

0.910 
09 

0.871 
57 

0.836 
32 

0.802 

77 

0.770 
85 

0.740 
36 

0.711 
81 

0.683 
95 

0.657 
06 

Log. 

Limit 

13 

14 

16 

17 

18 

20 

21 

22 

24 

25 

26 

27 

Min- 
utes 

Merid- 
ian 

81' 

) 

80' 

3 

79' 

■> 

78' 

3 

77' 

3 

76' 

3 

75° 

74' 

3 

73' 

3 

72' 

3 

71< 

3 

70° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/      // 

/     // 

1     " 

/      // 

/     // 

/     // 

/     // 

/     // 

1     II 

/     // 

/     // 

Min. 

4 

108 

105 

101 

0  58 

0  55 

0  52 

0  50 

0  47 

0  45 

0  43 

0  41 

0  39 

4 

8 

4  34 

4  19 

4  05 

3  51 

3  41 

3  30 

3  18 

3  09 

3  00 

2  51 

2  44 

2  37 

8 

12 

10  17 

9  42 

9  10 

8  41 

8  16 

7  51 

7  26 

7  05 

6  44 

6  26 

6  09 

5  52 

12 

16 

18  15 

17  14 

16  18 

15  27 

14  40 

13  57 

13  14 

12  35 

12  00 

11  26 

10  55 

10  24 

16 

20 

28  32 

26  56 

25  28 

24  08 

22  56 

2148 

20  40 

19  40 

18  44 

17  52 

17  04 

16  16 

20 

24 

4105 

38  47 

36  41 

34  46 

33  01 

3123 

29  46 

28  19 

26  59 

25  44 

24  35 

23  25 

24 

28 

55  56 

52  47 

49  55 

47  18 

44  57 

42  44 

40  30 

38  33 

36  43 

35  01 

33  27 

31  53 

28 

32 

73  03 

68  57 

65  11 

6146 

58  43 

55  49 

52  54 

50  21 

47  57 

45  44 

43  41 

41  39 

32 

36 

78  12 

74  18 

70  38 

66  58 

63  43 

60  42 

57  54 

55  18 

52  42 

36 

40 

9144 

87  12 

82  40 

78  40 

74  56 

71  28 

68  16 

65  04 

40 

44 

86  29 

82  36 

78  43 

44 

48 

93  42 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

" 

I' 

" 

II 

II 

II 

" 

II 

II 

A,h 

4.28 

4.04 

3.82 

3.62 

3.44 

3.27 

3.10 

2.95 

2.81 

2.68 

2.56 

2.44 

A,h 

Log. 

0.631 

0.606 

0.582 

0.558 

0.536 

0.514 

0.491 

0.469 

0.448 

0.428 

0.408 

0.387 

Log. 

44 

38 

06 

71 

56 

55 

36 

82 

71 

13 

24 

39 

Limit 

28 

29 

30 

31 

33 

34 

35 

36 

37 

38 

39 

40 

Min- 
utes 

Merid- 
ian 

69 

3 

68 

3 

67 

3 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

90 


Latitude  15°  Declination  Same  Name* 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

// 
2.33 

t     II 

0  35 

2  23 

5  21 

9  31 

14  52 

21  24 

29  09 

38  04 

48  10 

59  28 

7157 

85  38 

100  30 

II 
2.23 

1     II 

0  34 

2  16 

5  06 

9  06 

14  12 

20  27 

27  50 

36  21 

46  01 

56  48 

68  44 

81  46 

95  59 

II 
2.13 

/  // 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

91  29 

106  06 

II 
2.03 

1      II 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

51  44 

62  35 

74  30 

87  26 

10123 

II 
1.94 

/  // 

0  30 

158 

4  26 

7  54 

12  20 

17  46 

24  10 

31  34 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 

II 

1.85 

/  // 

0  28 

154 

4  16 

7  33 

1148 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 

II 

1.77 

/  // 

0  27 

148 

4  03 

7  13 

11  16 

16  14 

22  05 

28  50 

36  31 

45  04 

54  32 

64  53 

76  09 

88  20 

10124 
II 

1.69 

/  // 

0  26 
143 
3  53 
6  55 

10  48 
15  34 
21  10 
27  38 
35  00 
43  12 
52  17 
62  12 
73  00 
84  41 

97  12 

II 

1.62 

0  25 

1-39 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

4104 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

1     II 

0  23 

134 

3  32 

6  16 

9  48 

14  06 

19  13 

25  06 

3145 

39  12 

47  26 

56  27 

66  15 

76  50 

88  12 
II 

1.47 

/   // 

0  22 

1  30 
3  23 
601 
9  24 

13  32 
18  26 
24  04 
30  27 
37  36 
45  29 
54  09 
63  33 
73  41 
84  36 

1.41 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.367 
36 

0.348 
30 

0.328 
38 

0.307 
50 

0.287 
80 

0.267 
17 

0.247 
97 

0.227 
89 

0.209 
52 

0.187 
52 

0.167 
32 

0.149 
22 

Log. 

Limit 

41 

42 

43 

43 

45 

46 

48 

49 

50 

51 

53 

55 

Min- 
utes 

Alti- 
tudes 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   // 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

5127 

60  23 

70  02 

80  24 
II 

1.34 

1      II 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 

II 

1.28 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

II 

1.22 

/  // 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

II 

1.16 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

II 

1.04 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

51  44 

59  24 
II 

0.99 

1     II 

0  15 

1  00 

2  16 
4  00 
6  16 
9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
II 

0.94 

/  // 
0  14 

0  57 

2  08 

3  48 
5  56 
8  33 

1138 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 

/  // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 

50  24 

II 

0.84 

/  // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 

II 

0.79 

/  II 

0  12 

0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 

44  24 

II 

0.74 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

0.127 
10 

0.107 
21 

0.086 
36 

0.064 
46 

0.041 
39 

0.017 
03 

9.995 
64 

9.973 
13 

9.949 
39 

9.924 
28 

9.897 
63 

9.869 
23 

Log. 

Limit 

57 

59 

61 

63 

65 

67 

69 

71 

73 

75 

77 

79 

Min- 
utes 

Merid- 
ian 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

Alti- 
tudes 

Latitude  J  5°  Declination  Contrary  Name. 


91 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Mm. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

1 

1 

7 

17 
31 

48 

II 
7.3. 

// 

57 
49 
35 
17 
52 

J 

1 

1 

7 

16 
29 
45 
66 

II 
6.8J 

// 

50 
20 
31 
21 
52 
33 

1 
6 
15 
27 
43 
62 

II 
6.4 

43 
55 
34 
38 
12 
12 

3 

1 
6 
14 
26 
40 
58 
80 

II 
6.1 

// 

38 
32 
42 
10 
52 
51 
36 

3 

1 
6 
13 
24 
38 
55 
75 

II 
5.8 

// 

33 

12 
56 
48 
44 
47 
55 

I 

1 
5 
13 
23 
36 
53 
72 

II 
5.5 

// 

28 
53 

15 
33 

48 
DO 

08 

2 

1 
5 
12 
22 
35 
50 
68 

II 
5.2 

// 

24 
37 
38 
26 
04 
30 
14 

5 

/     // 

1  20 
5  22 
12  04 
21  28 
33  32 
48  17 
65  44 

II 
5.03 

/     // 

1  17 
5  08 
11  32 
20  32 
32  04 
46  11 
62  51 
82  05 

n 

4.81 

1     II 

1  14 
4  55 
1103 
19  41 
30  44 
44  16 
60  14 
78  40 

II 
4.61 

/     // 

1  10 
4  43 
10  37 
18  51 
29  28 
42  26 
57  46 
75  26 

II 
4.42 

1     II 

108 
4  32 
10  12 
18  08 
28  20 
40  48 
55  32 
72  32 

4.25 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.865 
10 

0.837 
59 

0.811 
58 

0.787 
46 

0.764 

18 

0.741 
94 

0.720 
99 

0.701 
57 

0.682 
15 

0.663 
70 

0.645 
42 

0.628 
39 

Log. 

Limit 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

Min- 
utes 

Merid- 
ian 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

/     // 

1     It 

/     II 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

105 

103 

101 

0  59 

0  57 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  46 

4 

8 

4  22 

4  12 

4  03 

3  54 

3  47 

3  39 

3  32 

3  26 

3  19 

3  13 

3  06 

3  02 

8 

12 

9  49 

9  28 

9  07 

8  47 

8  30 

8  13 

7  56 

7  42 

7  27 

7  13 

7  01 

6  49 

12 

16 

17  27 

16  48 

16  13 

15  37 

15  06 

14  35 

14  08 

13  42 

13  17 

12  51 

12  27 

12  07 

16 

20 

27  16 

26  16 

25  20 

24  24 

23  36 

22  48 

22  04 

2124 

20  44 

20  04 

19  28 

18  56 

20 

24 

39  16 

37  49 

36  29 

35  09 

33  59 

32  50 

3147 

30  49 

29  52 

28  54 

28  02 

27  16 

24 

28 

53  27 

5129 

49  39 

47  49 

46  15 

44  42 

43  15 

4157 

40  39 

39  20 

38  10 

37  06 

28 

32 

69  48 

67  15 

64  51 

62  27 

60  25 

58  22 

56  29 

44  47 

53  04 

51  22 

49  50 

48  28 

32 

36 

79  04 

76.28 

73  52 

71  30 

69  2C 

67  11 

65  01 

63  04 

61  21 

36 

40 

91  12 

88  16 

85  36 

82  56 

80  16 

77  52 

75  44 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

4.09 

3.94 

3.80 

3.66 

3.54 

3.42 

3.31 

3.21 

3.11 

3.01 

2.92 

2.84 

A,h 

Log. 

0.611 

0.595 

0.579 

0.563 

0.549 

0.534 

0.519 

0.506 

0.492 

0.478 

0.465 

0.453 

Log. 

72 

50 

78 

48 

00 

03 

83 

51 

76 

57 

38 

32 

Limit 

30 

31 

32 

32 

33 

34 

35 

35 

35 

36 

37 

38 

Min- 
utes 

Merid- 
ian 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

Alti- 
tudes 

92 


Latitude  15°  Declination  Contrary  Name 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 
,36 

40 

44 

48 

52 

56 

60 

A,h 

0  44 
2  56 
6  36 
1144 
18  20 
26  24 
35  56 
46  56 
59  24 
73  20 
88  44 

2.75 

0  43 
2  51 
6  24 
11  24 
17  48 
25  38 
34  53 
45  34 
57  41 
71  12 
86  10 

II 
2.67 

1     II 

0  42 
2  46 
6  14 
1106 
17  20 
24  58 
33  58 
44  22 
56  10 
69  20 
83  54 
99  50 

II 
2.60 

/      // 

0  40 
2  42 
6  04 
10  48 
16  52 
24  17 
33  04 
43  11 
54  39 
67  28 
8138 
97  09 

II 
2.53 

1     II 

0  39 
2  38 
5  55 
10  29 
16  24 
23  37 
32  09 
41  59 
53  08 
65  36 
79  22 
94  28 

II 
2.46 

/      // 

0  38 

2  33 

5  44 

10  12 

15  56 

22  57 

31  14 

40  47 

51  38 

63  44 

77  07 

91  46 

107  42 

II 
2.39 

0  37 

2  28 

5  34 

9  54 

15  28 

22  17 

30  19 

39  35 

50  07 

61  52 

74  52 

89  05 

104  33 

2.32 

r       II 

0  36 

2  25 

5  26 

9  38 

15  04 

2142 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

101  51 

II 
2.26 

/      // 

0  35 

2  21 

5  17 

9  23 

14  40 

2107 

28  45 

37  33 

47  31 

58  40 

70  59 

84  29 

99  09 

2.20 

/      // 

0  35 

2  17 

5  08 

9  08 

14  16 

20  33 

27  57 

36  31 

46  14 

57  04 

69  03 

82  10 

96  26 

II 
2.14 

/      // 

0  33 

2  13 

5  00 

8  52 

13  52 

19  58 

27  11 

35  30 

44  56 

55  28 

67  07 

79  52 

93  44 

II 
2.08 

/     // 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

91  29 

II 
2.03 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.439 
33 

0.426 
51 

0.414 
97 

0.403 
12 

0.390 
94 

0.378 
40 

0.365 
49 

0.354 
11 

0.342 
42 

0.330 
41 

0.318 
06 

0.307 
50 

Log. 

Limit 

39 

40 

41 

42 

43 

44 

45 

45 

46 

47 

48 

49 

Min- 
utes 

Merid- 
ian 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  31 

2  05 

4  44 

8  24 

13  08 

18  54 

25  45 

33  38 

42  33 

52  32 

63  34 

75  39 

88  47 

102  57 

II 
1.97 

1     II 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

4128 

51  12 

61  57 

73  44 

86  32 

100  21 

II 
1.92 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

31  55 

40  24 

49  52 

60  21 

71  48 

84  16 

97  45 

112  12 
II 

1.87 

/      // 

0  29 

156 

4  22 

7  46 

12  08 

17  29 

23  47 

3103 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 

n 

1.82 

/      // 

0  28 

154 

4  16 

7  33 

11  48 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 
II 

1.77 

1      II 

0  27 

150 

4  08 

7  20 

1128 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 

II 

1.72 

/     // 

0  27 

147 

4  02 

7  10 

11  12 

16  08 

2157 

28  40 

36  18 

44  48 

54  13 

64  30 

75  42 

87  49 

100  48 
II 

1.68 

/     // 

0  26 

144 

3  54 

6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 
II 

1.63 

/      // 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

61  03 

71  39 

83  06 

95  24 
II 

1.59 

/     II 

0  25 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

81  01 

93  00 
II 

1.55 

1       n 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 
90  36 

1.51 

/      // 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 

1.46 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.294 
47 

0.283 
30 

0.271 
84 

0.260 
07 

0.247 
97 

0.235 
53 

0.225 
31 

0.212 
19 

0.201 
40 

0.190 
33 

0.178 
98 

0.164 
35 

Log. 

Limit 

50 

51 

52 

52 

53 

54 

55 

56 

57 

58 

59 

60 

Min- 
utes 

Merid- 
ian 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

Alti- 
tudes 

Latitude  15°  Declination  Contrary  Name. 


93 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54°      55°      56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/       // 

0  22 

131 

3  25 

6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 

1.42 

/     // 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
II 

1.38 

/     // 

0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

51  50 

60  50 

70  34 

8100 
II 

1.35 

/     // 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 

1.31 

/     // 

0  20 
121 
3  03 
5  25 

8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
II 

1.27 

0  19 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

/      // 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
71  24 

1.19 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

51  49 

60  07 

69  00 
It 

1.15 

/      // 

0  18 

1  11 

2  41 

4  47 
7  28 
10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

1.12 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

41  51 

49  07 

56  58 

65  24 
II 

1.09 

/     // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

1.05 

1      II 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
II 

1.02 

Mill. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.152 
29 

0.139 

88 

0.130 
33 

0.117 

27 

0.103 

80 

0.089 
91 

0.075 
55 

0.060 
70 

0.049 
22 

0.037 
43 

0.021 
19 

0.008 
60 

Log. 

Limit 

61 

63 

64 

65 

67 

68 

70 

72 

73 

74 

75 

76 

Min- 
utes 

Merid- 
ian 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/       n 

/      // 

/      II 

1      II 

/      // 

/      // 

1      II 

/      // 

1     II 

/      // 

1      II 

Min. 

4 

0  15 

0  15 

0  14 

0  14 

0  14 

0  13 

0  12 

0  12 

Oil 

Oil 

0  11 

0  10 

4 

8 

102 

101 

0  58 

0  56 

0  54 

0  51 

0  50 

0  47 

0  45 

0  43 

0  41 

0  39 

8 

12 

2  22 

2  17 

2  11 

2  07 

2  02 

156 

152 

147 

142 

137 

133 

1  29 

12 

16 

4  10 

4  03 

3  53 

3  45 

3  38 

3  28 

3  19 

3  09 

3  02 

2  54 

2  47 

2  39 

16 

20 

6  32 

6  20 

6  04 

5  52 

5  40 

5  24 

5  12 

4  56 

4  44 

4  32 

4  20 

4  08 

20 

24 

9  24 

9  07 

8  44 

8  27 

8  10 

7  47 

7  29 

7  06 

6  49 

6  32 

6  15 

5  58 

24 

28 

12  49 

12  25 

11  54 

11  30 

1106 

10  35 

10  12 

9  40 

9  17 

8  53 

8  29 

8  06 

28 

32 

16  44 

16  13 

15  32 

15  01 

14  30 

13  49 

13  19 

12  38 

12  07 

1136 

11  05 

10  34 

32 

36 

21  10 

20  31 

19  39 

19  01 

18  22 

17  30 

16  51 

15  59 

15  20 

14  42 

14  03 

13  24 

36 

40 

26  08 

.25  20 

24  16 

23  28 

22  40 

21  36 

20  48 

19  44 

18  56 

18  08 

17  20 

16  32 

40 

44 

3137 

30  39 

29  21 

28  24 

27  26 

26  08 

25  10 

23  52 

22  54 

21  57 

20  59 

20  01 

44 

48 

37  38 

36  29 

34  57 

33  47 

32  38 

3106 

29  55 

28  23 

27  14 

26  06 

24  57 

23  48 

48 

52 

44  10 

42  49 

4101 

39  39 

38  18 

36  30 

35  09 

33  21 

32  00 

30  38 

29  17 

27  56 

52 

56 

51  13 

49  39 

47  33 

46  00 

44  26 

42  20 

40  46 

38  40 

37  06 

35  33 

33  59 

32  25 

56 

60 

58  48 

57  00 

54  36 

52  48 

5100 

48  36 

46  48 

44  24 

42  36 

40  48 

39  00 

37  12 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

It 

II 

II 

A,h 

0.98 

0.95 

0.91 

0.88 

0.85 

0.81 

0.78 

0.74 

0.71 

0.68 

0.65 

0.62 

A,h 

Log. 

9.991 

9.977 

9.959 

9.944 

9.929 

9.908 

9.892 

9.869 

9.851 

9.832 

9.812 

9.792 

Log. 

23 

72 

04 

48 

42 

49 

09 

23 

26 

51 

91 

39 

Limit 

78 

79 

79 

80 

80 

80 

82 

84 

86 

88 

90 

92 

Min- 
utes 

Merid- 
ian 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

Alti- 
tudes 

94 


Latitude  16°  Declination  Same  Name. 


Declixations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

7 
16 
29 
45 
65 

II 
6.8. 

50 
18 
26 
14 
10 
i6 

3 

1 

7 
17 
31 

48 

II 
7.2< 

56 
47 
30 
D6 
36 

2 

8 
18 
33 
52 

II 
7.8( 

// 

05 
19 
43 
17 
DO 

) 

/      II 

2  14 

8  56 

20  07 

36  45 

55  52 

II 
8.38 

2 

9 

21 

38 

II 
9.0 

25 
40 
45 
39 

5 

1 

2 
10 
23 
42 

II 
9.8. 

38 
30 
38 
32 

5 

2 
11 
25 
46 

II 
10.8 

53 
32 

57 
08 

I 

1     II 

3  11 

12  46 

28  46 

11.98 

/     // 

3  35 
14  20 
32  14 

II 
13.43 

4  05 
16  19 
36  43 

II 
15.30 

4  43 

18  58 

II 
17.78 

5  40 
22  41 

II 
21.26 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.835 
69 

0.862 
73 

0.892 
09 

0.923 
24 

0.957 
13 

0.993 
44 

1.033 
83 

1.078 
46 

1.128 
08 

1.184 
69 

1.249 
93 

1.327 
56 

Log. 

Limit 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

Min- 
utes 

Merid- 
ian 

74' 

' 

75' 

> 

76' 

) 

77° 

78' 

) 

79' 

> 

80' 

5 

81° 

82° 

83° 

84< 

3 

85< 

3 

Alti- 
tudes 

Declination's 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

II 

// 

II 

// 

/ 

II 

II 

/ 

// 

/ 

// 

II 

// 

II 

// 

1 
II 

II 

5 
21 

II 
20.2: 

23 
34 

4 
17 
40 

II 
16.7' 

28 
52 
11 

1 

1 

3 
15 
34 

II 
14.2( 

// 

48 
13 
14 

5 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.305 

78 

1.223 
76 

1.154 
12 

Log. 

Limit 

7 

6 

4 

2 

0 

2 

4 

6 

8 

9 

10        11 

Min- 
utes 

Merid- 
ian 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84°  1    83°     tt£ 

Latitude  16°  Declination  Same  Name. 


95 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

3 
13 
29 

II 
12.3 

18 
13 
14 

1 

2 

11 
26 
46 

II 
10.9 

54 
38 
14 
38 

3 

1 

2 
10 
23 
41 

II 
9.7 

36 
26 
27 
il 

7 

1 

2 

9 

21 

37 

II 

8.8 

21 
24 
38 
36 

I 

2 

8 

19 

34 

53 

II 
8.0 

// 

08 
33 
13 
13 

28 

2 

/     // 

158 

7  50 

17  37 

31  19 

48  56 

II 
7.34 

1 
7 

16 

28 

45 

64 

II 
6.7 

// 

49 
13 
14 
50 
34 
54 

3 

/     // 

140 
6  40 
15  00 
26  40 
41  40 
60  00 
8140 

II 
6.25 

1  33 
6  12 
13  56 
24  48 
38  44 
55  47 
75  55 

II 
5.81 

/      // 

126 
5  47 
12  59 
23  05 
36  04 
5156 
70  42 

II 
5.41 

1  21 
5  24 
12  09 
21  35 
33  44 
48  35 
66  07 

II 
5.06 

/     // 

1  16 
5  04 
11  24 
20  16 
31  40 
45  36 
62  02 
81  04 

II 
4.75 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.093 
07 

1.038 
62 

0.989 
89 

0.944 

98 

0.904 

17 

0.865 
70 

0.829 
95 

0.795 

88 

0.764 

18 

0.733 
20 

0.704 
15 

0.676 
69 

Log. 

Limit 

12 

13 

14 

15 

16 

17 

19 

21 

22 

23 

24 

26 

Min- 
utes 

Merid- 
ian 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/      // 

/     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

1     II 

Min. 

Min. 

4 

1  11 

107 

103 

100 

0  57 

0  54 

0  51 

0  49 

0  46 

0  44 

0  42 

0  40 

4 

8 

4  46 

4  30 

4  14 

4  00 

3  47 

3  36 

3  25 

3  15 

3  05 

2  56 

2  47 

2  40 

8 

12 

10  43 

10  06 

9  32 

9  00 

8  31      8  05 

7  41 

7  18 

6  56 

6  36 

6  17 

6  00 

12 

16 

19  01 

17  58 

16  56 

16  00 

15  09 

14  23 

13  39 

12  58 

12  20 

1144 

1111 

10  40 

16 

20 

29  44 

28  04 

26  28 

25  00 

23  40 

22  28 

21  20 

20  16 

19  16 

18  20 

17  28 

16  40 

20 

24 

42  48 

40  25 

38  06 

36  00 

34  05 

32  21 

30  43 

29  11 

27  45 

26  24 

25  10 

24  00 

24 

28 

58  17 

55  01 

51  53 

49  00 

46  23 

44  02 

41  49 

39  43 

37  46 

35  56 

34  14 

32  40 

28 

32 

76  07 

7151 

67  46 

64  00 

60  35 

57  31 

54  37 

5153 

49  19 

46  56 

44  42 

42  40 

32 

36 

76  41 

72  48 

69  07 

65  40 

62  26 

59  24 

56  36 

54  00 

36 

40 

89  52 

85  20 

8104 

77  04 

73  20 

69  52 

66  40 

40 

44 

88  44 

84  33 

80  40 

44 

48 

96  00 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

A,h 

4.46 

4.21 

3.97 

3.75 

3.55 

3.37 

3.20 

3.04 

2.89 

2.75 

2.62 

2.50 

A,h 

Log. 

0.649 

0.624 

0.598 

0.574 

0.550 

0.527 

0.505 

0.482 

0.460 

0.439 

0.418 

0.397 

33 

28 

79 

03 

23 

63 

15 

87 

90 

33 

30 

94 

Log. 

Limit 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

Min- 
utes 

Merid- 
ian 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

Alti- 
tudes 

96 


Latitude  J  6°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

/      // 

0  38 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 

1     II 
0  36 

/     // 
0  35 

0  33 

0  31 

/      II 
0  30 

0  29 

0  27 

0  27 

0  25 

/     // 
0  23 

0  22 

Min. 
4 

8 

2  33 

2  26 

2  19 

2  13 

2  06 

2  01 

155 

150 

145 

141 

136 

132 

8 

12 

5  43 

5  27 

5  12 

4  58 

4  46 

4  32 

4  19 

4  08 

3  56 

3  46 

3  35 

3  24 

12 

16 

10  09 

9  41 

9  16 

8  50 

8  26 

8  04 

7  41 

7  20 

7  00 

6  42 

6  21 

6  06 

16 

20 

15  52 

15  08 

14  28 

13  48 

13  12 

12  36 

12  00 

1128 

10  56 

10  28 

9  56 

9  32 

20 

24 

22  51 

2147 

20  50 

19  52 

19  00 

18  09 

17  17 

16  31 

15  45 

15  04 

14  18 

13  43 

24 

28 

3106 

29  40 

28  21 

27  03 

25  53 

24  42 

23  31 

22  29 

2125 

20  31 

19  29 

18  42 

28 

32 

40  37 

38  45 

37  02 

35  20 

33  48 

32  15 

30  43 

29  21 

27  59 

26  48 

25  26 

24  25 

32 

36 

5125 

49  02 

46  53 

44  43 

42  46 

40  50 

38  53 

37  09 

35  26 

33  55 

32  11 

30  53 

36 

40 

63  28 

60  32 

57  52 

55  12 

52  48 

50  24 

48  00 

45  52 

43  44 

4152 

39  44 

38  08 

40 

44 

76  48 

73  15 

70  02 

66  48 

63  53 

60  59 

58  05 

55  30 

52  55 

50  40 

48  04 

46  08 

44 

48 

9123 

87  10 

83  19 

79  29 

76  02 

72  34 

69  07 

66  01 

62  58 

60  17 

57  13 

54  55 

48 

52 

107  15 

102  18 

97  47 

93  17 

89  14 

85  10 

81  07 

77  31 

73  54 

70  45 

67  09 

64  27 

52 

56 

108  12 

103  29 

98  17 

94  05 

89  54 

85  43 

82  04 

77  52 

74  44 

56 

60 

113  24 

108  00 

103  12 

98  24 

94  12 

89  24 

85  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.38 

2.27 

2.17 

2.07 

1.98 

1.89 

1.80 

1.72 

1.64 

1.57 

1.49 

1.43 

A,h 

Log. 

0.376 

0.356 

0.336 

0.315 

0.296 

0.276 

0.255 

0.235 

0.214 

0.195 

0.173 

0.155 

Log. 

58 

03 

46 

97 

67 
45 

46 

27 

53 

84 

90 

19 

34 

Limit 

40 

41 

42 

44 

46 

47 

49 

50 

52 

54 

56 

Min- 
utes 

Merid- 
ian 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51= 

50° 

49° 

48° 

47° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

/     // 

/     II 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/      // 

1     II 

/      " 

Min. 

4 

0  22 

0  20 

0  19 

0  19 

0  18 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

4 

8 

1  27 

123 

119 

1  15 

1  11 

107 

104 

101 

0  57 

0  54 

0  51 

0  48 

8 

12 

3  16 

3  06 

2  57 

2  48 

2  39 

2  31 

2  24 

2  17 

2  10 

2  02 

155 

148 

12 

16 

5  48 

5  30 

5  15 

5  00 

4  45 

4  29 

4  16 

4  03 

3  50 

3  38 

3  25 

3  12 

16 

20 

9  04 

8  36 

8  12 

7  48 

7  24 

7  00 

6  40 

6  20 

6  00 

5  40 

5  20 

5  00 

20 

24 

13  04 

12  23 

1148 

11  14 

10  40 

10  05 

9  36 

9  07 

8  38 

8  10 

7  41 

7  12 

24 

28 

17  46 

16  52 

16  05 

15  17 

14  30 

13  43 

13  04 

12  25 

1146 

1106 

10  27 

9  48 

28 

32 

23  12 

22  01 

2100 

19  58 

18  56 

17  55 

17  04 

16  13 

15  22 

14  30 

13  39 

12  48 

32 

36 

29  23 

27  52 

26  34 

25  17 

23  59 

22  41 

2136 

20  31 

19  26 

18  22 

17  17 

16  12 

36 

40 

36  16 

34  24 

32  48 

31  12 

29  36 

28  00 

26  40 

25  20 

24  00 

22  40 

21  20 

20  00 

40 

44 

43  53 

4137 

39  41 

37  46 

35  49 

33  53 

32  16 

30  39 

29  02 

27  26 

25  49 

24  12 

44 

48 

52  13 

49  32 

47  14 

44  55 

42  37 

40  19 

38  24 

36  29 

34  34 

32  28 

30  43 

28  46 

48 

52 

61  17 

58  08 

55  26 

52  43 

50  01 

47  19 

45  04 

42  49 

40  34 

38  18 

36  03 

33  48 

52 

56 

7105 

67  25 

64  17 

61  10 

58  01 

54  53 

52  16 

49  39 

47  02 

44  26 

4149 

39  12 

56 

60 

81  36 

77  24 

73  48 

70  12 

66  36 

63  00 

60  00 

57  00 

54  00 

5100 

48  00 

45  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.36 

1.29 

1.23 

1.17 

1.11 
0.045 

1.05 
0.021 

1.00 
0.00 

0.95 

0.90 

0.85 

0.80 

0.75 

A,h 

Log. 

0.133 

0.110 

0.089 

0.068 

9.977 

9.954 

9.929 

9.903 

9.875 

Log. 

54 

59 

91 

19 

32 

19 

72 

24 

42 

09 

06 

Limit 

57 

59 

61 

63 

65 

66 

68 

70 

72 

74 

76 

78 

Min- 
utes 

Merid- 
ian 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

Alti- 
tudes 

Latitude  16°  Declination  Contrary  Name. 


97 


Declinations. 


Hour 
Angles 

0° 

1° 

2°    i     3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
■   20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

7 
16 
29 
45 
65 

ti 
6.8 

// 

50 
18 
26 
14 
iO 
16 

5 

143 
6  53 
15  29 
27  31 
43  00 
61  55 
84  17 

n 

6.45 

138 
6  30 
14  38 
26  02 
40  40 
58  34 
79  42 
. . . 

6.10 

1 

6 

13. 
24 

38 
55 
75' 

// 
5.7 

// 

J2 
11 
54 
12 
36 
35 
10 

J 

1 

5 
13 
23 
36 
52 
72 

II 
5.5 

28 
53 
13 
31 
14 
54 
30 

1 

1 

5. 
12 
22 
35  ( 
50 
68. 

II 
5.2 

// 

24 
36 
36 
24 
)0 
24 
36 

5 

1 

5 

12 
21 
33 
48  ( 
65- 

II 
5.0 

// 

20 

21 
)1 
23 
24 
)6 
28 

1 

1 

1 

5( 
11  . 
20- 
31  . 
45. 
62 
81' 

II 
4.7 

// 

16 
)7 
30 
26 
56 
59 
34 
15 

9 

/     // 

1  14 
4  54 
1102 
19  38 
30  40 
44  10 
60  06 
78  30 

II 
4.60 

/     // 

1  10 
4  43 
10  35 
18  49 
29  24 
42  20 
57  38 
75  16 

II 
4.41 

/     // 

108 
4  32 
10  11 
18  05 
28  16 
40  42 
55  24 
72  22 

II 
4.24 

/     // 

1  05 
4  21 
9  48 
17  24 
27  12 
39  10 
53  19 
69  38 

II 
4.08 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.835 
69 

20 

0.809 
56 

0.785 
33 

0.762 
68 

0.741 
15 

0.720 
16 

0.699 
84 

0.680 
34 

0.662 
76 

0.644 
44 

0.627 
37 

0.610 
66 

Log. 

Limit 

21 

22 

23 

24 

24 

25 

26 

27 

28 

29 

29 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/     // 

/      // 

/     // 

/     // 

/      // 

/     // 

/     II 

Win. 

Min. 

4 

102 

100 

0  59 

0  57 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  46 

0  44 

4 

8 

4  11 

4  03 

3  54 

3  47 

3  39 

3  32 

3  26 

3  19 

3  13 

3  07 

3  02 

2  57 

8 

12 

9  26 

9  06 

8  47 

8  30 

8  13 

7  56 

7  42 

7  27 

7  15 

7  02 

6  49 

6  38 

12 

16 

16  46 

16  10 

15  37 

15  06 

14  35 

14  08 

13  42 

13  17 

12  53 

12  30 

12  07 

11  46 

16 

20 

26  12 

25  16 

24  24 

23  36 

22  48 

22  04 

21  24 

20  44 

20  08 

19  32 

18  56 

18  24 

20 

24 

37  43 

36  23 

35  09 

33  59 

32  50 

31  47 

30  49 

29  52 

29  00 

28  07 

27  16 

26  30 

24 

28 

51  22 

49  32 

47  49 

46  15 

44  42 

43  15 

4157 

40  38 

39  28 

38  18 

37  06 

36  04 

28 

32 

67  05 

64  41 

62  27 

60  25 

58  22 

56  29 

54  47 

53  04 

51  32 

50  01 

48  28 

47  06 

32 

36 

79  04 

76  28 

73  52 

71  30 

69  20 

67  11 

65  14 

63  17 

61  21 

59  37 

36 

40 

91  12 

88  16 

85  36 

82  56 

80  32 

78  08 

75  44 

73  36 

40 

44 

44 

48 

48 

52 

. . . 

52 

56 

56 

60 

60 

II 

" 

II 

II 

II 

n 

II 

II 

n 

II 

II 

II 

Ajh 

3.93 

3.79 

3.66 

3.54 

3.42 

3.31 

3.21 

3.11 

3.02 

2.93 

2.84 

2.76 

A,h 

Log. 

0.594 

0.578 

0.563 

0.549 

0.534 

0.519 

0.506 

0.492 

0.480 

0.466 

0.453 

0.440 

Log. 

39 

64 

48 

00 

03 

83 

51 

76 

01 

87 

32 

91 

Limit 

30 

30 

31 

32 

33 

34 

35- 

36 

36 

37 

38 

39 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

98 


Latitude  \6°  Declination  Contrary  Name* 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      // 

0  43 
2  51 
6  26 
11  26 
17  52 
25  44 
35  01 
45  44 
57  54 
71  28 
86  29 

II 
2.68 

/     // 

0  42 

2  47 
6  15 
1109 
17  24 
25  04 
34  06 
44  32 
56  23 
69  36 
84  13 

2.61 

/     // 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  11 
43  21 
54  52 
67  44 
8157 

2.54 

/      // 

0  39 

2  39 
5  56 
10  32 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 
94  51 

II 
2.47 

/      // 

0  38 

2  34 

5  46 

10  14 

16  00 

23  02 

31  22 

40  58 

51  50 

64  00 

77  26 

92  10 

108  10 

II 
2.40 

/      // 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

2.33 

/     // 

0  36 

2  26 

5  27 

9  41 

15  08 

21  47 

29  40 

38  45 

49  02 

60  32 

73  15 

87  10 

102  18 

II 
2.27 

/      II 

0  35 

2  22 

5  18 

9  26 

14  44 

21  13 

28  53 

37  43 

47  44 

58  56 

71  18 

84  52 

99  36 

II 
2.21 

0  35 

2  17 
5  09 
9  11 
14  20 
20  39 
28  05 
36  41 
46  27 
57  20 
69  23 
82  33 
96  53 

II 
2.15 

/      // 

0  34 

2  14 
5  02 
8  58 
14  00 
20  10 
27  26 
35  50 
45  22 
56  00 
67  46 
80  38 
94  38 

2.10 

/      // 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

4^04 

54  24 

65  49 

78  20 

9156 

2.04 

/      // 

0  31 

2  07 
4  47 
8  29 
13  16 
19  06 
26  01 
33  58 
42  59 
53  04 
64  12 
76  25 
89  41 

II 
1.99 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.428 
13 

0.416 
64 

0.404 
83 

0.392 
70 

0.380 
21 

0.367 
36 

0.356 
03 

0.344 
39 

0.332 
44 

0.322 
22 

0.309 
63 

0.298 
85 

Log. 

Limit 

40 

41 

42 

43 

44 

45 

46 

46 

47 

48 

49 

50 

Min- 
utes 

Merid- 
ian 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tiuies 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Anglea 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

Min. 

Min. 

4 

0  31 

0  30 

0  30 

0  28 

0  28 

0  27 

0  27 

0  26 

0  25 

0  24 

0  23 

0  22 

4 

8 

2  04 

2  01 

1  58 

1  55 

152 

1  48 

145 

142 

141 

138 

1  35 

133 

8 

12 

4  40 

4  32 

4  25 

4  18 

411 

4  03 

3  57 

3  51 

3  46 

3  40 

3  34 

3  28 

12 

16 

8  16 

8  04 

7  51 

7  38 

7  25 

7  13 

7  03 

6  53 

6  42 

6  32 

6  18 

6  08 

16 

20 

12  56 

12  36 

12  16 

1156 

11  36 

11  16 

1100 

10  44 

10  28 

10  12 

9  52 

9  36 

20 

24 

18  37 

18  09 

17  40 

17  11 

16  42 

16  14 

15  51 

15  28 

15  04 

14  41 

14  12 

13  49 

24 

28 

25  21 

24  42 

24  02 

23  24 

22  44 

22  05 

2133 

21  02 

20  31 

20  00 

19  21 

18  49 

28 

32 

33  07 

32  15 

31  24 

30  33 

29  42 

28  50 

28  09 

27  28 

26  48 

26  07 

25  16 

24  35 

32 

36 

4154 

40  50 

39  45 

38  40 

37  35 

36  31 

35  39 

34  47 

33  55 

33  03 

31  58 

3106 

36 

40 

5144 

50  24 

49  04 

47  44 

46  24 

45  04 

44  00 

42  56 

41  52 

40  48 

39  28 

38  24 

40 

44 

62  35 

60  59 

59  22 

57  45 

56  08 

54  32 

53  15 

51  57 

50  40 

49  22 

47  45 

46  27 

44 

48 

74  30 

72  34 

70  39 

68  42 

66  47    64  53 

63  21 

61  49 

60  17 

58  45 

56  50 

55  18 

48 

52 

87  26 

85  10 

82  55 

80  40 

78  25 

76  09 

74  21 

72  33 

70  45 

68  57 

66  42 

64  54 

52 

56 

101  23 

98  47 

96  10 

93  33 

90  56 

88  20 

86  15 

84  09 

82  04 

79  58 

77  21 

75  15 

56 

1  60 

113  24 

110  24 

107  24 

104  24 

10124 

99  00 

96  36 

94  12 

9148 

88  48 

86  24 

60 

II 

II 

It 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.94 

1.89 

1.84 

1.79 

1.74 

1.69 

1.65 

1.61 

\.hl 

1.53 

1.48 

1.44 

A,h 

Log. 

0.287 

0.276 

0.264 

0.252 

0.240   0.227 

0.217 

0.206 

0.195 

0.184 

0.170 

0.158 

Log. 

80 

46 

82 

85 

55 

89 

48 

83 

90 

69 

26 

36 

Limit 

50 

51 

52 

53 

54 

54 

55 

56 

57 

58 

59 

60 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

Alti- 
tudes 

Latitude  i6°  Declination  Contrary  Name* 


99 


Declinations. 


Hour 

Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


48° 


49°   50° 


Log. 


Limit 


0  22 

1  30 
3  23 
6  01 
9  24 

13  32 
18  26 
24  04 
30  27 
37  36 
45  29 
54  09 
63  33 
73  41 
84  36 

1.41 


0.149 
22 


61 


0  22 

1  28 
3  17 
5  51 
9  08 

13  09 
17  54 
23  23 
29  36 
36  32 
44  13 
52  36 
6144 
71  37 

82  12 

II 

1.37 


0.136 
72 


63 


0  21 
125 
3  11 
5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

51041 

59  56 

69  31 

79  48 
II 

1.33 


51= 


52°   53°   54° 


0.123 
85 


64 


0  20 

1  23 
3  06 
5  30 
8  36 

12  23 
16  52 
22  01 
27  52 
34  24 
41  37 
49  32 
58  08 
67  25 
77  24 

1.29 


0.110 
59 


66 


0  20 

1  20 
3  00 
5  20 
8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
II 

1.25 


0.096 
91 


67 


0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  29 
63  46 
73  12 


55= 


0  19 

1  15| 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 
70  48 


56°      57° 


1.22      1.18 


0.086 
36 


69 


0.071 


71 


0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
II 

1.14 


0.056 
90 


73 


0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 


0.045 
32 


74 


0  17 

1  08 

2  34 
4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
II 

1.07 


58= 


cQo      Hour 
*"*       Angles 


0  17 
107 
2  30 
4  26 
6  56 
9  59 
13  35 
17  45 
22  28 
27  44 
33  33 
39  56 
46  52 
54  21 
62  24 

1.04 


0.029   0.017 
38        03 


75 


76 


0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

21  49 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 


0.004 
32 


77 


Merid- 
ian 


26°      25° 


24°      23° 


22= 


21= 


20° 


19° 


18= 


17= 


16= 


15= 


Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

1       II 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

II 

0.97 

/      // 

0  15 

1  00 

2  16 
4  00 
6  16 
9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
II 

0.94 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

II 

0.91 

/      // 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  29 

52  12 
// 

0.87 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 

50  24 

II 

0.84 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

4149 

48  00 
II 

0.80 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

0.77 

/      II 

0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 

15  59 

19  44 

23  52 

28  23 

33  21 

38  40 

44  24 
II 

0.74 

1     II 

Oil 
0  45 
142 

3  02 

4  44 
6  49 
9  17 

12  07 

15  20 

18  56 

22  54 

27  14 

32  00 

37  06 

42  36 
II 

0.71 

/      // 

Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

1136 

14  42 

18  08 

2157 

26  06 

30  38 

35  33 

40  48 
II 

0.68 

Oil 

0  41 

133 

2  47 

4  20 

6  15 

8  29 

1105 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 
II 

0.65 

/ 

II 
II 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Aih 

Log. 

9.986 

77 

9.973 
13 

9.959 
04 

9.939 
52 

9.924 
28 

9.903 
09 

9.886 
49 

9.869 
23 

9.851 
26 

9.832 
51 

9.812 
91 

Log. 

Limit 

78 

79 

80 

81 

82 

83 

84 

85 

86 

87 

88 

Min- 
utes 

Merid- 
ian 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

Alti- 
tudes 

100 


Latitude  17°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11°  1 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

6 
15 
27 
42 
61 
83 

II 
6.4 

12 
51 
25 
23 
18 
38 
54 

2 

1 
7 
16 
29 
45 
65 

II 
6.8 

49 
16 
20 
04 
24 
23 

1 

1 

7 

17 

30 

48 

II 

7.2 

// 

56 
44 
24 
56 
20 

5 

2( 

8 

18. 
33  ( 
51' 

II 
1.1 

)4 
16 
J6 
)4 
10 

5 

2 

8. 
19 
35 
55 

II 
8.3 

// 

13 
53 
59 
33 
32 

3 

1 

2i 
9. 
21 

38. 

II 
9.0 

// 

24 
36 
36 
24 

0 

2: 

10  2 
23. 
41  ' 

II 
9.7 

36 
27 
30 
16 

9 

1 

2. 
11  i 
25^ 
45' 

n 

10.7 

n 

51 
27 
15 
17 

3 

/      // 

3  10 

12  41 
28  32 

II 
11.89 

3  34 
14  13 
3159 

II 
13.33 

4  03 
16  11 
36  24 

15.17 

4  43 

18  48 

II 
17.63 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.807 
54 

0.833 
15 

0.860 
34 

0,889 
30 

0.920 
65 

0.954 
24 

0.990 

78 

1.030 
60 

1.075 
18 

1.124 
83 

1.180 
99 

10 

1.246 
25 

Log. 

Limit 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

8 

Min- 
utes 

Merid- 
ian 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

,13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

5 
22. 

21.0 

37 
29 

7 

/ 

// 

// 

1 

II 

// 

1 

. 

II 

II 

II 

// 

1 

II 

// 

II 

// 

II 

// 

/ 

// 

// 

/      // 

5  19 
21  18 

II 
19.98 

/ 

4 
17 
39 

II 
16.5' 

25 
39 
42 

1 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.323 
66 

1.300 
60 

1.218 
54 

Log. 

Limit 

7 

6 

5 

3 

2 

0 

1 

3 

5 

7 

8 

9 

Min- 
utes 

Merid- 
ian 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

Alti- 
tudes 

Latitude  J  7°  Declination  Same  Namc« 


101 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/     // 

3  45 
15  01 
33  48 

14.08 

3 

13  ( 
29- 

It 
12.2 

16 
)3 
21 

3 

/      // 

2  52 
1131 
25  54 
46  02 

// 
10.79 

1 

2[ 
10 
23  ( 
41( 

9.6 

14 

16 
)6 
)6 

3 

/      // 

2  19 

9  16 

20  51 

37  05 

57  56 

8.69 

2( 

8 

18. 
33' 
52' 

II 
7.9 

// 

)6 
25 

58 
12 
10 

D 

1. 

7' 
17. 
30. 
48 

II 
7.2 

// 

55 
13 
21 
51 
12 

3 

1' 
7( 

15. 

28 

44 

63. 

II 
6.6 

17 
35 
57 
23 
20 
51 

5 

139 
6  33 
14  45 
26  15 
4100 
59  03 
80  21 

II 
6.15 

131 
6  06 
13  42 
24  22 
38  04 
54  49 
74  37 

II 
5.71 

125 
5  40 
12  46 
22  42 
35  28 
5105 
69  31 

II 
5.32 

1  19 
5  18 
11  58 
21  14 
33  12 
47  48 
65  03 

II 
4.98 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.148 
60 

1.087 
43 

1.033 
02 

0.983 
63 

0.939 
02 

0.897 
63 

0.859 
14 

0.822 

82 

0.788 
88 

0.756 
64 

0.725 
91 

0.697 
23 

Log. 

Limit 

10 

12 

13 

14 

15 

16 

18 

19 

20 

21 

23 

25 

Min- 
utes 

Merid- 
ian 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/      '/ 

/            // 

/      /' 

/      // 

Miu. 

Min. 

4 

1  15 

1  10 

106 

102 

0  59 

0  55 

0  53 

0  50 

0  47 

0  45 

0  43 

0  41 

4 

8 

4  59 

4  40 

4  24 

4  09 

3  55 

3  43 

3  31 

3  20 

3  10 

3  01 

2  52 

2  44 

8 

12 

11  12 

10  31 

9  54 

9  22 

8  50 

8  22 

7  55 

7  30 

7  10 

6  47 

6  27 

6  09 

12 

16 

19  56 

18  41 

17  38 

16  38 

15  42 

14  50 

14  05 

13  22 

12  42 

12  05 

1129 

10  55 

16 

20 

3108 

29  12 

27  32 

26  00 

24  32 

23  12 

22  00 

20  52 

19  52 

18  52 

17  56 

17  04 

20 

24 

44  50 

42  03 

39  39 

37  26 

35  20 

33  24 

3141 

30  03 

28  36 

27  10 

25  50 

24  35 

24 

28 

6101 

57  14 

53  58 

50  58 

48  05 

45  29 

43  07 

40  54 

38  57 

36  59 

35  09 

33  27 

28 

32 

79  42 

74  45 

70  29 

66  34 

62  48 

59  24 

56  19 

53  25 

50  52 

48  18 

45  54 

43  41 

32 

36 

79  30 

75  10 

71  17 

67  37 

64  22 

6108 

58  07 

55  18 

36 

40 

88  00 

83  28 

79  28 

75  28 

7144 

68  16 

40 

44 

86  48 

82  36 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

// 

II 

II 

// 

1' 

// 

II 

II 

A,h 

4.67 

4.38 

4.13 

3.90 

3.68 

3.48 

3.30 

3.13 

2.98 

2.83 

2  69 

2.56 

A,h 

Log. 

0.669 

0.641 

0.615 

0.591 

0.565 

0.541 

0.518 

0.495 

0.474 

0.451 

0.429 

0.408 

Log. 

32 

47 

95 

06 

85 

58 

51 

54 

22 

79 

75 

24 

Limit 

27 

28 

29 

30 

31         32 

33 

34        35 

36 

37 

38 

Min- 
utes 

Merid- 
ian 

71° 

70° 

69° 

68° 

67°      66°  1   65° 

64°      63° 

62°  1   61° 

60° 

Alti- 
tudes 

102 


Latitude  \7°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      // 

0  39 
2  37 
5  52 
10  24 
16  16 
23  25 
3153 
41  39 
52  42 
65  04 
78  43 
93  42 

2.44 

0  37 

2  28 

5  34 

9  54 

15  28 

22  17 

30  19 

39  35 

50  07 

61  52 

74  52 

89  05 

104  33 

II 
2.32 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

7138 

85  15 

100  03 

. 

II 

2.22 

1     II 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

II 
2.11 

1     II 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

9102 

105  35 

II 
2.02 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

41  28 

51  12 

61  57 

73  44 

86  32 

100  21 

1.92 

/      II 

0  29 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
II 

1.83 

/     // 

0  28 

1  52 
4  12 

7  28 

1140 

16  48 

22  52 

29  52 

37  48 

46  40 

56  28 

67  10 

78  52 

91  28 

105  00 
II 

1.75 

0  27 

1  47 
4  00 
7  08 

11  08 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 
II 

1.67 

1     II 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

6103 

71  39 

83  06 

95  24 

II 

1.59 

/      // 

0  24 

1  37 
3  39 
6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 
II 

1.52 

/     // 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
II 

1.45 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.387 
39 

0.365 
49 

0.346 
35 

0.324 

28 

0.305 
35 

0.283 
30 

0.262 
45 

0.243 
04 

0.222 
72 

0.201 
40 

0.181 

84 

0.161 
37 

Log. 

Limit 

39 

40 

41 

43 

44 

45 

46 

48 

49 

51 

53 

55 

Min- 
utes 

Merid- 
ian 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

Declination.s. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       " 

0  22 

1  28 
3  19 
5  53 
9  12 

13  15 
18  02 
23  33 
29  49 
36  48 
44  32 
52  59 
62  11 
72  08 
82  48 

1.38 

/      // 

0  21 

1  23 

3  08 
5  36 
8  44 
12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

1.31 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 

1.25 

/      // 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 
15  33 
20  18 
25  43 
31  44 
38  24 
45  41 
53  37 
62  12 

7124 

II 

1.19 

/      // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1  12 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

21  49 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 

/      // 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

0.96 
9.982 
27 

/     // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 

15  32 

19  39 

24  16 

29  21 

34  57 

41  01 

47  33 

54  36 
II 

0.91 

/     // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

/     // 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 

13  39 

17  17 

2120 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/     // 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
II 

0.75 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.139 

88 

0.117 
27 

0.096 
91 

0.075 
55 

0.049 
22 

0.025 
31 

0.004 
32 

9.959 
04 

9.929 
42 

9.903 
09 

9.875 
06 

Log. 

Limit 

56 

58 

60 

62 

64 

66 

67 

69 

71 

73 

75 

77 

Min- 
utes 

Merid- 
ian 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

Alti- 
tudes 

Latitude  17°  Declination  Contrary  Name. 
Declinations. 


103 


Hour 
Angles 

0° 

1° 

2° 

3° 

40 

5° 

6° 

70 

8° 

9° 

10° 

11° 

Hour 
Angles 

/     '/ 

/      /' 

Mill. 

Mill. 

4 

142 

1  37 

1  32 

1  27 

123 

1  19 

1  16 

1  13 

1  10 

107 

1  05 

1  02       4 

8 

6  51 

6  29 

6  09 

5  51 

5  35 

5  19 

5  06 

4  53 

4  42 

4  31 

4  21 

411;       8 

12 

15  25 

14  36 

13  50 

13  10 

12  33 

1159 

11  29 

1100 

10  34 

10  09 

9  46 

9  26      12 

16 

27  23 

25  56 

24  34 

23  22 

22  19 

21  17 

20  23 

19  32 

18  46 

18  03 

17  22 

16  46      16 

20 

42  48 

40  32 

38  24 

36  32 

34  52 

33  16 

31  52 

30  32 

29  20 

28  12 

27  08 

26  12      20 

24 

61  38 

58  22 

55  18 

52  36 

50  12 

47  54 

45  53 

43  58 

42  14 

40  36 

39  04 

37  43      24 

28 

83  54 

79  27 

75  16 

71  37 

68  21 

65  11 

62  26 

59  51 

57  30 

55  17 

53  11 

51  22 

28 

32 

81  35 

78  10 

75  06 

72  12 

69  28 

67  05 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

A,h 

6.42 

6.08 

5.76 

5.48 

5.23 

4.99 

4.78 

4.58 

4.40 

4.23 

4.07 

3.93 

Ajh 

Log. 

0.807 

0.783 

0.760 

0.738 

0.718 

0.698 

0.679 

0.660 

0.643 

0.626 

0.609 

0.594 

54 

90 

42 

78 

50 

10 

43 

87 

45 

34 

59 

39 

Log. 

Limit 

21 

22 

23 

24 

25 

25 

26 

27 

28 

29 

30 

31 

Min- 
utes 

Merid- 
ian 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65°      64° 

63° 

62° 

Alti- 
tudes 

Declin.\tions. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/       // 

/      II 

/      // 

/      // 

/      // 

/      II 

/      // 

Min. 

Min. 

4 

100 

0  59 

0  57 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  46 

0  44 

0  43 

4 

8 

4  03 

3  54 

3  47 

3  39 

3  32 

3  26 

3  19 

3  13 

3  07 

3  02 

2  58 

2  52 

8 

12 

9  06 

8  47 

8  30 

8  13 

7  56 

7  42 

7  27 

7  15 

7  02 

6  50 

6  39 

6  27 

12 

16 

16  10 

15  37 

15  06 

14  35 

14  08 

13  42 

13  17 

12  53 

12  30 

12  10 

11  49 

1129 

16 

20 

25  16 

24  24 

23  36 

22  48 

22  04 

21  24 

20  44 

20  08 

19  32 

19  00 

18  28 

17  56 

20 

24 

36  23 

35  09 

33  59 

32  50 

31  47 

30  49 

29  52 

29  00 

28  07 

27  22 

26  35 

25  50 

24 

28 

49  32 

47  49 

46  15 

44  42 

43  15 

41  57 

40  38 

39  28 

38  18 

37  14 

36  12 

35  09 

28 

32 

64  41 

62  27 

60  25 

58  22 

56  29 

54  47 

53  04 

51  32 

50  01 

48  38 

47  17 

45  54 

32 

36 

79  04 

76  28 

73  52 

71  30 

69  20 

67  11 

65  14 

63  17 

6134 

59  50 

58  07 

36 

40 

91  12 

88  16 

85  36 

82  56 

80  32 

78  08 

76  00 

73  52 

71  44 

40 

44 

86  48 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

" 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Aih 

3.79 

3.66 

3.54 

3.42 

3.31 

3.21 

3.11 

3.02 

2.93 

2.85 

2.11 

2.69 

Ajh 

Log. 

0.578 

0  563 

0.549 

0.534 

0.519 

0.506 

0.492 

0.480 

0.466 

0.454 

0.442 

0.429 

Log. 

64 

48 

00 

03 

83 

51 

76 

01 

87 

84 

48 

75 

Limit 

32 

32 

33 

33 

34 

35 

35 

36 

37 

38 

39 

40 

Min- 
utes 

Merid- 
ian 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

Alti- 
tudes 

104 


Latitude  J  7°  Declination  Contrary  Name. 


Declinations. 


Hour       nAo 
Angles     ^^ 

25'» 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  42 
2  47 
6  15 
1109 
17  24 
25  04 
34  06 
44  32 
56  23 
69  36 
84  13 

It 
2.61 

/     // 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  ]1 
43  21 
54  52 
67  44 
8157 

n 

2.54 

/     // 

0  39 
2  39 
5  56 
10  32 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 
94  51 

2.47 

/      // 

0  38 
2  35 
5  47 
10  17 
16  04 
23  08 
3130 
41  08 
52  03 
64  16 
77  45 
92  33 

II 
2.41 

0  38 

2  30 

5  37 

9  59 

15  36 

22  28 

30  34 

39  56 

50  33 

62  24 

75  30 

89  51 

105  27 

II 
2.34 

/     // 

0  36 

2  26 

5  29 

9  43 

15  12 

21  53 

29  48 

38  55 

49  15 

60  48 

73  34 

87  33 

102  45 

II 
2.28 

1     II 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

71  38 

85  15 

100  03 

II 
2.22 

/     // 

0  35 

2  19 

5  12 

9  16 

14  28 

20  50 

28  51 

37  02 

46  53 

57  52 

70  02 

83  19 

97  47 

II 
2.17 

/     // 

0  34 

2  15 
5  03 
9  01 
14  04 
20  16 
27  34 
36  00 
45  35 
56  16 
68  05 
81  01 
95  05 

II 
2.11 

/     // 

0  33 

2  12 

4  57 

8  47 

13  44 

19  47 

26  55 

35  09 

44  30 

54  56 

66  28 

79  06 

92  50 

II 
2.06 

/     // 

0  32 

2  08 
4  48 
8  32 
13  20 
19  12 
26  08 
34  08 
43  12 
53  20 
64  32 
76  48 
90  08 

II 
2.00 

'      " 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

II 
1.95 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
69 

A,h 

Log. 

0.416 
64 

0.404 
83 

0.392 
70 

0.382 
02 

0.369 
22 

0.357 
93 

0.346 
35 

0.336 
46 

0.324 

28 

0.313 

87 

0.301 
03 

0.290 
03 

Log. 

Limit 

41 

42 

43 

44 

45 

46 

46 

47 

48 

49 

50 

50 

Min- 
utes 

Merid- 
ian 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39" 

38° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/      // 

1     II 

/     // 

1     II 

/     // 

/     // 

/     // 

/      // 

'     " 

/     // 

/     // 

Min. 

4 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

0  26 

0  25 

0  25 

0  24 

0  23 

0  22 

4 

8 

2  01 

158 

156 

153 

150 

147 

144 

141 

139 

136 

134 

131 

8 

12 

4  34 

4  26 

4  20 

4  14 

4  06 

4  00 

3  54 

3  48 

3  42 

3  36 

3  31 

3  25 

12 

16 

8  06 

7  54 

7  44 

7  30 

7  18 

7  08 

6  58 

6  44 

6  34 

6  24 

6  13 

6  03 

16 

20 

12  40 

12  20 

12  04 

1144 

11  24 

1108 

10  52 

10  32 

10  16 

10  00 

9  44 

9  28 

20 

24 

18  14 

17  46 

17  23 

16  54 

16  25 

16  02 

15  39 

15  10 

14  47 

14  24 

14  01 

13  38 

24 

28 

24  50 

24  10 

23  39 

23  00 

22  21 

2149 

21  18 

20  39 

20  07 

19  36 

19  05 

18  34 

28 

32 

32  26 

3134 

30  53 

30  02 

29  11 

28  30 

27  49 

26  58    26  17 

25  36 

24  55 

24  14 

32 

36 

41  02 

39  58 

39  06 

38  01 

36  56 

36  05 

35  13 

34  08 

33  16 

32  24 

31  32 

30  40 

36 

40 

50  40 

49  20 

48  16 

46  56 

45  36 

44  32 

43  28 

42  08 

41  04 

40  00 

38  56 

37  52 

40 

44 

61  18 

59  42 

58  24 

56  47 

55  10 

53  54 

52  36 

50  59 

49  41 

48  24 

47  06 

45  49 

44 

48 

72  58 

7102 

69  30 

67  33 

65  38 

64  07 

62  35 

60  40 

59  08 

57  36 

56  04:  54  32 

48 

52 

85  38 

83  22 

81  34 

79  19 

77  04 

75  15 

73  27 

71  12 

69  24 

67  36 

65  48 

64  00 

52 

56 

99  18 

96  42 

94  36 

9159 

89  22 

87  18 

85  12 

82  35 

80  29 

78  24 

76  18 

74  13 

56 

60 

114  00 

11100 

108  36 

105  36 

102  36 

100  12 

97  48 

94  48 

92  24 

90  00 

87  36 

85  12 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

n 

II 

A,h 

1.90 

1.85 

1.81 

1.76 

1.71 

1.67 

1.63 

1.58 

1.54 

1.50 

1.46 

1.42 

A,h 

Log. 

0.278 

0.267 

0.257 

0.245 

0.233 

0.222 

0.212 

0.198 

0.187 

0.176 

0.164 

0.152 

Log. 

75 

17 

68 

51 

00 

72 

19 

66 

52 

09 

35 

29 

Limit 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

Latitude  \T  Declination  Contrary  Name. 


105 


Declinations. 


Hour   ^Qo 
Angles  *'> 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
.36 
40 
44 
48 
52 
56 
60 

A,h 

0  22 
129 
3  20 

5  56 
9  16 
13  21 
18  10 
23  43 
30  02 
37  04 
44  51 
53  22 
62  38 
72  39 
83  24 

1.39 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

8100 
II 

1.35 

1        n 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 
II 

1.31 

/  // 

0  20 
121 
3  03 
5  25 

8  28 
12  11 
16  36 
21  41 
27  26 
33  52 
40  59 
48  46 
57  14 
66  23 

76  12 

II 

1.27 

/  II 

0  20 

120 

2  59 

5  17 

8  16 

11  54 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
II 

1.24 

I  II 

0  19 

1  17 

2  53 
5  07 
8  00 

II  31 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
II 

1.20 

I  II 

0  19 

1  15 

2  48 
5  00 
7  48 

II  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/  // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

/  // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
II 

1.10 

/  // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

/  // 

0  16 
106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 
II 

1.03 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

1.00 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.143 
01 

0.130 
33 

0.117 

27 

0.103 
80 

0.093 
42 

0.079 
18 

0.068 
19 

0.053 

08 

0.041 
39 

0.025 
31 

0.012 

84 

0.00 

Log. 

Limit 

62 

64 

65 

67 

68 

69 

71 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/   // 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

II 

0.96 

/  // 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
II 

0.93 

/  // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

11  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

n 

0.90 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

1122 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

n 

0.87 

/  // 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

/  II 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/   // 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
II 

0.77 

/  // 

Oil 

0  47 

1  45 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

/  // 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 
II 

0.70 

Oil 

0  42 

136 

2  52 

4  28 

6  26 

8  45 

1126 

14  29 

17  52 

21  38 

25  43 

30  11 

35  02 

40  12 
„ 

0.67 

II 

II 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.982 
27 

9.968 
48 

9.954 
24 

9.939 
52 

9.919 
08 

9.903 
09 

9.886 
49 

9.863 
32 

9.845 
10 

9.826 
07 

Log. 

Limit 

79 

80 

81 

82 

84 

85 

86 

87 

88 

89 

90 

91 

Min- 
utes 

Merid- 
ian 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

Alti- 
tudes 

106 


Latitude  J 8°  Decimation  Same  Name« 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 
6 

14 

25 

40 

57 

78 

II 
6.0 

37 
27 
30 
16 
16 
59 
55 

1 

1 

6 
15 
27 
42 
61 
83 

II 
6.3 

// 

12 
49 
20 
16 
36 
21 
31 

1 
7 

16 

28 

45 

64 

II 
6.7 

// 

49 

14 
15 
53 
38 
59 

7 

1 

1 

7 

17 

30 

48 

II 
7.2 

// 

55 

42 
18 
46 
34 

1 

2 

8 
18 
32 
51 

II 
7.7 

// 

33 
13 
29 
51 
20 

3 

t 
2 
8 

19 

35 

55 

II 
8.2 

// 

12 
50 
51 
17 
38 

1 

1 

.2 

9 

21 

38 

II 
8.9 

22 
31 
26 
36 

3 

/ 

2 
10 
23 
41 

II 
9.7 

35 
22 
18 
26 

1 

/     // 

2  51 
11  21 
25  33 
45  27 

10.65 

/     // 

3  08 
12  35 

28  18 

II 
11.79 

/       // 

3  31 
14  06 
31  42 

II 
13.21 

/           // 

4  01 
16  03 
36  06 

II 
15.04 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.781 
04 

0.805 
50 

0.830 
59 

0.857 
94 

0.886 
49 

0.917 
51 

0.950 

85 

0.987 
22 

1.027 
35 

1.071 
51 

1.120 
90 

1.177 
25 

Log. 

Limit 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

Min- 
utes 

Merid- 
ian 

72 

3 

73 

3 

74 

3 

75 

3 

76 

3 

77 

D 

78 

3 

79 

D 

80 

3 

81 

3 

82 

3 

83° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

4 
18. 

17.4 

39 
39 

7 

r 

5 

22 

•  ■ 

II 
20.8 

// 

34 
16 

3 

II 

/■/ 

II 

// 

II 

// 

II 

// 

II 

// 

II 

// 

1 
II 

// 

1 
II 

1 
II 

5  15 
2102 

19.72 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.242 
29 

1.319 
73 

1.294 
91 

Log. 

Limit 

10 

9 

7 

5 

3 

1 

0 

1 

4 

6 

7 

8 

Min- 
utes 

Merid- 
ian 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

Alti- 
tudes 

UNIVERSITY 

Of 


Latitude  13°  Declination  Same  Name* 

Declinations. 


107 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30°- 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

4 

17 
39 

n 

16.3 

21 
24 
10 

2 

1      II 

3  42 
14  49 
33  20 

II 
13.89 

/ 

3 

12 

28 

II 
12.0 

13 
52 

57 

5 

2 
11 
25 
45 

II 
10.6 

51 

21 
32 
24 

4 

2 

10 
22 
40 

II 
9.5 

32 

D8 
48 
32 

D 

/      // 

2  17 

9  08 
20  33 
36  31 
57  04 

II 
8.56 

/ 
2 
8 

18 

33 

51 

II 
7.7 

D4 
18 
il 
11 
52 

8 

1 

7 
17 
30 
47 

7.1 

54 
35 
35 
23 

28 

2 

145 
6  59 
15  43 
27  57 
43  40 
62  53 

II 
6.55 

137 

6  27 
14  31 
25  49 
40  20 
58  05 
79  03 

II 
6.05 

1     II 

130 

5  59 
13  27 
23  57 
37  24 
53  52 
73  18 

II 
5.61 

123 
5  35 
12  33 
22  19 
34  52 
50  12 
68  21 

II 
5.23 

Min. 
4 

,^ 

16 

20 

24 

28 

32 

36 

40. 

44 

48 

52 

56 

60 

A,h 

Log. 

1.212 
72 

1.142 
70 

1.081 
35 

1.026 
94 

0.977 

72 

0.932 
47 

0.890 
98 

0.852 

48 

0.816 
24 

0.781 
76 

0.748 
96 

0.718 
50 

Log. 

Limit 

9 

11 

12 

13 

14 

15 

17 

18 

20 

21 

22 

24 

Min- 
utes 

Merid- 
ian 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/       II 

/      II 

/           ft 

/      // 

/      " 

/      // 

/      // 

/          // 

Min. 

Min. 

4 

118 

1  13 

1  09 

105 

101 

0  58 

0  54 

0  51 

0  49 

0  46 

0  44 

0  42 

4 

8 

5  13 

4  53 

4  35 

4  19 

4  05 

3  51 

3  39 

3  27 

3  16 

3  06 

2  57 

2  48 

8 

12 

1144 

1100 

10  19 

9  43 

9  10 

8  39 

8  11 

7  45 

7  21 

6  59 

6  38 

6  18 

12 

16 

20  52 

19  32 

18  21 

17  17 

16  18 

15  25 

14  33 

13  47 

13  03 

12  25 

11  46 

11  14      16 

20 

32  36 

30  32 

28  40 

27  00 

25  28 

24  04 

22  44 

21  32 

20  24 

19  24 

18  24 

17  32      20 

24 

46  57 

43  58 

41  17 

38  53 

36  41 

34  40 

32  44 

3100 

29  23 

27  56 

26  30 

25  15     24 

28 

63  54 

59  51 

56  11 

52  55 

49  55 

47  10 

44  34 

42  13 

39  59 

38  02 

36  04 

34  22      28 

32 

83  27 

78  10 

73  23 

69  07 

65  11 

61  36 

58  12 

55  08 

52  13 

49  40 

47  06 

44  53      32 

36 

77  59 

73  39 

69  46 

66  06 

62  51 

59  37 

56  49|     36 

40 

90  56 

86  08 

8136 

77  36 

73  36 

70  08j     40 

44 

84  52 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

" 

II 

// 

II 

II 

II 

// 

A,h 

4.89 

4.58 

4.30 

4.05 

3.82 

3.61 

3.41 

3.23 

3.06 

2.91 

2.76 

2.63 

A,h 

Log. 

0.689 

0.660 

0.633 

0.607 

0.582 

0.557 

0.532 

0.509 

0.485 

0.463 

0.440 

0.419 

Log. 

31 

87 

47 

46 

06 

51 

75 

20 

72 

89 

91 

96 

Limit 

26 

27 

28 

29 

30 

31 

32 

33 

34 

36 

37 

38 

Min- 
utes 

Merid- 
ian 

72< 

> 

71° 

70 

3 

69' 

3 

68< 

> 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

Alti- 
tudes 

108 


Latitude  J  8°  Declination  Same  Name. 


Declixatioxs. 


Hour 
Angles 

r  48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/     '/ 

/      // 

/     // 

1     II 

/      // 

/      // 

/      // 

/     // 

/      " 

/      // 

/      // 

Min. 

4 

0  40 

0  38 

0  36 

0  35 

0  33 

0  31 

0  30 

0  28 

0  27 

0  26 

0  25 

0  23 

4 

8 

2  40 

2  32 

2  26 

2  18 

2  12 

2  05 

2  CO 

154 

149 

143 

139 

134 

8 

12 

6  00 

5  43 

5  27 

511 

4  57 

4  43 

,     4  29 

4  17 

4  05 

3  53 

3  42 

3  32 

12 

16 

10  40 

10  09 

9  41 

9  13 

8  47 

8  21 

7  59 

7  35 

7  15 

6  55 

6  34 

6  16 

16 

20 

16  40    15  52 

15  08 

14  24 

13  44 

13  04 

12  28 

1152 

1120 

10  48 

10  16 

9  48 

20 

24 

24  00;  22  51 

2147 

20  45 

19  47 

18  49 

17  57 

17  05 

16  19 

15  34 

14  47 

14  06 

24 

28 

32  40 

3106 

29  40 

28  13 

26  55 

25  37 

24  26 

23  16 

22  13 

21  10 

20  07 

19  13 

28 

32 

42  40 

40  37 

38  45 

36  51 

35  09 

33  27 

3155 

30  23 

29  01 

27  38 

26  17 

25  06 

32 

36 

54  00 

5125 

49  02 

46  40 

44  30 

42  20 

40  24 

38  27 

36  43 

35  00 

33  16 

31  45 

36 

40 

66  40 

63  28 

60  32 

57  36 

54  56 

52  16 

49  52 

47  28 

45  20 

43  12 

41  04 

39  12 

40 

44 

80  40 

76  48 

73  15 

69  42 

66  28 

63  14 

60  21 

57  26 

54  51 

52  17 

49  41 

47  26 

44 

48 

96  00 

91  23 

87  10 

82  56 

79  06 

75  16 

7148 

68  19 

65  15 

62  12 

59  08 

56  27 

48 

52 

107  15 

102  18 

97  20 

92  50 

88  20 

84  16 

80  13 

76  37 

73  00 

69  24 

66  15 

52 

56 

107  40 

102  26 

97  45 

93  02 

88  51 

84  41 

80  29 

76  50 

56 

60 

// 

n 

II 

II 

II 

II 

112  12  106  48  102  00 
//          //     1     // 

97  12 

92  24 
II 

88  12 

60 

Ajh 

2.50 

2.38 

2.27 

2.16 

2.06 

1.96 

1.87 

1.78 

1.70 

1.62 

1.54 

1.47 

A,h 

Log. 

0.397 

C.376 

0.356 

0.334 

0.313 

0.292 

0.271 

0.250 

0.230 

0.209 

0.187 

0.167 

Log. 

94 

58 

03 

45 

87 

26 

84 

42 

45 

52 

52 

32 

Limit 

39 

40 

41 

42 

44 

45 

46 

47 

48 

50 

52 

54 

Min- 
utes 

Merid- 
ian 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

/      // 

/      // 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

1     II 

Min. 

4 

0  22 

0  21 

0  20 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

4 

8 

130 

125 

121 

1  17 

1  13 

109 

105 

101 

0  58 

0  55 

0  51 

0  49 

8 

12 

3  22 

3  11 

3  02 

2  53 

2  44 

2  36 

2  27 

2  19 

2  11 

2  04 

156 

150 

12 

16 

5  58 

5  41 

5  22 

5  07 

4  52 

4  36 

4  21 

4  05 

3  53 

3  40 

3  28 

3  14 

16 

20 

9  20 

8  52 

8  24 

8  00 

7  36 

7  12 

6  48 

6  24 

6  04 

5  44 

5  24 

5  04 

20 

24 

13  26 

12  46 

12  06 

11  31 

10  57 

10  22 

9  48 

9  13 

8  44 

8  16 

7  47 

7  18 

24 

28 

18  18 

17  23 

16  28 

15  41 

14  53 

14  07 

13  20 

12  33 

1154 

11  14 

10  35 

9  56 

28 

32 

23  54 

22  42 

2130 

20  29 

19  27 

18  26 

17  24 

16  23 

15  32 

14  40 

13  49 

12  58 

32 

36 

30  14 

28  44 

27  13 

25  55 

24  38 

23  20 

22  02 

20  44 

19  39 

18  35 

17  30 

16  25 

36 

40 

37  20 

35  28 

33  36 

32  00 

30  24 

28  48 

27  12 

25  36 

24  16 

22  56 

21  36 

20  16 

40 

44 

45  10 

42  55 

40  39 

38  43 

36  47 

34  51 

32  55 

30  58 

29  21 

27  45 

26  08 

24  31 

44 

48 

53  46 

5104 

48  23 

46  05 

43  46 

4128 

39  10 

36  52 

34  57 

33  01 

3106 

29  09 

48 

52 

63  06 

59  56 

56  47 

54  05 

5122 

48  40 

45  58 

43  16 

41  01 

38  45 

36  30 

34  15 

52 

56 

73  10 

69  31 

65  51 

62  43 

59  35 

56  27 

53  19 

50  10 

47  33 

44  57 

42  20 

39  43 

56 

60 

84  00 

79  48 

75  36 

72  00 

68  24 

64  48 

61  12 

57  36 

54  36 

5136 

48  36 

45  36 

60 

II 

II 

II 

II 

II 

" 

II 

II 

" 

II 

" 

II 

Ajh 

1.40 

1.33 

1.26 

1.20 

1.14 

1.08 

1.02 

0.96 

0.91 

0.86 

0.81 

0.76 

A,h 

Log. 

0.146 

0.123 

0.100 

0.079 

0.056 

0.033 

0.008 

9.982 

9.959 

9.934 

9.908 

9.880 

Log. 

13 

85 

37 

18 

90 

42 

60 

27 

04 

50 

49 

81 
76 

Limit 

56 

57 

59 

61 

63 

65 

66 

68 

70 

72 

74 

Min- 
utes 

Merid- 
ian 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

Alti- 
tudes 

Latitude  J  8°  Declination  Contrary  Name. 


109 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

40 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

6 
14 
25 
40 
57 
78 

II 
6.0 

37 
27 
30 
46 
16 
59 
55 

4 

1 
6 
13 
24 
38 
55 
74 

5.7 

31 
07 
45 
27 
12 
OO 
53 

3 

127 
5  50 
13  07 
23  17 
36  24 
52  25 
71  21 

5.46 

1     II 

123 
5  33 
12  29 
22  11 
34  40 
49  55 
67  57 

5.20 

/ 

1 
5 
11 
21 
33 
47 
64 

4.9 

// 

19 
18 
56 
12 
08 
42 
57 

r 

1 

1 

5 

11 

20 

31 

45 
62 
81 

4.7 

16 
05 
26 
18 
44 
42 
10 
14 

5 

1 
4 
10 
19 
30 
43 
59 
78 

II 
4.5 

13 
53 
58 
30 
28 
52 
43 
30 

1 

1  10 
4  41 
10  32 
18  44 
29  16 
42  09 
57  22 
74  55 

4.39 

/     // 

107 
4  30 
10  08 
18  00 
28  08 
40  31 
55  09 
72  01 

II 
4.22 

r       II 

105 
4  20 
9  45 
17  19 
27  04 
38  59 
53  03 
69  17 

4.06 

/     // 

1  02 
4  10 
9  25 
16  43 
26  08 
37  38 
51  14 
66  54 

3.92 

100 
4  02 
9  05 
16  07 
25  12 
36  17 
49  24 
64  31 

II 
3.78 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.781 
04 

0.758 
15 

0.737 
19 

0.716 
00 

0.696 
36 

0.677 
61 

0.659 
92 

0.642 
46 

0.625 
31 

0.608 
53 

0.593 
29 

0.577 
49 

Log. 

Limit 

22 

23 

24 

25 

26 

26 

27 

28 

29 

30 

31 

31 

Min- 
utes 

Merid- 
ian 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

/     // 

/     // 

/      /' 

/      // 

/      // 

/     // 

/      // 

/     // 

/      // 

,      II 

/     // 

Min. 

4 

0  59 

0  56 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  46 

0  44 

0  43 

0  42 

4 

8 

3  53 

3  46 

3  39 

3  32 

3  26 

3  19 

3  13 

3  07 

3  02 

2  58 

2  52 

2  47 

8 

12 

8  45 

8  28 

8  13 

7  56 

7  42 

7  27 

7  15 

7  02 

6  50 

6  39 

6  27 

6  17 

12 

16 

15  35 

15  04 

14  35 

14  08 

13  42 

13  17 

12  53 

12  30 

12  10 

1149 

11  29 

11  11 

16 

20 

24  20 

23  32 

22  48 

22  04 

2124 

20  44 

20  08 

19  32 

19  00 

18  28 

17  56 

17  28 

20 

24 

35  03 

33  53 

32  50 

3147 

30  49 

29  52 

29  00 

28  07 

27  22 

26  35 

25  50 

25  10 

24 

28 

47  41 

46  08 

44  42 

43  15 

4157 

40  38 

39  28 

38  18 

37  14 

36  12 

35  09 

34  14 

28 

32 

62  17 

60  15 

58  22 

56  29 

54  47 

53  04 

51  32 

50  01 

48  38 

47  17 

45  54 

44  42 

32 

36 

78  51 

76  15 

73  52 

7130 

69  20 

67  11 

65  14 

63  17 

61  34 

59  50 

58  07 

56  36 

36 

40 

91  12 

88  16 

85  36 

82  56 

80  32 

78  08 

76  00 

73  52 

7144 

69  52 

40 

44 

86  48 

84  33 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

" 

" 

" 

II 

II 

II 

II 

Ajh 

3.65 

3.53 

3.42 

3.31 

3.21 

3.11 

3.02 

2.93 

2.85 

2.77 

2.69 

2.62 

A,h 

Log. 

0.562 

0.547 

0.534 

0.519 

0.506 

0.492 

0.480 

0.466 

0.454 

0.442 

0.429 

0.418 

29 

77 

03 

83 

51 

76 

01 

87 

84 

48 

75 

30 

Log. 

Limit 

32 

32 

33 

34 

34 

35 

36 

37 

38 

39 

39 

40 

Min- 
utes 

Merid- 
ian 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

110 


Latitude  18°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  41 
2  43 
6  07 
10  53 
17  00 
24  29 
33  19 
43  31 
55  05 
68  00 
82  17 

II 
2.55 

0  39 
2  39 
5  58 
10  34 
16  32 
23  48 
32  25 
42  20 
53  34 
66  08 
80  01 
95  14 

II 
2.48 

0  38 
2  35 
5  49 
10  19 
16  08 
23  14 
31  38 
41  18 
52  16 
64  32 
78  05 
92  56 

II 
2.42 

1     II 

0  38 

2  30 

5  38 

10  02 

15  40 

22  34 

30  42 

40  06 

50  46 

62  40 

75  50 

90  14 

105  54 

II 
2.35 

0  36 

2  27 

5  30 

9  46 

15  16 

2159 

29  56 

39  05 

49  28 

6104 

73  53 

87  56 

103  12 

2.29 

/      // 

0  35 

2  23 

5  21 

9  31 

14  52 

2124 

29  09 

38  04 

48  10 

59  28 

71  57 

85  38 

100  30 

II 
2.23 

/      // 

0  35 

2  19 

5  14 

9  18 

14  32 

20  56 

28  29 

37  12 

47  06 

58  08 

70  21 

83  42 

98  14 

II 
2.18 

1      II 

0  34 
2  15 
5  05 
9  03 

14  08 
20  22 
27  42 
36  10 
45  48 
56  32 
68  25 
8124 
95  32 

II 
2.12 

/      // 

0  33 

2  13 

4  58 

8  50 

13  48 

19  52 

27  03 

35  20 

44  43 

55  12 

66  48 

79  29 

93  17 

II 
2.07 

/      // 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

9102 

II 
2.02 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

II 
1.96 

1     II 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

4128 

51  12 

61  57 

73  44 

86  32 

II 
1.92 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.406 
54 

0.394 
45 

0.383 

82 

0.371 
07 

0.359 
84 

0.348 
30 

0.338 
46 

0.326 
34 

0.315 
97 

0.305 
35 

0.292 
26 

0.283 
30 

Log. 

Limit 

41 

42 

44 

45 

46 

47 

47 

47 

48 

49 

50 

51 

Min- 
utes 

Merid- 
ian 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

0  30 

0  29 

/      // 
0  28 

0  27 

0  27 

/      // 
0  27 

0  26 

/      // 
0  25 

/      // 
0  24 

0  23 

/      // 
0  22 

/      // 
0  22 

Min. 
4 

8 

2  00 

156 

154 

151 

1  48 

145 

142 

140 

1  37 

1  35 

133 

130 

8 

12 

4  29 

4  22 

4  16 

4  09 

4  03 

3  56 

3  50 

3  45 

3  39 

3  34 

3  28 

3  22 

12 

16 

7  59 

7  46 

7  33 

7  23 

7  13 

7  00 

6  50 

6  39 

6  29 

6  18 

6  08 

5  58 

16 

20 

12  28 

12  08 

1148 

11  32 

11  16 

10  56 

10  40 

10  24 

10  08 

9  52 

9  36 

9  20 

20 

24 

17  57 

17  29 

16  59 

16  36 

16  14 

15  45 

15  22 

14  59 

14  36 

14  12 

13  49 

13  26 

24 

28 

24  26 

23  47 

23  08 

22  37 

22  05 

2125 

20  54 

20  23 

19  52 

19  21 

18  49 

18  18 

28 

32 

31  55 

31  03 

30  13 

29  32 

28  50 

27  59 

27  18 

26  37 

25  56 

25  16 

24  35 

23  54 

32 

36 

40  24 

39  19 

38  14 

37  22 

36  31 

35  26 

34  34 

33  42 

32  50 

3158 

3106 

30  14 

36 

40 

49  52 

48  32 

47  12 

46  08 

45  04 

43  44 

42  40 

4136 

40  32 

39  28 

38  24 

37  20 

40 

44 

60  21 

58  44 

57  07 

55  49 

54  32 

52  55 

5138 

50  20 

49  03 

47  45 

46  27 

45  10 

44 

48 

71  48 

69  53 

67  56 

66  24 

64  53 

62  58 

61  26 

59  54 

58  22 

56  50 

55  18 

53  46 

48 

52 

84  16 

82  01 

79  46 

77  58 

76  09 

73  54 

72  06 

70  18 

68  30 

66  42 

64  54 

63  06 

52 

56 

97  45 

95  08 

92  31 

90  25 

88  20 

85  43 

83  38 

8132 

79  27 

77  21 

75  15 

73  10 

56 

60 

112  12 

109  12 

106  12 

103  48 

II 

10124 
II 

98  24 
II 

96  00 

II 

93  36 
II 

91  12 

II 

88  48 
II 

86  24 
II 

84  00 

II 

60 

A,h 

1.87 

1.82 

1.77 

1.73 

1.69 

1.64 

1.60 

1.56 

1.52 

1.48 

1.44 

1.40 

A,h 

Log. 

0.271 
84 

0.260 
07 

0.247 
97 

0.238 
05 

0.227 
89 

0.214 

84 

0.204 
12 

0.193 
12 

0.181 
84 

0.170 
26 

0.158 
36 

0.146 
13 

Log. 

Limit 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

Min- 
utes 

Merid- 
ian 

36° 

35° 

34°  1   33°  1   32° 

31° 

30° 

29° 

28°      27° 

26° 

25° 

Alti- 
tudes 

Latitude  t8°  Declination  Contrary  Name* 


111 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      i> 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

6144 

71  37 

82  12 

1.37 

0  21 

1  25 
3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

51  04 

59  56 

69  31 

79  48 
// 

1.33 

/        n 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 

n 

1.29 

/     // 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 

16  28 

2130 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
// 

1.26 

/     // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  29 
63  46 
73  12 

ir 

1.22 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

3144 

38  24 

45  41 

53  37 

62  12 

7124 
It 

1.19 

/      // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 
69  00 

1.15 

/     // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

1.12 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

4151 

49  07 

56  58 

65  24 
II 

1.09 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/     // 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
II 

1.02 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

31  56 

38  01 

44  37 

51  44 

59  24 
II 

0.99 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.136 
72 

0.123 

85 

0.110 
59 

0.100 
37 

0.086 
36 

0.075 
55 

0.060 
70 

0.049 
22 

0.037 
43 

0.021 
19 

0.008 
60 

9.995 
64 

Log. 

Limit 

63 

64 

66 

67 

68 

70 

72 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

■1  go        Alti- 

•'■'5        tudes 

Declinations. 


Hour 
Angles 

60° 

61°      62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

0.95 

/      // 

0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 
15  42 
19  52 
24  32 
29  41 
35  20 
41  28 
48  05 
55  12 

0.92 

/     // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  19 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 

0.89 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

51  36 
II 

0.86 

/      // 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 

0.83 

1     II 
0  12 

0  51 

1  54 
3  22 
5  16 
7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

/     // 

0  12 

0  49 

1  50 
3  14 
5  04 
7  18 
9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 
II 

0.76 

/     // 

Oil 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

/      // 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 
II 

0.70 

II 

// 

/ 

// 

/      // 
II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.977 
72 

9.963 
79 

9.949 
39 

9.934 
50 

9.919 
08 

9.897 
63 

9.880 
81 

9.863 
32 

9.845 
10 

Log. 

Limit 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

Min- 
utes 

Merid- 
ian 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

Alti- 
tudes 

112 


Latitude  i9°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

131 
6  05 
13  41 
24  19 
38  00 
54  43 
74  29 

5.70 

1 
6 
14 
25 
40 
57 
78 

6.0 

// 

36 

25 
25 
39 
D4 
42 
32 

I 

/     // 

142 
6  46 
15  14 
27  06 
42  20 
60  58 
82  59 

6.35 

1 

7 
16 
28 
44 
64 

II 
6.7. 

// 

47 
11 
09 
43 
52 
36 

1 

7 
17 
30 
47 

7.1( 

55 
38 
11 
33 
44 

5 

r 

2 

8 
18 
32 
50 

II 
7.6^ 

11 

03 
09 
20 
36 
56 

I 

/     II 

2  11 

8  46 

19  42 

35  02 

54  44 

8.21 

1     II 

2  22 

9  27 

21  16 

37  48 

II 
8.86 

/     // 

2  34 
10  17 
23  08 
41  08 

•  •  ■ 

II 
9.64 

/     // 

2  49 
11  16 
25  21 
45  03 

10.56 

/     // 

3  07 
12  28 
28  03 

II 
11.69 

/     // 

3  29 

13  58 
31  25 

II 
13.09 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.755 

87 

0.778 
87 

0.802 

77 

0.828 
02 

0.854 
91 

0.883 
09 

0.914 
34 

0.947 
43 

0.984 
08 

1.023 
66 

1.067 
81 

1.116 
94 

Log. 

Limit 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

Min- 
utes 

Merid- 
ian 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

3  58 
15  53 
35  46 

II 
14.90 

/ 
4 
18 

II 
17.3 

37 

28 

I 

/     // 

5  31 
22  03 

. . . 

II 
20.67 

1 

II 

// 

1 

// 

1 

// 

II 

II 

// 

1 

// 

// 

II 

// 

1 

. . 
II 

// 

II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.173 
19 

1.238 
30 

1.315 
34 

Log. 

Limit 

11 

10 

8 

6 

4 

3 

1 

0 

1 

4 

6 

7 

Min- 
utes 

Merid- 
ian 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

Alti- 
tudue 

Latitude  i9°  Declination  Same  Name. 


113 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

5 
20' 

II 
19.4 

II 

11 

16 

5 

4 

17 
38 

II 
16.1 

18 
10 
38 

3 

14 
32 

II 
13.6 

39 
35 
50 

9 

1 

3 
12 

28 

II 
11.8 

10 

il 
32 

9 

1 
2 
4 

10 

2 

1 
5 
4 

II 
.4 

i7 
11 
10 
12 

8 

2 

9 
22 
39. 

II 
9.3 

30 
58 
26 
54 

5 

2 

9 
20 
35 
56 

II 
8.4 

14 
00 
14 

58 
12 

3 

2 

8 
18 
32 
51 

II 
7.6 

// 

03 
09 
21 
39 
30 

5 

/     // 

152 

7  28 
16  48 
29  52 
46  40 
67  12 

II 
7.00 

143 
6  53 
15  28 
27  28 
42  56 
6149 
84  09 

II 
6.44 

/      II 

1  35 
6  20 
14  17 
25  23 
39  40 
57  07 
77  45 

II 
5.95 

1  28 
5  53 
13  15 
23  33 
36  48 
53  00 
72  08 

II 
5.52 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.289 
14 

1.206 
83 

1.136 
40 

1.075 
18 

1.020 
36 

0.970 
81 

0.925 
83 

0.883 
66 

0.845 
10 

0.808 
89 

0.774 
52 

0.741 
'      94 

Log. 

Limit 

8 

9 

10 

12 

14 

15 

16 

18 

19 

21 

22 

23 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/       // 

/      // 

/      // 

/      // 

/      // 

/     // 

/      // 

1     II 

Min. 

Min. 

4 

123 

1  17 

1  11 

107 

103 

100 

0  56 

0  54 

0  51 

0  47 

0  46 

0  43 

4 

8 

5  29 

5  07 

4  48 

4  30 

4  14 

4  00 

3  46 

3  34 

3  22 

3  11 

3  02 

2  52 

8 

12 

12  20 

11  31 

10  47 

10  08 

9  32 

8  59 

8  28 

8  01 

7  35 

7  11 

6  49 

6  27 

12 

16 

21  56 

20  29 

19  09 

18  00 

16  56 

15  57 

15  04 

14  15 

13  29 

12  45 

12  07 

1129 

16 

20 

34  16 

32  00 

29  56 

28  08 

26  28 

24  56 

23  32 

22  16 

2104 

19  56 

18  56 

17  56 

20 

24 

49  21 

46  05 

43  05 

40  31 

38  06 

35  54 

33  53 

32  04 

30  21 

28  42 

27  16 

25  50 

24 

28 

67  09 

62  43 

58  41 

55  09 

5153 

48  52 

46  08 

43  38 

41  17 

39  05 

37  06 

35  09 

28 

32 

8155 

76  38 

72  01 

67  46 

63  50 

60  15 

57  00 

53  55 

5102 

48  28 

45  54 

32 

36 

76  15 

72  09 

68  16 

64  35 

6121 

58  07 

36 

40 

89  04 

84  16 

79  44 

75  44 

7144 

40 

44 

86  48 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

" 

II 

Ajh 

5.14 

4.80 

4.49 

4.22 

3.97 

3.74 

3.53 

3.34 

3.16 

2.99 

2.84 

2.69 

A,h 

Log. 

0.710 

0.681 

0.652 

0.625 

0.598 

0.572 

0.547 

0.523 

0.499 

0.475 

0.453 

0.429 

Log. 

96 

24 

25 

31 

79 

87 

77 

75 

69 

67 

32 

75 

Limit 

25 

26 

27 

29 

30 

31 

32 

33 

34 

35 

36 

37 

Min- 
utes 

Merid- 
ian 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

Alti- 
tudes 

114 


Latitude  19°  Declination  Same  Name. 
Declinations. 


Hour 

Angles 


JMin. 
4 
8 
12 
16 
20 
24 
'  28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Limit 


Merid- 
ian 


48°      49= 


0  41 
2  44 
6  09 
10  55 
17  04 
24  35 
33  27 
43  41 
55  18 
68  16 
82  36 


2.56 


0.408 
24 


38 


61= 


0  39 
2  37 
5  52 
10  24 
16  16 
23  25 
31  53 
41  39 
52  42 
65  04 
78  43 
93  42 


2.44 


50° 


0.387 
39 


39 


60°   59° 


0  37 

2  28 

5  34 

9  54 

15  28 

22  17 

30  19 

39  35 

50  07 

61  52 

74  52 

89  05 

104  33 


2.32 


51= 


0.365 
49 


40 


0  35 

2  21 
5  17 
9  23 
14  40 
21  07 
28  45 
37  33 
47  31 
58  40 
70  59 
84  29 
99  09 


2.20 


0.342 
42 


42 


58° 


52° 


0  34 

2  14 

5  02 

8  58 

14  00 

20  10 

27  26 

35  50 

45  22 

56  00 

67  46 

80  38 

94  38 


2.10 


53° 


0  32 
2  08 

4  48 
8  32 
13  20 
19  12 
26  08 
34  08 
43  12 
53  20 
64  32 
76  48 
90  08 
104  32 


2.00 


54°   55 


0.322  0.301 


22 


44 


57° 


03 


45 


0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

41  02{ 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 

1.90 


0.278 

75 


46 


56°  I  55° 


0 

1 

4 

7 

12 

17 

23 

30 

39 

48 

58 

69 

81 

94 

108 


56° 


1.81 


0.257 


47 


54° 


0  27 

1  51 
4  09 
7  23 

11  32 
16  36 
22  37 
29  32 
37  22 
46  08 
55  49 
66  24 
77  58 
90  25 
103  48 

1.73 


57° 


0.238 
05 


48 


53° 


0  27 

1  45 
3  56 

7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
If 

1.64 


58° 


0.214 
84 


50 


52° 


0  25 

140 

3  45 

6  39 

10  24 

14  59 

20  23 

26  37 

33  42 

41  36 

50  20 

59  54 

70  18 

81  32 

93  36 


59° 


52 


51° 


Hour 

Angles 


0  23 

1  36 
3  35 
6  21 
9  56 

14  18 
19  29 
25  26 
32  11 
39  44 
48  04 
57  13 
67  09 
77  52 
89  24 

n 

1.49 
0.173 
19 


54 


50° 


Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Min- 
utes 


Alti- 
tudes 


Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/       /' 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      II 

1     II 

/      // 

/      // 

/     // 

>Iin. 

4 

0  22 

0  22 

0  20 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  14 

0  13 

0  12 

4 

8 

1  31 

126 

122 

1  17 

1  13 

1  10 

106 

102 

0  58 

0  55 

0  52 

0  50 

8 

12 

3  25 

3  14 

3  05 

2  54 

2  45 

2  37 

2  28 

2  20 

2  13 

2  05 

1  58 

1  51 

12 

16 

6  03 

5  46 

5  27 

5  10 

4  55 

4  39 

4  24 

4  08 

3  55 

3  43 

3  30 

3  17 

16 

20 

9  28 

9  00 

8  32 

8  04 

7  40 

7  16 

6  52 

6  28 

6  08 

5  48 

5  28 

5  08 

20 

24 

13  38 

12  58 

12  17 

1137 

1103 

10  28 

9  53 

9  18 

8  50 

8  21 

7  53 

7  23 

24 

28 

18  34 

17  38 

16  44 

15  49 

15  01 

14  15 

13  28 

12  41 

12  02 

11  22 

10  43 

10  04 

28 

32 

24  14 

23  02 

21  51 

20  39 

19  37 

18  36 

17  35 

16  34 

15  42 

14  51 

13  59 

13  09 

32 

36 

30  40 

29  10 

27  39 

26  08 

24  51 

23  33 

22  15 

20  57 

19  52 

18  48 

17  43 

16  38 

36 

40 

37  52 

36  00 

34  08 

32  16 

30  40 

29  04 

27  28 

25  52 

24  32 

23  12 

21  52 

20  32 

40 

44 

45  49 

43  34 

41  18 

39  02 

37  07 

35  10 

33  14 

31  18 

29  41 

28  05 

26  28 

24  51 

44 

48 

54  32 

5150 

49  09 

46  28 

44  09 

4151 

39  33 

37  15 

35  20 

33  24 

31  29 

29  32 

48 

52 

64  00 

60  50 

57  41 

54  32 

51  49 

49  07 

46  25 

43  43 

41  28 

39  12 

36  57 

34  42 

52 

56 

74  13 

70  34 

66  54 

63  14 

60  07 

56  58 

53  50 

50  42 

48  05 

45  29 

42  52 

40  15 

56 

60 

85  12 

1/ 

8100 

76  48 

72  36 

// 

69  00 

65  24 

6148 

58  12 

II 

55  12 
II 

52  12 

H 

49  12 

46  12 

60 

Ajh 

1.42 

1.35 

1.28 

1.21 

1.15 

1.09 

1.03 

0.97 

0.92 

0.87 

0.82 

0.77 

A,h 

Log. 

0.152 

0.130 

0.107 

0.082 

0.060 

0.037 

0.012 

9.986 

9.963 

9.939 

9.913 

9.886 

Log. 

29 

33 

21 

79 

70 

43 

84 

77 

79 

52 

81 

49 

Limit 

55 

57 

59 

61 

63 

64 

65 

67 

69 

71 

73 

75 

Min- 
utes 

Merid- 
ian 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

Alti- 
tudes 

Latitude  19°  Declination  G)ntrary  Name* 


115 


Declination- 

^. 

Hour  i 
Angles 

3° 

1° 

2° 

3° 

40 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

ff 

/      // 

/      // 

Mill. 

Min. 

4          1 

31 

126 

123 

1  19 

1  16 

1  13 

1  10 

107 

105 

102 

100 

0  59 

4 

8         6 

05 

5  48 

5  31 

5  16 

5  04 

4  51 

4  40 

4  29 

4  19 

4  10 

4  02 

3  53 

8 

12       13 

41 

13  02 

12  26 

11  53 

11  23 

10  55 

10  29 

10  05 

9  43 

9  23 

9  03 

8  44 

12 

16       24 

19 

23  10 

22  06 

21  07    20  13 

19  25 

18  39 

17  55 

17  17 

16  41 

16  05 

15  32 

16 

20       38 

00 

36  12 

34  32 

33  OOj  31  36 

30  20 

29  08 

28  00 

27  00 

26  04 

25  08 

24  16 

20 

24       54 

43 

52  07 

49  44 

47  31    45  30 

43  41 

4157 

40  19 

38  53 

37  32 

36  11 

34  57 

24 

28       74 

29 

70  58 

67  41 

64  41    61  54 

59  27 

57  06 

54  53 

52  55 

51  06 

49  16 

47  33 

28 

32 

80  54 

77  39 

74  34 

71  41 

69  07 

66  44 

64  21 

62  07 

32 

36 

78  38 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h     5; 

?0 

5.43 

5.18 

4.95 

4.74 

4.55 

4.37 

4.20 

4.05 

3.91 

Z.ll 

3.64 

A,h 

Log. 

r55 

0.734 

0.714 

0.694 

0.675 

0.658 

0.640 

0.623 

0.607 

0.592 

0.576 

0.561 

Log. 

87 

80 

33 

61 

78 

01 

48 

25 

46 

18 

34 

10 

Limit       2 

J 

24 

25 

26 

27 

27 

28 

28 

30 

30 

31 

31 

Min- 
utes 

Merid-      17 1 
ian        "■ 

0 

70° 

69° 

68° 

1 

•67° 

1 

66° 

65° 

64° 

63= 

1 

62° 

61= 

60° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/       /' 

/     // 

/     // 

/      /' 

1      II 

/      // 

Min. 

Min. 

4 

0  56 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  46 

0  44 

0  43 

0  42 

0  41 

4 

8 

3  46 

3  39 

3  32 

3  26 

3  19 

3  13 

3  07 

3  02 

2  58 

2  53 

2  47 

2  43 

8 

12 

8  28 

8  11 

7  56 

7  42 

7  27 

7  15 

7  02 

6  50 

6  39 

6  29 

6  17 

6  07 

12 

16 

15  04 

14  33 

14  08 

13  42 

13  17 

12  53 

12  30 

12  10 

11  49 

11  31 

11  11 

10  53 

16 

20 

23  32 

22  44 

22  04 

21  24 

20  44 

20  08 

19  32 

19  00 

18  28 

18  00 

17  28 

17  00 

20 

24 

33  53 

32  44 

31  47 

30  49 

29  52 

29  00 

28  07 

27  22 

26  35 

25  55 

25  10 

24  29 

24 

28 

46  08 

44  34 

43  15 

41  57 

40  38 

39  28 

38  18 

37  14 

36  12 

35  17 

34  14 

33  19 

28 

32 

60  15 

58  12 

56  29 

54  47 

53  04 

51  32 

50  01 

48  38 

47  17 

46  05 

44  42 

43  31 

32 

36 

76  15 

73  39 

71  30 

69  20 

67  11 

65  14 

63  17 

61  34 

59  50 

58  19 

56  36 

55  05 

36 

40 

90  56 

88  16 

85  36 

82  56 

80  32 

78  08 

76  00 

73  52 

72  00 

69  52 

68  00 

40 

44 

87  07 

84  33 

82  17 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

// 

Ajh 

3.53 

3.41 

3.31 

3.21 

3.11 

3.02 

2.93 

2.85 

2.77 

2.70 

2.62 

2.55 

A,h 

Log. 

0.547 

0.532 

0.519 

0.506 

0.492 

0.480 

0.466 

0.454 

0.442 

0.431 

0.418 

0.406 

77 

75 

83 

51 

76 

01 

87 

84 

48 

36 

30 

54 

Log. 

Limit 

32 

33 

34 

35 

35 

36 

37 

38 

39 

40 

41 

42 

Min- 
utes 

Merid- 
ian 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

116 


Latitude  J 9°  Declination  Contrary  Name. 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      II 

/      // 

/      // 

/      // 

r       II 

/      // 

/      // 

1     II 

/      // 

/      // 

Min. 

4 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

0  34 

0  33 

0  32 

0  31 

0  30 

0  30 

4 

8 

2  40 

2  35 

2  31 

2  27 

2  24 

2  19 

2  16 

2  13 

2  10 

2  06 

2  03 

2  00 

8 

12 

5  59 

5  49 

5  40 

5  31 

5  23 

5  14 

5  06 

5  00 

4  82 

4  46 

4  38 

4  31 

12 

16 

10  37 

10  19 

10  04 

9  49 

9  33 

9  18 

9  06 

8  52 

8  40 

8  26 

8  14 

8  01 

16 

20 

16  36 

16  08 

15  44 

15  20 

14  56 

14  32 

14  12 

13  52 

13  32 

13  12 

12  52 

12  32 

20 

24 

23  54 

23  14 

22  40 

22  05 

21  30 

20  56 

20  27 

19  58 

19  29 

19  00 

18  31 

18  03 

24 

28 

32  33 

31  38 

30  50 

30  03 

29  16 

28  29 

27  50 

27  11 

26  32 

25  83 

25  14 

24  34 

28 

32 

42  30 

41  18 

40  16 

39  15 

38  14 

37  12 

36  21 

35  20 

34  39 

33  48 

32  57 

32  05 

32 

36 

53  47 

52  16 

50  59 

49  41 

48  23 

47  06 

46  01 

44  56 

43  81 

42  46 

41  41 

40  37 

36 

40 

66  24 

64  32 

62  56 

6120 

59  44 

58  08 

56  48 

55  28 

54  08 

52  48 

5128 

50  08 

40 

44 

80  20 

78  05 

76  09 

74  13 

72  16 

70  21 

68  44 

67  07 

65  30 

63  53    62  16 

60  40 

44 

48 

95  37 

92  56 

90  37 

88  19 

86  01 

83  42 

8146 

79  52 

77  57 

76  02    74  07 

72  11 

48 

52 

106  21 

103  39 

100  57 

98  14 

95  59 

93  44 

9129 

89  14 

86  59 

84  43 

52 

56 

106  06 

103  29 

100  52 

98  15 

56 

60 

112  48 

60 

It 

// 

II 

II 

11 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.49 

2.42 

2.36 

2.30 

2.24 

2.18 

2.13 

2:08 

2.03 

1.98 

1.93 

1.88 

A,h 

Log. 

0.396 

0.383 

0.372 

0.361 

0.350 

0.338 

0.328 

0.318 

0.307 

0.296 

0.285 

0.274 

Log. 

20 

82 

91 

73 

25 

46 

38 

06 

50 

67 

56 

16 

Limit 

42 

43 

44 

45 

46 

47 

48 

48 

49 

50 

51 

52 

Min- 
utes 

Merid- 
ian 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40°« 

39° 

38° 

37° 

36° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

Min. 

4 

0  29 

0  28 

0  28 

0  27 

0  27 

0  26 

0  25 

0  25 

0  24 

0  23 

0  22 

0  22 

4 

8 

157 

155 

152 

149 

146 

143 

141 

139 

136 

134 

131 

1  29 

8 

12 

4  23 

4  18 

4  11 

4  05 

3  59 

3  53 

3  48 

3  42 

3  36 

3  31 

3  25 

3  20 

12 

16 

7  49 

7  38 

7  25 

7  15 

7  05 

6  55 

6  44 

6  34 

6  24 

6  13 

6  03 

5  56 

16 

20 

12  12 

1156 

1136 

1120 

1104 

10  48 

10  32 

10  16 

10  00 

9  44 

9  28 

9  16 

20 

24 

17  34 

17  11 

16  42 

16  19 

15  57 

15  34 

15  10 

14  47 

14  24 

14  01 

13  38 

13  21 

24 

28 

23  55 

23  24 

22  44 

22  13 

2141 

21  10 

20  39 

20  07 

19  36 

19  05 

18  34 

18  10 

28 

32 

31  13 

30  33 

29  42 

29  01 

28  19 

27  38 

26  58 

26  17 

25  36 

24  55 

24  14 

23  43 

32 

36 

39  32 

38  40 

37  35 

36  43 

35  52 

35  00 

34  08 

33  16 

32  24 

3132 

30  40 

30  02 

36 

40 

48  48 

47  44 

46  24 

45  20 

44  16 

43  12 

42  08 

4104 

40  00 

38  56 

37  52 

37  04 

40 

44 

59  03 

57  45 

56  08 

54  51 

53  34 

52  17 

50  59 

49  41 

48  24 

47  06 

45  49 

44  51 

44 

48 

70  16 

68  42 

66  47 

65  15 

63  44 

62  12 

60  40 

59  08 

57  36 

56  04 

54  32 

53  22 

48 

52 

82  28 

80  40 

78  25 

76  37 

74  48 

73  00 

71  12 

69  24 

67  36 

65  48 

64  00 

62  38 

52 

56 

95  39 

93  33 

90  56 

88  51 

86  46 

84  41 

82  35 

80  29 

78  24 

76  18 

74  13 

72  39 

56 

60 

109  48 

107  24 

104  24 

102  00 

99  36 

97  12 

94  48 

92  24 

90  00 

87  36 

85  12 

83  24 

60 

II 

It 

It 

It 

It 

It 

ti 

ti 

ti 

ti 

II 

It 

A,h 

1.83 

1.79 

1.74 

1.70 

1.66 

1.62 

1.58 

1.54 

1.50 

1.46 

1.42 

1.39 

Ajh 

Log. 

0.262 

0.252 

0.240 

0.230 

0.220 

0.209 

0.198 

0.187 

0.176 

0.164 

0.152 

0.143 

Log. 

45 

85 

55 

45 

11 

52 

66 

52 

09 

35 

29 

01 

Limit 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

Min- 
utes 

Merid- 
ian 

35 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

Latitude  19°  Declination  Contrary  Name. 


117 


Declinations. 


Hour 
Angles 


48°  I  49^^ 


0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

8100 
// 

1.35 
0.130  0.117 
33    27 


0  21 

1  23 
3  08 
5  36 

8  44 
12  35 
17  07 
22  21 
28  18 
34  56 
42  16; 
50  18 
59  02 
68  28 
78  36 

n 

1.31 


50° 


64 


23'^ 


65 


22° 


0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

21  51 

27  39 

34  08! 

41  18| 

49  09; 

57  41' 

66  54 

76  48, 

n 

1.28 


51= 


0  20 

1  20 

2  59 
5  17 

8  16 
11  54 
16  12 
21  10 
26  47 
33  04 
40  00 
47  37 
55  53 
64  48' 
74  241 


52° 


53= 


54° 


55° 


0  19 

1  17 

2  54 
5  10 
8  04 

11  37 
15  49: 
20  39 
26  08; 
32  16 
39  02 
46  28| 
54  32 
63  14' 
72  36 


0.107 
21 


67 


21° 


1.24  I  1.21 


0  19 

1  15 

2  48 
5  00 
7  48! 

11  14 

15  17' 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
// 

1.17 


0.093 
42 


0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  381 
30  24' 
36  47 
43  46' 
51  22' 
59  351 
68  24i 

1.14 


68 


20° 


0.082  0.068  0.056 
79    19    90 


69 


19° 


71   73 


18= 


17° 


0  18 

1  10 

2  38 
4  42 

7  20 
10  34 
14  22 

18  46 
23  46 
29  20j 
35  30 

42  14| 

49  34J 

57  30i 

66  00 
II 

1.10 


56° 


0.041 
39 


75 


16° 


0  17 

1  08 

2  34 
4  34 

7  08, 
10  16 
13  59 
18  16! 
23  07' 
28  32 
34  32 
41  05 
48  13! 
55  56, 
64  12 

1.07 


57°  I  58° 


0.029 
38 


0  17 

107 

2  30 

4  26 

6  56| 

9  59( 

13  35 

17  45, 

22  28 

27  44' 

33  33 

39  56' 

46  52' 

54  21 

62  24 


0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

21  49, 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 


59° 


0  19 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

31  37 

37  38 

44  10 

51  13 

58  48 


1.04  i  1.01  !  0.98 


Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 


76 


15° 


0.017i 
031 


0.004 
321 


9.991 
23 


77        78 


79 


14°      13°  I    12= 


Log. 


Min- 
utes 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65°      66° 

67°      68°  \  69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
II 

0.95 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 

15  32 

19  39 

24  16 

29  21 

34  57 

41  01 

47  33 

54  36 
It 

0.91 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 

52  48 

II 

0.88 

/      // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 

5100 

II 

0.85 

/      // 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

n 

0.82 

/      // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 

0.79 

/      // 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  43 

45  36 

n 

0.76 

/      // 

Oil 
0  46 
144 

3  04 

4  48 
6  55 
9  25 

12  17 

15  33 

19  12 

23  14 

27  37 

32  27 

37  38 

43  12 
// 

0.72 

II 

// 

/ 

II 

/ 

II 

II 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.977 
72 

9.959 
04 

9.944 
48 

9.929 
42 

9.913 
81 

9.897 
63 

9.880 
81 

9.857 
33 

Log. 

Limit 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

Min- 
utes 

Merid- 
ian 

11° 

10° 

9°        8° 

7° 

6°    1     5° 

4° 

3° 

2° 

1° 

0° 

Alti- 
tudes 

118 


Latitude  20°  Declination  Same  Name* 


3i:CLIN.\TION 

s. 

Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5°        6° 

70 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

1      It 

'      " 

/      /' 

/        n 

/      // 

/       '/     /       // 

1      It 

/      // 

1     It 

/     It 

1     It 

Min. 

4 

•    126 

131 

135 

1  41 

147 

154 

2  01 

2  10 

2  20 

2  33 

2  47 

3  05 

4 

8 

5  45 

6  03 

6  22 

6  43 

7  07 

7  34 

8  05 

8  41 

9  23 

10  11 

11  10 

12  22 

8 

12 

12  56 

13  36 

14  20 

15  07 

16  02 

17  02 

18  12 

19  32 

2106 

22  55 

25  07 

27  49 

12 

16 

23  00 

24  12 

25  28 

26  53 

28  30 

30  18 

32  20 

34  44 

37  30 

40  45 

44  37 

16 

20 

35  56 

37  48 

39  48 

42  00 

44  32 

47  20 

50  32 

54  16 

20 

24 

5145 

54  26 

57  18 

60  29 

64  08 

• 

24 

28 

70  26 

74  05 

78  01 

82  19 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

" 

II 

It 

II 

It 

" 

It 

It 

II 

It 

A,h 

5.39 

5.67 

5.97 

.6.30 

6.68 

7.10 

7.58 

8.14 

8.79 

9.55 

10.46 

11.58 

Ajh 

0.731 

0.753 

0.775 

0.799 

0.824 

0.851 

0.879 

0.910 

0.943 

0.980 

1.019 

1.063 

Log. 

59 

58 

97 

34 

78 

26 

67 

62 

99 

00 

53 

71 

Limit 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

Min- 
utes 

Merid- 
ian 

70° 

71° 

72° 

73° 

74° 

75° 

•  76° 

77° 

78° 

79° 

80° 

81° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16°      1' 

1° 

18° 

] 

L9°      20 

=      21 

^      22 

^      23 

0      Hour 
Angles 

Min . 

/       // 

1     It 

1       n 

/       n 

1       n     1 

II 

/      // 

1 

//    1 

//    1 

It    1 

"    ' 

"      Min. 

4 

3  27 

3  56 

4  35 

5  27 

4 

8 

13  50 

15  44 

18  16 

2148 

8 

12 

3108 

35  24 

12 

16 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

. . 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

II 

II 

It 

II            II 

II 

II          II 

'I 

II 

It 

A,h 

12.97 

14.75 

17.13 

20.45 

Ajh 

Log. 

1.112 

94 

1.168 
79 

1.233 
76 

1.310 
69 

Log. 

Limit 

12 

11 

10 

8 

6          A 

t         3     ! 

1         0 

2 

4 

6 

Min- 
utes 

Merid- 
ian 

82' 

) 

83' 

84' 

> 

85' 

86°  t    8' 

r° 

8E 

!° 

I 

9°      90' 

89' 

88= 

87' 

Alti- 
tudes 

Latitude  20°  Declination  Same  Name* 


119 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29' 

3 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1 

5 
20 

// 
19.1< 

37 
28 

1 

4 
16 
38 

n 

15.8' 

14 
36 
35 

1 

3 

14 
32 

II 
13.4 

35 
24 
23 

3 

1 

3 
12 

28 

II 
11.7 

37 
30 
36 

I 

2 
11 
24 
44  ( 

n 

10.3 

15 
30 
16 
32 

2 

1 

2 
9 

22 

39 

II 
9.2 

27 
19 
35 
15 

3 

2  12 

8  51 

19  54 

35  22 

55  16 

II 
8.29 

/      // 

2  00 

8  02 

18  04 

32  08 

50  12 

II 
7.53 

1  50 
7  20 
16  31 
29  21 
45  52 
66  03 

II 
6.88 

1  41 
6  44 
15  10 
26  58 
42  08 
60  41 
82  35 

II 
6.32 

1  34 
6  14 
14  01 
24  55 
38  56 
56  04 
76  18 

II 
5.84 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Aih 

Log. 

1.283 
07 

1.200 

58 

1.130 
01 

1.068 
56 

1.013 
68 

0.963 
79 

0.918 
55 

0.876 
79 

0.837 
59 

0.800 

72 

0.766 
41 

Log. 

Limit 

7 

8 

9 

10 

11 

13 

15 

16 

17 

19 

21 

22 

Min- 
utes 

Merid- 
ian 

8( 

)° 

85' 

> 

84' 

■> 

83' 

J 

82' 

3 

81' 

3 

80 

3 

79 

3 

78 

D 

77 

D 

76 

3 

75 

3 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

'  126 

1     II 
121 

1  15 

1  10 

1      II 
106 

/      // 
1  02 

0  59 

0  55 

1     II 
0  52 

/      // 
0  49 

/      II 
0  46 

0  44 

Min. 
4 

8 

5  47 

5  23 

5  01 

4  42 

4  24 

4  09 

3  54 

3  41 

3  29 

3  18 

3  06 

2  58 

8 

12 

13  01 

12  06 

11  17 

10  34 

9  54 

9  20 

8  47 

8  17 

7  50 

7  25 

7  01 

6  39 

12 

16 

23  07 

21  30 

20  03 

18  46 

17  38 

16  36 

15  37 

14  43 

13  54 

13  11 

12  27 

11  49 

16 

20 

36  08 

33  36 

31  20 

29  20 

27  32 

25  56 

24  24 

23  00 

21  44 

20  36 

19  28 

18  28 

20 

24 

52  02 

48  23 

45  07 

42  14 

39  39 

37  21 

35  09 

33  07 

31  18 

29  40 

28  02 

26  35 

24 

28 

70  50 

65  51 

61  25 

57  30 

53  58 

50  50 

47  49 

45  05 

42  36 

40  23 

38  10 

36  12 

28 

32 

80  13 

75  06 

70  29 

66  23 

62  27 

58  53 

55  38 

52  44 

49  50 

47  17 

32 

36 

79  04 

74  31 

70  25 

66  45 

63  04 

59  50 

36 

40 
44 
48 
52 
56 
60 

II 

II 

II 

II 

II 

II 

II 

92 
II 

00 

86. 
II 

56 

82. 
II 

24 

77. 
II 

52 

73 

II 

52 

40 
44 
48 
52 
56 
60 

A,h 

5.42 

5.04 

4.70 

4.40 

4.13 

3.89 

3.66 

3.45 

3.26 

3.09 

2.92 

2.11 

A,h 

Log. 

0.734 

0.702 

0.672 

0.643 

0.615 

0.589 

0.563 

0.537 

0.513 

0.489 

0.465 

0.442 

00 

43 

11 

45 

95 

95 

48 

82 

22 

96 

38 

48 

Log. 

Limit 

24 

25 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64' 

3 

63' 

3  " 

Alti- 
tudes 

120 


Latitude  20°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  42 
2  48 
6  18 
11  14 
17  32 
25  15 
34  22 
44  53 
56  49 
70  08 
84  52 

II 
2.63 

/      // 

0  40 
2  40 
6  00 
10  40 
16  40 
24  00 
32  40 
42  40 
54  00 
66  40 
80  40 
96  00 

II 
2.50 

/     II 

0  38 

2  32 

5  41 

10  07 

15  48 

22  45 

30  58 

40  27 

51  12 

63  12 

76  39 

91  00 

106  48 

II 
2.37 

1      II 

0  36 

2  24 

5  24 

9  36 

15  00 

21  36 

29  24 

38  24 

48  36 

60  00 

72  36 

86  24 

10124 

II 
2.25 

/      // 

0  35 

2  17 

5  08 

9  08 

14  16 

20  33 

27  57 

36  31 

46  14 

57  04 

69  03 

82  10 

96  26 

II 
2.14 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

44  04 

54  24 

65  49 

78  20 

9156 

106  37 

II 
2.04 

/      // 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

4154 

5144 

62  35 

74  30 

87  26 

10123 

II 
1.94 

/     // 

0  30 

1  58 
4  26 
7  54 

12  20 

17  46 

24  10 

3134 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 
II 

1.85 

0  28 

1  53 
4  14 
7  30 

1144 
16  54 
23  00 
30  02 
38  01 
46  56 
56  47 
67  33 
79  19 
9159 

105  36 

II 

1.76 

/      // 

0  27 

1  47 
4  00 
7  08 

1108 
16  02 
2149 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 
87  18 

100  12 

II 

1.67 

/     // 

0  25 

1  42 
3  49 
6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

6103 

71  39 

83  06 

95  24 
II 

1.59 

/      // 

0  24 

1  36 
3  37 
6  27 

10  04 

14  30 

19  44 

25  46 

32  37 

40  16 

48  43 

57  59 

68  03 

78  55 

90  36 
II 

1.51 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.419 
96 

0.397 
94 

0.374 
75 

0.352 
18 

0.330 
41 

0.309 
63 

0.287 
80 

0.267 
17 

0.245 
51 

0.222 
72 

0.201 
40 

0.178 
98 

Log. 

Limit 

37 

38 

39 

41 

42 

44 

45 

46 

47 

49 

51 

53 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     // 

1     II 

/     // 

/      // 

/     // 

/     // 

/      /' 

/      // 

1     II 

/     // 

/      // 

Min. 

4 

0  22 

0  22 

0  20 

0  19 

0  19 

0  18 

0  17 

0  15 

0  14 

0  14 

0  13 

0  12 

4 

8 

133 

1  27 

1  23 

1  19 

1  14 

1  10 

107 

1  02 

0  59 

0  56 

0  52 

0  49 

8 

12 

3  28 

3  16 

3  06 

2  57 

2  47 

2  38 

2  30 

2  22 

2  14 

2  07 

1  58 

1  50 

12 

16 

6  08 

5  48 

5  30 

5  15 

4  57 

4  42 

4  26 

4  10 

3  58 

3  45 

3  30 

3  14 

16 

20 

9  36 

9  04 

8  36 

8  12 

7  44 

7  20 

6  56 

6  32 

6  12 

5  52 

5  28 

5  04 

20 

24 

13  49 

13  04 

12  23 

11  48 

1109 

10  34 

9  59 

9  24 

8  55 

8  27 

7  53 

7  18 

24 

28 

18  49 

17  46 

16  52 

16  05 

15  09 

14  22 

13  35 

12  49 

12  10 

1130 

10  43 

9  56 

28 

32 

24  35 

23  12 

22  01 

21  00 

19  47 

18  46 

17  45 

16  44 

15  53 

15  01 

13  59 

12  58 

32 

36 

3106 

29  23 

27  52 

26  34 

25  04 

23  46 

22  28 

21  10 

20  05 

19  01 

17  43 

16  25 

36 

40 

38  24 

36  16 

34  24 

32  48 

30  56 

29  20 

27  44 

26  08 

24  48 

23  28 

2152 

20  16 

40 

44 

46  27 

43  53 

41  37 

39  41 

37  26 

35  30 

33  33 

31  37 

30  00 

28  24 

26  28 

24  31 

44 

48 

55  18 

52  13 

49  32 

47  14 

44  32 

42  14 

39  56 

37  38 

35  43 

33  47 

31  29 

29  09 

48 

52 

64  54 

61  17 

58  08 

55  26 

52  16 

49  34 

46  52 

44  10 

4155 

39  39 

36  57 

34  15 

52 

56 

75  15 

7105 

67  25 

64  17 

60  38 

57  30 

54  21 

51  13 

48  36 

46  00 

42  52 

39  43 

56 

60 

86  24 

8136 

77  24 

73  48 

69  36 

66  00 

62  24 

58  48 

55  48 

52  48 

49  12 

45  36 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

" 

A,h 

1.44 

1.36 

1.29 

1.23 

1.16 

1.10 

1.04 

0.98 

0.93 

0.88 

0.82 

0.76 

A,h 

Log. 

0.158 

0.133 

0.110 

0.089 

0.064 

0.041 

0.017 

9.991 

9.968 

9.944 

9.913 

9.880 

Log. 

36 

54 

59 

91 

46 

39 

03 

23 

48 

48 

81 

81 

Limit 

54 

56 

58 

60 

62 

64 

66 

68 

70 

72 

74 

76 

Min- 
utes 

Merid- 
ian 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tudes 

Latitude  20"  Declination  Contrary  Name. 


121 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Mln. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

1 

5 
12 
23 
35 
51 
70 

n 

5.3< 

// 

26 
45 
56 
30 
56 
15 
26 

1 

5 
12 
21 
34 
49 
67 

II 
5.L 

// 

23 
29 
21 
59 
20 
27 
17 

/     // 

1  18 
5  14 
11  49 
20  59 
32  48 
47  14 
64  18 

II 
4.92 

/ 

1 
5 
11 
20 
31 
45 
61 
80 

II 
4.7 

// 

15 

32 
20 
38 
28 
19 
il 
33 

I 

1 
4 
10 
19 
30 
43 
59 
77 

II 
4.5 

// 

12 
50 
52 
20 
12 
29 
12 
19 

J 

1 

4 
10 
18 
29 
41 
56 
74 

II 
4.3, 

// 

10 
38 
26 
34 
30 
t6 
50 
14 

1 

4 
10 
17 
27 
40 
54 
71 

II 
4.1' 

// 

07 
28 
03 
53 
56 
14 
i5 
30 

3 

/     // 

104 
4  18 
9  40 
17  12 
26  52 
38  41 
52  40 
68  47 

II 
4.03 

/      II 

1  02 
4  09 
9  20 
16  36 
25  56 
37  21 
50  20 
66  23 

II 
3.89 

/     // 

1  00 
4  01 
9  02 
16  02 
25  04 
36  06 
49  08 
64  10 

II 
3.76 

/     // 

0  58 
3  52 
8  42 
15  30 
24  12 
34  51 
47  26 
6157 
78  25 

II 
3.63 

/           // 

0  56 
3  45 

8  27 
15  01 
23  28 
33  48 
46  00 
60  04 
76  02 

II 
3.52 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.731 
59 

0.711 

81 

0.691 
97 

0.673 
94 

0.656 
10 

0.638 
49 

0.622 
21 

0.605 
31 

0.589 
95 

0.575 
19 

0.559 
91 

0.546 
54 

Log. 

Limit 

24 

25 

26 

27 

28 

28 

29 

30 

30 

31 

32 

33 

Min- 
utes 

Merid- 
ian 

70= 

69= 

68° 

67= 

■> 

66= 

) 

65' 

) 

64= 

> 

63=' 

62 

o 

61° 

60< 

3 

59= 

> 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

/     // 

/      // 

/     // 

/      // 

1     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  54 

0  53 

0  51 

0  50 

0  48 

0  47 

0  46 

0  44 

0  43 

0  42 

0  41 

0  39 

4 

8 

3  39 

3  31 

3  25 

3  19 

3  13 

3  07 

3  02 

2  58 

2  53 

2  48 

2  44 

2  40 

8 

12 

8  11 

7  55 

7  41 

7  27 

7  15 

7  02 

6  50 

6  39 

6  29 

6  18 

6  09 

5  59 

12 

16 

14  33 

14  05 

13  39 

13  17 

12  53 

12  30 

12  10 

11  49 

11  31 

11  14 

10  55 

10  37 

16 

20 

22  44 

22  00 

21  20 

20  44 

20  08 

19  32 

19  00 

18  28 

18  00 

17  32 

17  04 

16  36 

20 

24 

32  44 

31  41 

30  43 

29  52 

29  00 

28  07 

27  22 

26  35 

25  55 

25  15 

24  35 

23  54 

24 

28 

44  34 

43  07 

41  49 

40  38 

39  28 

38  18 

37  14 

36  12 

35  17 

34  22 

33  27 

32  33 

28 

32 

58  12 

56  19 

54  37 

53  04 

5132 

50  01 

48  38 

47  17 

46  05 

44  53 

43  41 

42  30 

32 

36 

73  39 

71  17 

69  07 

67  11 

65  14 

63  17 

61  34 

59  50 

58  19 

56  49 

55  18 

53  47 

36 

40 

90  56 

88  00 

85  20 

82  56 

80  32 

78  08 

76  00 

73  52 

72  00 

70  08 

68  16 

66  24 

40 

44 

87  07 

84  52 

82  36 

80  20 

44 

48 

95  37 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

" 

II 

" 

II 

II 

" 

II 

" 

II 

A,h 

3.41 

3.30 

3.20 

3.11 

3.02 

2.93 

2.85 

2.77 

2.70 

2.63 

2.56 

2.49 

A,h 

Log. 

0.532 

0.518 

0.505 

0.492 

0.480 

0.466 

0.454 

0.442 

0.431 

0.419 

0.408 

0.396 

Log. 

75 

51 

15 

76 

01 

87 

84 

48 

36 

96 

24 

20 

Limit 

33 

34 

35 

36 

36 

37 

37 

38 

39 

40 

41 

42 

Min- 
utes 

Merid- 
ian 

58° 

57° 

56° 

55° 

54° 

53° 

52°  , 

51° 

50° 

49° 

48° 

47° 

Alti- 
tudes 

1L>2 


Latitude  20°  Decimation  Contrary  Name. 
Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

/      // 

0  38 
2  36 
5  50 
10  22 
16  12 
23  19 
31  46 
4129 
52  29 
64  48 
78  24 
93  19 

// 
2.43 

1     II 

0  38 

2  31 

5  40 

10  04 

15  44 

22  40 

30  50 

40  16 

50  59 

62  56 

76  09 

90  37 

106  21 

II 
2.36 

/     // 

0  37 

2  28 

5  32 

9  52 

15  24 

22  11 

30  11 

39  25 

49  54 

61  36 

74  32 

88  42 

104  06 

II 
2.31 

/      // 

0  36 

2  24 

5  24 

9  36 

15  00 

21  36 

29  24 

38  24 

48  36 

60  00 

72  36 

86  24 

10124 

II 
2.25 

/     // 

0  35 

2  20 

5  15 

9  21 

14  36 

21  02 

28  37 

37  22 

47  19 

58  24 

70  40 

84  05 

98  41 

II 
2.19 

0  35 

2  17 

5  08 

9  08 

14  16 

20  33 

27  57 

36  31 

46  14 

57  04 

69  03 

82  10 

96  26 

II 
2.14 

0  33 

2  14 

5  01 

8  55 

13  56 

20  04 

27  19 

35  40 

45  09 

55  44 

67  26 

80  15 

94  11 

II 
2.09 

/     // 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

44  04 

54  24 

65  49 

78  20 

91  56 

106  37 

II 
2.04 

/     // 

0  31 

2  07 

4  47 

8  29 

13  16 

19  06 

26  01 

33  58 

42  59 

53  04 

64  12 

76  25 

89  41 

104  01 

1.99 

/      // 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

51  44 

62  35 

74  30 

87  26 

101  23 

II 
1.94 

/     // 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 

II 

1.89 

1     II 

0  30 

158 
4  26 
7  54 
12  20 
17  46 
24  10 
31  34 
39  58 
49  20 
59  42 
71  02 
83  22 
96  42 

111  00 

II 

1.85 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.385 
61 

0.372 
91 

0.363 
61 

0.352 
18 

0.340 
44 

0.330 
41 

0.320 
15 

0.309 
63 

0.298 
85 

0.287 
80 

0.276 
46 

0.267 

17 

Log. 

Limit 

43 

44 

45 

46 

47 

48 

48 

48 

49 

50 

51 

52 

Min- 
utes 

Merid- 
ian 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/      // 

/      // 

/      // 

1     II 

/      /' 

Min. 

4 

0  29 

0  28 

0  27 

0  27 

0  26 

0  25 

0  25 

0  24 

0  23 

0  22 

0  22 

0  22 

4 

8 

155 

153 

1  50 

1  47 

1  44 

1  42 

1  39 

1  36 

1  35 

1  33 

1  30 

1  28 

8 

12 

4  19 

4  14 

4  06 

4  00 

3  54 

3  49 

3  43 

3  37 

3  34 

3  28 

3  22 

3  17 

12 

16 

7  41 

7  30 

7  18 

7  08 

6  58 

6  47 

6  37 

6  27 

6  18 

6  08 

5  58 

5  51 

16 

20 

12  00 

11  44 

1124 

1108 

10  52 

10  36 

10  20 

10  04 

9  52 

9  36 

9  20 

9  08 

20 

24 

17  17 

16  54 

16  25 

16  02 

15  39 

15  16 

14  53 

14  30 

14  12 

13  49 

13  26 

13  09 

24 

28 

23  31 

23  00 

22  21 

21  49 

21  18 

20  47 

20  15 

19  44 

19  21 

18  49 

18  18 

17  54 

28 

32 

30  43 

30  02 

29  11 

28  30 

27  49 

27  08 

26  27 

25  46 

25  16 

24  35 

23  54 

23  23 

32 

36 

38  53 

38  01 

36  56 

36  05 

35  13 

34  21 

33  29 

32  37 

31  58 

31  06 

30  14 

29  36 

36 

40 

48  00 

46  56 

45  36 

44  32 

43  28 

42  24 

41  20 

40  16 

39  28 

38  24 

37  20 

36  32 

40 

44 

58  05 

56  47 

55  10 

53  54 

52  36 

51  18 

50  01 

48  43 

47  45 

46  27 

45  10 

44  13 

44 

48 

69  07 

67  33 

65  38 

64  07 

62  35 

61  03 

59  31 

57  59 

56  50 

55  18 

53  46 

52  36 

48 

52 

8107 

79  19 

77  04 

75  15 

73  27 

71  39 

69  51 

68  03 

66  42 

64  54 

63  06 

61  44 

52 

56 

94  05 

9159 

89  22 

87  18 

85  12 

83  06 

8101 

78  55 

77  21 

75  15 

73  10 

71  36 

56 

60 

108  00 

105  36 

102  36 

100  12 

97  48 

95  24 

93  00 

90  36 

88  48 

86  24 

8100 

82  12 

60 

II 

II 

II 

// 

n 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.80 

1.76 

1.71 

1.67 

1.63 

1.59 

1.55 

1.51 

1.48 

1.44 

1.40 

1.37 

A,h 

Log. 

0.255 

0.245 

0.233 

0.222 

0.212 

0.201 

0.190 

0.178 

0.170 

0.158 

0.146 

0.136 

Log. 

27 

•       51 

00 

72 

19 

40 

33 

98 

26 

36 

13 

72 

Limit 

53 

54 

55 

56 

57 

58 

59 

61 

61 

62 

63 

64 

Min- 
utes 

Merid- 
ian 

34° 

33° 

32° 

31° 

30°      29°  1 

28° 

27° 

26° 

25° 

24° 

23° 

Alti- 
tudes 

Latitude  20°  Declination  Contrary  Name. 
Declinations. 


123 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  // 

0  21 

1  25 
311 
5  41 
8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

51  04 

59  56 

69  31 

79  48 
n 

1.33 

/  // 

0  21 

1  23 
3  07 
5  33 
8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 
II 

1.30 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 

II 

1.26 

/  // 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 
16  05 
21  00 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 

73  48 

II 

1.23 

/   // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

3144 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

/  II 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 

15  09 

19  47 

25  04 

30  56 

37  26 

44  32 

52  16 

60  38 

69  36 
II 

1.16 

1     II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

55  55 

59  04 

67  48 
II 

1.13 

/  // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

4151 

49  07 

56  58 

65  24 
II 

1.09 

/   // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

II 

1.06 

/  // 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

/  // 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

II 

1.00 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 
16  34 
20  57 
25  52 
31  18 
37  15 
43  43 
50  42 

58  12 

II 

0.97 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.123 
85 

0.113 
94 

0.100 
37 

0.089 
91 

0.075 
55 

0.064 
46 

0.053 
08 

0.037 
43 

0.025 
31 

0.012 
84 

0.00 

9.986 
77 

Log. 

Limit 

65 

66 

68 

69 

70 

71 

73 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1     II 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
II 

0.94 

/  // 
0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

II 

0.91 

/  // 

'  0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

1122 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

II 

0.87 

/  // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

/  // 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

31  06 

36  30 

42  20 

48  36 
II 

0.81 

/  // 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

/  // 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

0.75 

/ 

// 

// 

/ 

// 

// 

II 

// 

/ 

// 

II 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.973 
13 

9.959 
04 

9.939 
52 

9.924 
28 

9.908 
49 

9.892 
09 

9.875 
06 

Log. 

Limit 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

Min- 
utes 

Merid- 
ian 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3°  1  2° 

1° 

0° 

1° 

Alti- 
tudes 

124 


Latitude  2t°  Declination  Same  Name, 

Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4°    1 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1  22 
5  27 
12  17 
2151 
34  08 
49  10 
66  54 

5.12 

126 
5  43 
12  52 
22  52 
35  44 
51  28 
70  02 

// 
5.36 

130 
6  00 
13  30 
24  02 
37  32 
54  03 
73  34 

5.63 

1 

i: 

6 
14 
25 
39: 
56. 
77. 

II 
5.9 

\\ 

8 
3 
15 
28 
50 
22 

2 

1 

1  \ 
6^ 
15  ( 
26^ 
41  ' 
60  ( 
81^ 

6.2 

iO 
10 
)0 
10 
10 
)0 
10 

5 

/      // 

146 

7  04 
15  54 
28  18 
44  12 
63  39 

6.63 

M 

7: 

16  J 
30  ( 
46. 

II 

II 

)3 
\\ 
>4 
)2 
)6 

4 

1 

2( 

8( 

18  ( 

32  ( 

50  ( 

II 
7.5 

)0 
)1 
)3 
)5 

)8 

2 

2  09 

8  37 

19  22 

34  26 

53  48 

II 
8.07 

2  19 

9  18 

20  54 

37  10 

58  04 

II 
8.71 

/     // 

2  31 
10  06 
22  43 
40  21 

II 
9.46 

/     // 

2  46 
11  03 
24  52 
44  12 

II 
10.36 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.709 
27 

0.729 
16 

0.750 
51 

0.772 
32 

0.795 

88 

0.821 
51 

0.847 
57 

0.876 
22 

0.906 

87 

0.940 
02 

0.975 
89 

1.015 
36 

Log. 

Limit 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

Min- 
utes 

Merid- 
ian 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 


12° 


Log. 


Limit 


3  03 
12  14 
27  31 
48  53 


13= 


3  25 
13  41 
30  47 


11.46 


1.059 
18 

13 


14° 


3  53 
15  34 
35  01 


12.83 


15= 


4  31 
18  04 
40  40 


14.59 


1.108    1.164 
23        06 

12 


81°      82° 


11 
83° 


16= 


5  23 
21  34 


16.94 


1.228 
91 


84° 


17° 


18° 


20.22 


1.305 

78 


fi5° 


86= 


19° 


20= 


87= 


88= 


21= 


22° 


89° 


90= 


23= 


89= 


Hour 
Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


88= 


Log. 

Min- 
utes 
Alti- 
tudes 


Latitude  2J°  Declination  Same  Name. 


125 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

n 

/ 

// 

2 
18 

5 
0 

// 
.9 

32 
39 

3 

/ 

1 
3 

15 

4 
6 
7 

// 
.6 

10 
10 
JO 

J 

1 

3 
14 
31 

n 

13.2 

?2 
10 
53 

3( 

12 
27 

II 

11.5: 

34 
17 
39 

I 

/     // 

2  43 
10  49 
24  21 
43  19 

II 
10.15 

2 

9 
21 
38 

II 
9.0. 

II 

25 
39 
i3 
37 

5 

/     II 

2  11 

8  41 

19  33 

34  47 

54  20 

II 
8.15 

/     // 

158 

7  53 

17  44 

31  32 

49  16 

7.39 

/     // 

149 
7  13 
16  14 
28  50 
45  04 
64  54 

II 
6.76 

/     II 

139 
6  38 
14  54 
26  30 
4124 
59  37 
8109 

6.21 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.276 
46 

1.193 
96 

1.123 
20 

1.061 
45 

1.006 
47 

0.956 
65 

0.911 
16 

0.868 
64 

0.829 
95 

0.793 
09 

Log. 

Limit 

5 

7 

8 

9 

10 

12 

14 

15 

17 

18 

19 

21 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40°      41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

1     II 

1     II 

1     II 

/      // 

/      II 

/     // 

/     // 

Min. 

Min. 

4 

131 

125 

1  18 

1  14 

109 

105 

101 

0  57 

0  54 

0  51 

0  48 

0  46 

4 

8 

6  07 

5  40 

5  16 

4  55 

4  36 

4  19 

4  03     3  49| 

3  36 

3  24 

3  13 

3  02 

8 

12 

13  45 

12  44 

1152 

1103 

10  20 

9  42 

9  07 

8  36 

8  05 

7  39 

7  13 

6  50 

12 

16 

24  27 

22  40 

2104 

19  41 

18  24 

17  14 

16  13 

15  16 

14  23 

13  37 

12  51 

12  10 

16 

20 

38  12 

35  24 

32  56 

30  44 

28  44 

26  56 

25  20 

23  52 

22  28 

21  16 

20  04 

19  00 

20 

24 

55  00 

50  59 

47  25 

44  16 

4123 

38  47 

36  29 

34  22 

32  21 

30  38 

28  54 

27  22 

24 

28 

74  53 

69  23 

64  33 

60  14 

56  19 

52  47 

49  39 

46  47 

44  02 

41  41 

39  20 

37  14 

28 

32 

78  40 

73  33 

68  57 

64  51 

61  06 

57  31 

54  26 

5122 

48  38 

32 

36 

77  20 

72  48 

68  55 

65  01 

61  34 

36 

40 

89  52 

85  04 

80  16 

76  00 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

A,h 

5.73 

5.31 

4.94 

4.61 

4.31 

4.04 

3.80 

3.58 

3.37 

3.19 

3.01 

2.85 

A,h 

Log. 

0.758 

0.725 

0.693 

0.663 

0.634 

0.606 

0.579 

0.553 

0.527 

0.503 

0.478 

0.454 

Log. 

15 

09 

73 

70 

48 

38 

78 

88 

63 

79 

57 

84 

Limit 

23 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

Min- 
utes 

Merid- 
ian 

75° 

74 

0 

73° 

72° 

71° 

70 

3 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

126 


Latitude  21°  Declination  Same  Name* 


Declination 

s. 

Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/        n 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     '/ 

/     // 

Min. 

4 

0  43 

0  41 

0  38 

0  37 

0  35 

0  33 

0  31 

0  30 

0  28 

0  27 

0  26 

0  24 

4 

8 

2  53 

2  44 

2  36 

2  28 

2  20 

2  13 

2  06 

2  00 

1  55 

1  49 

142 

138 

8 

12 

6  29 

6  09 

5  50 

5  32 

5  15 

5  00 

4  46 

4  31 

4  18 

4  05 

3  51 

3  40 

12 

16 

1131 

10  55 

10  22 

9  52 

9  21 

8  52 

8  26 

8  01 

7  38 

7  15 

6  53 

6  32 

16 

20 

18  00 

17  04 

16  12 

15  24 

14  36 

13  52 

13  12 

12  32 

1156 

1120 

10  44 

10  12 

20 

24 

25  55 

24  35 

23  19 

22  11 

21  02 

19  58 

19  00 

18  03 

17  11 

16  19 

15  28 

14  41 

24 

28 

35  17 

33  27 

3146 

30  11 

28  37 

27  11 

25  53 

24  34 

23  24 

22  13 

21  02 

20  00 

28 

32 

46  05 

43  41 

41  29 

39  25 

37  22 

35  30 

33  48 

32  05 

30  33 

29  01 

27  28 

26  07 

32 

36 

58  19 

55  18 

52  29 

49  54 

47  19 

44  56 

42  46 

40  37 

38  40 

36  43 

34  47 

33  03 

36 

40 

72  00 

68  16 

64  48 

61  36 

58  24 

55  28 

52  48 

50  08 

47  44 

45  20 

42  56 

40  48 

40 

44 

87  07 

82  36 

78  24 

74  32 

70  40 

67  07 

63  53 

60  40 

57  45 

54  51 

5157 

49  22 

44 

48 

98  18 

93  19 

88  42 

84  05 

79  52 

76  02 

72  11 

68  42 

65  15 

61  49 

58  45 

48 

52 

104  06 

98  41 

93  44 

89  14 

84  43 

80  40 

76  37 

72  33    68  57 

52 

56 

108  43 

103  29 

98  15 

93  33 

88  51 

84  09    79  58 

56 

60 

112  48 

107  24 

102  00 

96  36 

9148 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

" 

II 

A,h 

2.70 

2.56 

2.43 

2.31 

2.19 

2.08 

1.98 

1.88 

1.79 

1.70 

1.61 

1.53 

A,h 

Log. 

0.431 

0.408 

0.385 

0.363 

0.340 

0.318 

0.296 

0.274 

0.252 

0.230 

0.206 

0.184 

Log. 

36 

24 

61 

61 

44 

06 

67 

16 

85 

45 

83 

69 

Limit 

36 

38 

39 

40 

41 

43 

45 

46 

47 

48 

50 

52 

Min- 
utes 

Merid- 
ian 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

Alti- 
tudes 

Declinations, 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

3132 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
II 

1.46 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
II 

1.38 

/     // 

0  21 
123 
3  08 
5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 
II 

1.31 

/     // 

0  20 

120 

2  59 

5  17 

8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 

II 

1.24 

/     // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

/     // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 

/     // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

// 

1.05 

/     // 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

2123 

26  24 

3156 

38  01 

44  37 

51  44 

59  24 

II 

0.99 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

II 

0.94 

/     // 
0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 
52  48 

0.88 

/     // 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

II 

0.78 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.164 
35 

0.139 

88 

0.117 

27 

0.093 

42 

0.071 

88 

0.045 
32 

0.021 
19 

9.995 
64 

9.973 
13 

9.944 

48 

9.919 
08 

9.892 
09 

Log. 

Limit 

54 

55 

57 

59 

61 

62 

64 

66 

68 

70 

72    1    74 

Min- 
utes 

Merid- 
ian 

51° 

50° 

49° 

48° 

47° 

46° 

45°  j   44° 

43° 

42° 

41°  \   40° 

Alti- 
tudes 

Latitude  2J°  Declination  Contrary  Name. 


127 


Declixations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

1 

5 
12 
21 
34 
49 
66 

II 
5.1 

n 

22 
27 
17 
51 
38 
10 
54 

2 

1 
5 
11 
20 
32 
46 
63 

4.8 

18 
13 
44 

52 
36 
57 
54 

/      // 

1  15 
5  00 
11  15 
20  01 
31  16 
45  02 
61  17 
80  02 

II 
4.69 

1 

1 
4 
10 
19 
30 
43 
58 
76 

II 
4.5 

// 

12 

48 
48 
12 
00 
12 
48 
48 

3 

/ 

1 
4 
10 
18 
28 
41 
56 
73 

II 
4.3 

// 

09 
37 
23 
29 
52 
34 
35 
53 

3 

/ 

1 
4 
10 
17 
27 
40 
54 
71 

II 
4.1 

// 

07 
27 
OO 
48 
48 
32 
29 
10 

1 

/ 

1 

4 
9 
17 
26 
38 
52 
68 

II 
4.0 

// 

04 
17 

39 
09 
48 
36 
32 
36 

2 

1 
4 
9 
16 
25 
37 
50 
66 

II 
3.8 

// 

02 
08 
19 
33 
52 
15 
42 
13 

3 

/     // 

100 

4  00 
8  59 
15  57 
24  56 
35  54 
48  52 
63  50 

II 
3.74 

/     // 

0  58 
3  51 
8  41 
15  27 
24  08 
34  46 
47  18 
61  46 
78  12 

3.62 

/     // 

0  56 
3  45 
8  25 
14  59 
23  24 
33  42 
45  52 
59  54 
75  49 

II 
3.51 

1     It 

0  54 

3  38 

8  10 

14  30 

22  40 

32  38 

44  26 

58  02 

73  26 

90  40 

II 
3.40 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

iiOg. 

0.709 
27 

0.689 
31 

0.671 
17 

0.653 
21 

0.636 
49 

0.620 
14 

0.604 
23 

0.588 
83 

0.572 

87 

0.558 
71 

0.545 
31 

0.531 

48 

Log. 

Limit 

25 

26 

27 

28 

29 

29 

29 

30 

31 

32 

33 

33 

Min- 
utes 

Merid- 
ian 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/      /' 

/      II 

/      /' 

/     // 

/     // 

/     // 

/      // 

/     // 

/      // 

// 

/      // 

Min. 

4 

0  52 

0  51 

0  50 

0  48 

0  46 

0  46 

0  44 

0  43 

0  42 

0  41 

0  39 

0  38 

4 

8 

3  31 

3  24 

3  18 

3  13 

3  07 

3  02 

2  58 

2  53 

2  48 

2  44 

2  40 

2  36 

8 

12 

7  54 

7  39 

7  26 

7  13 

7  02 

6  50 

6  39 

6  29 

6  18 

6  09 

5  59 

5  50 

12 

16 

14  02 

13  37 

13  14 

12  51 

12  30 

12  10 

1149 

1131 

11  14 

10  55 

10  37 

10  22 

16 

20 

21  56 

21  16 

20  40 

20  04 

19  32 

19  00 

18  28 

18  00 

17  32 

17  04 

16  36 

16  12 

20 

24 

31  35 

30  38 

29  46 

28  54 

28  07 

27  22 

26  35 

25  55 

25  15 

24  35 

23  54 

23  19 

24 

28 

43  00 

41  41 

40  30 

39  20 

38  18 

37  14 

36  12 

35  17 

34  22 

33  27 

32  33 

31  46 

28 

32 

56  09 

54  26 

52  54 

51  22 

50  01 

48  38 

47  17 

46  05 

44  53 

43  41 

42  30 

4129 

32 

36 

7104 

68  55 

66  58 

65  01 

63  17 

6134 

59  50 

58  19 

56  49 

55  18 

53  47 

52  29 

36 

40 

87  44 

85  04 

82  40 

80  16 

78  08 

76  00 

73  52 

72  00 

70  08 

68  16 

66  24 

64  48 

40 

44 

87  07 

84  52 

82  36 

80  20 

78  24 

44 

48 

95  37 

93  19 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

Ajh 

3.29 

3.19 

3.10 

3.01 

2.93 

2.85 

2.77 

2.70 

2.63 

2.56 

2.49 

2.43 

Aih 

Log. 

0.517 

0.503 

0.491 

0.478 

0.466 

0.454 

0.442 

0.431 

0.419 

0.408 

0.396 

0.385 

Log. 

20 

79 

36 

57 

87 

84 

48 

36 

96 

24 

20 

61 

Limit 

34 

35 

36 

37 

37 

38 

39 

39 

40 

41 

42 

43 

Min- 
utes 

Merid- 
ian 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

128 


Latitude  21°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

1      II 

/     // 

/     ti 

/     // 

/      // 

/     // 

/     // 

/      II 

/     II 

/     // 

/     // 

/      // 

Min. 

4 

0  38 

0  37 

0  36 

0  35 

0  35 

0  33 

0  33 

0  31 

0  31 

0  30 

0  30 

0  29 

4 

8 

2  32 

2  28 

2  24 

2  21 

2  17 

2  14 

2  11 

2  07 

2  04 

2  01 

159 

156 

8 

12 

5  41 

5  32 

5  24 

5  17 

5  08 

5  01 

4  54 

4  47 

4  41 

4  34 

4  28 

4  20 

12 

16 

10  07 

9  52 

9  36 

9  23 

9  08 

8  55 

8  42 

8  29 

8  19 

8  06 

7  56 

7  44 

16 

20 

15  48 

15  24 

15  00 

14  40 

14  16 

13  56 

13  36 

13  16 

13  00 

12  40 

12  24 

12  04 

20 

24 

22  45 

22  11 

2136 

2107 

20  33 

20  04 

19  35 

19  06 

18  43 

18  14 

17  52 

i;23 

24 

28 

30  58 

30  11 

29  24 

28  45 

27  57 

27  19 

26  39 

26  01 

25  29 

24  50 

24  18 

23  39 

28 

32 

40  27 

39  25 

38  24 

37  33 

36  31 

35  40 

34  49 

33  58 

33  17 

32  26 

3144 

30  53 

32 

36 

51  12 

49  54 

48  36 

47  31 

46  14 

45  09 

44  04 

42  59 

42  07 

4102 

40  11 

39  06 

36 

40 

63  12 

6136 

60  00 

58  40 

57  04 

55  44 

54  24 

53  04 

52  00 

50  40 

49  36 

48  16 

40 

44 

76  39 

74  32 

72  36 

70  59 

69  03 

67  26 

65  49 

64  12 

62  55 

61  18 

60  01 

58  24 

44 

48 

9100 

88  42 

86  24 

84  29 

82  10 

80  15 

78  20 

76  25 

74  53 

72  58 

7125 

69  30 

48 

52 

106  48 

104  06 

101  24 

99  09 

96  26 

94  11 

9156 

89  41 

87  53 

85  38 

83  49 

81  34 

52 

56 

11151 

109  14 

106  37 

104  01 

101  55 

99  18 

97  13 

94  36 

56 

60 

114  00 

11136 

108  36 

60 

II 

" 

II 

II 

II 

II 

" 

II 

II 

// 

II 

II 

A,h 

2.37 

2.31 

2.25 

2.20 

2.14 

2.09 

2.04 

1.99 

1.95 

1.90 

1.86 

1.81 

A,h 

Log. 

0.374 

0.363 

0.352 

0.342 

0.330 

0.320 

0.309 

0.298 

0.290 

0.278 

0.269 

0.257 

Log. 

75 

61 

18 

42 

41 

15 

63 

85 

03 

75 

51 

68 

Limit 

44 

45 

46 

47 

48  . 

49 

49 

50 

51 

52 

53 

53 

Min- 
utes 

Merid- 
ian 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      /' 

/     // 

/      // 

1     II 

/      // 

/      // 

/     // 

/     // 

/      // 

/     // 

/     // 

/      // 

Min. 

4 

0  28 

0  27 

0  27 

0  27 

0  26 

0  25 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

4 

8 

154 

151 

148 

145 

142 

140 

138 

136 

133 

131 

128 

1  26 

8 

12 

4  16 

4  09 

4  03 

3  56 

3  50 

3  45 

3  40 

3  35 

3  29 

3  25 

3  19 

3  14 

12 

16 

7  33 

7  23 

7  13 

7  00 

6  50 

6  39 

6  32 

6  21 

6  11 

6  03 

5  53 

5  46 

16 

20 

1148 

1132 

11  16 

10  56 

10  40 

10  24 

10  12 

9  56 

9  40 

9  28 

9  12 

9  00 

20 

24 

16  59 

16  36 

16  14 

15  45 

15  22 

14  59 

14  41 

14  18 

13  55 

13  38 

13  15 

12  58 

24 

28 

23  08 

22  37 

22  05 

2125 

20  54 

20  23 

20  00 

19  29 

18  57 

18  34 

18  02 

17  38 

28 

32 

30  13 

29  32 

28  50 

27  59 

27  18 

26  37 

26  07 

25  26 

24  45 

24  14 

23  33 

23  02 

32 

36 

38  14 

37  22 

36  31 

35  26 

34  34 

33  42 

33  03 

32  11 

31  19 

30  40 

29  49 

29  10 

36 

40 

47  12 

46  08 

45  04 

43  44 

42  40 

41  36 

40  48 

39  44 

38  40 

37  52 

36  48 

36  00 

40 

44 

57  07 

55  49 

54  32 

52  55 

5138 

50  20 

49  22 

48  04 

46  47 

45  49 

44  32 

43  34 

44 

48 

67  56 

66  24 

64  53 

62  58 

61  26 

59  54 

58  45 

57  13 

55  41 

54  32 

52  59 

5150 

48 

52 

79  46 

77  58 

76  09 

73  54 

72  06 

70  18 

68  57 

67  09 

65  21 

64  00 

62  11 

60  50 

52 

56 

92  31 

90  25 

88  20 

85  43 

83  38 

8132 

79  58 

77  52 

75  37 

74  13 

72  08 

70  34 

56 

60 

106  12 

103  48 

10124 

98  24 

96  00 

93  36 

91  48 

89  24 

87  00 

85  12 

82  48 

8100 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.77 

1.73 

1.69 

1.64 

1.60 

1.56 

1.53 

1.49 

1.45 

1.42 

1.38 

1.35 

A,h 

Log. 

0.247 

0.238 

0.227 

0.214 

0.204 

0.193 

0.184 

0.173 

0.161 

0.152 

0.139 

0.130 

Log. 

97 

05 

89 

84 

12 

12 

69 

19 

37 

29 

88 

33 

Limit 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

63 

64 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

Latitude  2t°  Declination  Contrary  Name. 


129 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/      II 

1     II 

/     // 

/     II 

/      // 

/     // 

/      // 

1     II 

/     // 

/      // 

/     // 

/      // 

Min. 

4 

0  21 

0  20 

0  20 

0  19 

0  19 

0  19 

0  18 

0  17 

0  17 

0  16 

0  15 

0  15 

4 

8 

123 

1  22 

1  20 

1  17 

1  15 

1  13 

1  11 

109 

107 

1  05 

103 

101 

8 

12 

3  08 

3  05 

3  00 

2  54 

2  50 

2  45 

2  39 

2  36 

2  31 

2  27 

2  23 

2  19 

12 

16 

5  36 

5  27 

5  20 

5  10 

5  02 

4  55 

4  45 

4  36 

4  29 

4  21 

4  13 

4  05 

16 

20 

8  44 

8  32 

8  20 

8  04 

7  52 

7  40 

7  24 

7  12 

7  00 

6  48 

6  36 

6  24 

20 

24 

12  35 

12  17 

12  00 

1137 

1120 

1103 

10  40 

10  22 

10  05 

9  48 

9  30 

9  13 

24 

28 

17  07 

16  44 

16  20 

15  49 

15  25 

15  01 

14  30 

14  07 

13  43 

13  20 

12  57 

12  33 

28 

32 

22  21 

2151 

21  20 

20  39 

20  08 

19  37 

18  56 

18  26 

17  55 

17  24 

16  54 

16  23 

32 

36 

28  18 

27  39 

27  00 

26  08 

25  30 

24  51 

23  59 

23  20 

22  41 

22  02 

21  23 

20  44 

36 

40 

34  56 

34  08 

33  20 

32  16 

31  28 

30  40 

29  36 

28  48 

28  00 

27  12 

26  24 

25  36 

40 

44 

42  16 

41  18 

40  20 

39  02 

38  05 

37  07 

35  49 

34  51 

33  53 

32  55 

3156 

30  58 

44 

48 

50  18 

49  09 

48  00 

46  28 

45  18 

44  09 

42  37 

41  28 

40  19 

39  10 

38  01 

36  52 

48 

52 

59  02 

57  41 

56  20 

54  32 

53  10 

51  49 

50  01 

48  40 

47  19 

45  58 

44  37 

43  16 

52 

56 

68  28 

66  54 

65  20 

63  14 

6141 

60  07 

58  01 

56  27 

54  53 

53  19 

51  44 

50  10 

56 

60 

78  36 

76  48 

75  00 

72  36 

70  48 

69  00 

66  36 

64  48 

63  00 

61  12 

59  24 

57  36 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.31 

1.28 

1.25 

1.21 

1.18 

1.15 

1.11 

1.08 

1.05 

1.02 

0.99 

0.96 

A,h 

Log. 

0.117 

0.107 

0.096 

0.082 

0.071 

0.060 

0.045 

0.033 

0.021 

0.008 

9.995 

9.982 

Log. 

27 

21 

91 

79 

88 

70 

32 

42 

19 

60 

64 

27 

Limit 

65 

67 

69 

70 

71 

72 

74 

76 

77 

78 

79 

80 

Min- 
utes 

Merid- 
ian 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

^5  48 
II 

0.93 

/      II 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

11  46 

15  22 

19  26 

24  00 

29  02 

34  34 

40  34 

47  02 

54  00 
II 

0.90 

/     // 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  29 

52  12 
II 

0.87 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

/      // 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

31  06 

36  30 

42  20 

48  36 
II 

0.81 

1     II 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

II 

// 

II 

II 

// 

II 

// 

1 
II 

// 

/ 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.968 
48 

9.954 
24 

9.939 
52 

9.924 

28 

9.908 
49 

9.892 
09 

Log. 

Limit 

81 

82 

83 

84 

85 

86 

Min- 
utes 

Merid- 
ian 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

Alti- 
tudes 

130 


Latitude  22°  Declination  Same  Name« 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

1 

5 
11 
20 
32 
46 
63 
82 

4.8( 

18 
11 
10 
i4 
24 
iO 
30 
56 

3 

1 

1 

5 
12 
21 
33 
48 
66 

II 
5.0i 

// 

21 
25 
12 
40 
52 
i6 
23 

I 

/ 

1 

5 
12 
22 
35 
51 
69 

5.3. 

// 

25 
10 
46 
42 
28 
35 
31 

I 

1 

1 

5 
13 
23 
37 
53 
72 

5.5? 

// 

29 
57 
24 
48 
12 
34 
53 

/ 

1 

6 
14 
25 
39 
56 
76 

5.8i 

34 
16 

D7 
35 
12 
27 
50 

3 

1 

1 
6 

14 
26 
41 
59 
81 

6.2( 

// 

39 
37 
53 
27 
20 
31 
31 

) 

1 

7 
15 
28 
43 
63 

6.5' 

45 
01 
46 

02 
48 
04 

1 

1 

7 

16 
29 
46 

6.9i 

// 

51 
26 
46 
46 
32 

3 

/      // 

159 

7  57 

17  53 

31  47 

49  40 

II 
7.45 

/      // 

2  07 

8  31 

19  11 

34  05 

53  16 

7.99 

/      // 

2  18 

9  11 

20  41 

36  47 

57  28 

II 
8.62 

/     // 

2  30 
10  00 
22  29 
39  59 

II 
9.37 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.686 
64 

0.705 
86 

0.725 
91 

0.746 
63 

0.769 
38 

0.792 
39 

0.817 
57 

0.843 
86 

0.872 
16 

0.902 
55 

0.935 
51 

0.971 
74 

Log. 

Limit 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

Min- 
utes 

Merid- 
ian 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18 

=      19 

"      20° 

21° 

22 

°  1   23° 

Hour 
Angles 

Min. 

1       II 

1     II 

1      II 

/     // 

1      II 

/      // 

1 

//    1 

II    1      II 

/        n 

1 

//    1     II 

Min. 

4 

2  44 

3  02 

3  23 

3  50 

4  28 

5  19 

4 

8 

10  56 

12  06 

13  32 

15  24 

17  52 

21  18 

8 

12 

24  36 

27  13 

30  27 

34  38 

40  11 

12 

16 

43  44 

48  23 

54  0» 

6134 

16 

20 

68  20 

75  36 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

n 

// 

// 

Ajh 

10.25 

11.34 

12.69 

14.43 

16.74 

19.98 

A,h 

Log. 

1.010 

72 

1.054 
61 

1.103 
46 

1.159 

27 

1.223 
76 

1.300 
60 

Log. 

Limit 

14 

13 

12 

11 

10 

9 

8 

6 

3 

1 

0 

2 

Min- 
utes 

Merid- 
ian 

1 

30 

3 

81 

3 

82 

3 

83 

3 

84' 

J 

85' 

> 

86' 

87' 

'      88' 

8 

9' 

1 

9 

0= 

89° 

Alti- 
tudes 

Latitude  22°  Declination  Same  Name. 


131 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

/      // 

/      /' 

/      /' 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

4  58 

4  oe;  3  29 

3  01 

2  39 

2  22 

2  08 

156 

146 

4 

8 

19  51 

16  24    13  57 

12  05 

10  38 

9  29 

8  32 

7  45 

7  04 

8 

12 

36  551  31  22 

27  11 

23  58 

21  20 

19  12 

17  26 

15  54 

12 

16 

55  46 

48  21 

42  34 

37  56 

34  08 

30  58 

28  18 

16 

20 

53  20 

48  24 

44  12 

20 

24 

63  39 

24 

28 

28 

32 

...    1    . . 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

ir 

n 

i> 

// 

n 

II 

II 

II 

II 

II 

II 

A,h 

18.61 

15.38 

13.07 

11.33 

9.98 

8.89 

8.00 

7.26 

6.63 

Ajh 

Log. 

1.269 

1.186 

1.116 

1.054 

0.999 

0.948 

0.903 

0.860 

0.821 

75 

96 

28 

23 

13 

90 

09 

94 

51 

Log. 

Limit 

4 

5 

6 

7 

9 

11 

12 

14 

15 

17 

19 

20 

Min- 
utes 

Merid- 
ian 

88°      87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46°      47° 

Hour 
Angles 

f          ff 

f          ff 

Min. 

Min. 

4 

137 

130 

1  23 

1  18 

1  12 

107 

103 

0  59 

0  56 

0  52 

0  50 

0  47 

4 

8 

6  30 

5  59 

5  33 

5  10 

4  49 

4  30 

4  13 

3  59 

3  44 

3  31 

3  19 

3  08 

8 

12 

14  37 

13  29 

12  29 

11  37 

10  49 

10  08 

9  31 

8  56 

8  24 

7  54 

7  27 

7  04 

12 

16 

25  59 

23  59 

22  11 

20  39 

19  15 

18  00 

16  53 

15  52 

14  56 

14  02 

13  17 

12  32 

16 

20 

40  36 

37  28 

34  40 

32  16 

30  04 

28  08 

26  24 

24  48 

23  20 

2156 

20  44 

19  36 

20 

24 

58  28 

53  58 

49  55 

46  28 

43  18 

40  31 

38  01 

35  43 

33  36 

31  35    29  52 

28  13 

24 

28 

79  35 

73  26 

67  57 

63  14 

58  56 

55  09 

5145 

48  37 

45  44 

43  00|  40  38 

38  25 

28 

32 

82  36 

76  58 

72  01 

67  35 

63  29 

59  44 

56  09 

53  04 

50  11 

32 

36 

75  36 

71  04 

67  11 

63  30 

36 

40 

87  44 

82  56 

78  24 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

. .  . 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

II 

// 

A.h 

6.09 

5.62 

5.20 

4.84 

4.51 

4.22 

3.96 

3.72 

3.50 

3.29 

3.11 

2.94 

A,h 

Log. 

0.784 

0.749 

0.716 

0.684 

0.654 

0.625 

0.597 

0.570 

0.544 

0.517 

0.492 

0.468 

Log. 

62 

74 

00 

85 

18 

31 

70 

54 

07 

20 

76 

35 

Limit 

22 

24 

25 

26 

27 

28 

29 

30 

31 

33 

34 

35 

Min- 
utes 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

ceo       Alti- 
0^     1  tudes 

132 


Latitude  22°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/      /' 

/      // 

/      '/ 

/      // 

/     /' 

1     II 

/      // 

/     // 

/     " 

Min. 

4 

0  44 

0  42 

0  39 

0  38 

0  36 

0  34 

0  32 

0  30 

0  29 

0  27 

0  27 

0  25 

4 

8 

2  58 

2  48 

2  40 

2  31 

2  24 

2  16 

2  09 

2  02 

156 

1  51 

145 

140 

8 

12 

6  41 

6  18 

5  59 

5  40 

5  23 

5  06 

4  51 

4  37 

4  22 

4  09 

3  56 

3  45 

12 

16 

11  51 

11  14 

10  37 

10  04 

9  33 

9  06 

8  37 

8  11 

7  46 

7  23 

7  00 

6  39 

16 

20 

18  32 

17  32 

16  36 

15  44 

14  56 

14  12 

13  28 

12  48 

12  08 

11  32 

10  56 

10  24 

20 

24 

26  41 

25  15 

23  54 

22  40 

21  30 

20  27 

19  24 

18  26 

17  29 

16  36 

15  45 

14  59 

24 

28 

36  20 

34  22 

32  33 

30  50 

29  16 

27  50 

26  24 

25  06 

23  47 

22  37 

21  25 

20  23 

28 

32 

47  27 

44  53 

42  30 

40  16 

38  14 

36  21 

34  28 

32  46 

3103 

29  32 

27  59 

26  37 

32 

36 

60  03 

56  49 

53  47 

50  59 

48  23 

46  01 

43  38 

41  28 

39  19 

37  22 

35  26 

33  42 

36 

40 

74  08 

70  08 

66  24 

62  56 

59  44 

56  48 

53  52 

51  12 

48  32 

46  08 

43  44 

4136 

40 

44 

84  52 

80  20 

76  09 

72  16 

68  44 

65  11 

6157 

58  44 

55  49 

52  55 

50  20 

44 

48 

95  37 

90  37 

86  01 

8146 

77  34 

73  44 

69  53 

66  24 

62  58 

59  54 

48 

52 

106  21 

100  57 

95  59 

9102 

86  32 

82  01 

77  58 

73  54 

70  18 

52 

56 

105  35 

100  21 

95  08 

90  25 

85  43 

8132 

56 

60 

109  12 

103  48 

98  24 

93  36 

60 

It 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.78 

2.63 

2.49 

2.36 

2.24 

2.13 

2.02 

1.92 

1.82 

1.73 

1.64 

1.56 

A,h 

Log. 

0.444 

0.419 

0.396 

0.372 

0.350 

0.328 

0.305 

0.283 

0.260 

0.238 

0.214 

0.193 

Log. 

04 

96 

20 

91 

25 

38 

35 

30 

07 

05 

84 

12 

Limit 

36 

37 

38 

39 

41 

43 

44 

45 

45 

47 

49 

51 

Min- 
utes 

Merid- 
ian 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  23 

1  35 
3  34 
6  18 
9  52 

14  12 

19  21 

25  16 

3158 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

/     // 

0  21 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 
II 

1.33 

/     // 

0  20 

121 

3  02 

5  22 

.  8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
II 

1.26 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 

15  33 

20  18 

25  43 

3144 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

/     // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
II 

1.07 

/     // 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 

/     // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

0.95 

/     // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 

/      // 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

/     // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.170 
26 

0.146 
13 

0.123 

85 

0.100 
37 

0.075 
55 

0.053 
08 

0.029 
38 

0.004 
32 

9.977 
72 

9.949 
39 

9.924 
28 

9.897 
63 

Log. 

Limit 

53 

55 

57 

59 

61 

62 

63 

65 

67 

69 

71 

73 

Min- 
utes 

Merid- 
ian 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

Alti- 
tudes 

Latitude  22°  Decimation  Contrary  Name. 


133 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

/ 

1 
5 
11 
20 
32 
46 
63 
82 

II 
4.8 

// 

18 
11 
40 
44 
24 
40 
30 
56 

3 

/ 

1 
4 
11 
19 
31 
44 
60 
79 

II 
4.6 

// 

15 
58 
11 
53 
04 
45 
53 
31 

5 

1 
4 
10 
19 
29 
42 
58 
76 

II 
4.4 

11 

47 
44 
04 
48 
53 
25 
18 

1 

/ 

1 

4 
10 

18 
28 
41 
56 
73 

II 
4.3( 

// 

09 
35 
19 
21 
40 
17 
11 
23 

) 

/ 

1 
4 
9 
17 
27 
39 
54 
70 

II 
4.1 

// 

07 
25 
56 
40 
36 
45 
05 
39 

4 

/ 

1 
4 
9 
17 
26 
38 
52 
68 

II 
3.9 

// 

03 
15 
35 
01 
36 
18 
09 
06 

3 

1 
4 
9 
16 
25 
37 
50 
65 

II 
3.8 

// 

02 

07 
16 

28 
44 
04 
26 
52 

3 

/      // 

0  59 
4  00 
8  57 
15  55 
24  52 
35  48 
48  45 
63  40 

II 
3.73 

0  58 
3  51 
8  39 
15  25 
24  04 
34  40 
47  10 
6136 
77  59 

II 
3.61 

/     // 

0  55 
3  44 
8  23 
14  53 
23  16 
33  30 
45  37 
59  34 
75  23 

II 
3.49 

/     // 

0  54 
3  36 
8  07 
14  25 
22  32 
32  27 
44  10 
57  41 
73  01 
90  08 

II 
3.38 

/     // 

0  52 
3  30 
7  53 
13  59 
21  52 
3129 
42  52 
55  59 
70  51 
87  28 

II 
3.28 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.686 
64 

0.668 
39 

0.650 
31 

0.633 
47 

0.617 
00 

0.600 

97 

0.586 
59 

0.571 
71 

0.557 
51 

0.542 
83 

0.528 
92 

0.515 

87 

Log. 

Limit 

26 

27 

28 

29 

30 

30 

30 

31 

32 

32 

33 

34 

Min- 
utes 

Merid-     roo 
ian        *>*» 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/      // 

/      // 

/     II 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  51 

0  49 

0  48 

0  46 

0  46 

0  44 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

4 

8 

3  23 

3  18 

3  13 

3  06 

3  02 

2  58 

2  52 

2  47 

2  44 

2  40 

2  36 

2  32 

8 

12 

7  38 

7  25 

7  13 

7  01 

6  49 

6  39 

6  27 

6  17 

6  09 

5  59 

5  50 

5  41 

12 

16 

13  34 

13  11 

12  51 

12  27 

12  07 

1149 

1129 

11  11 

10  55 

10  37 

10  22 

10  07 

16 

20 

21  12 

20  36 

20  04 

19  28 

18  56 

18  28 

17  56 

17  28 

17  04 

16  36 

16  12 

15  48 

20 

24 

30  32 

29  40 

28  54 

28  02 

27  16 

26  35 

25  50 

25  10 

24  35 

23  54 

23  19 

22  45 

24 

28 

4133 

40  23 

39  20 

38  10 

37  06 

36  12 

35  09 

34  14 

33  27 

32  33 

3146 

30  58 

28 

32 

54  16 

52  44 

5122 

49  50 

48  28 

47  17 

45  54 

44  42 

43  41 

42  30 

4129 

40  27 

32 

36 

68  42 

66  45 

65  01 

63  04 

6121 

59  50 

58  07 

56  36 

55  18 

53  47 

52  29 

51  12 

36 

40 

84  48 

82  24 

80  16 

77  52 

75  44 

73  52 

7144 

69  52 

68  16 

66  24 

64  48 

63  12 

40 

44 

86  48 

84  33 

82  36 

80  20 

78  24 

76  39 

44 

48 

95  37 

93  19 

9100 

48 

52 

106  48 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.18 

3.09 

3.01 

2.92 

2.84 

2.77 

2.69 

2.62 

2.56 

2.49 

2.43 

2.37 

A,h 

Log. 

0.502 

0.489 

0.478 

0.465 

0.453 

0.442 

0.429 

0.418 

0.408 

0.396 

0.385 

0.374 

Log. 

43 

96 

57 

38 

32 

48 

75 

30 

24 

20 

61 

75 

Limit 

35 

35 

36 

37 

38 

39 

40 

40 

41 

42 

43 

44 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

Alti- 
tudes 

134 


Latitude  22°  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  37 

2  28 

5  32 

9  52 

15  24 

22  11 

30  11 

39  25 

49  54 

6136 

74  32 

88  42 

104  06 

2.31 

/     // 

0  36 

2  25 

5  26 

9  38 

15  04 

2142 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

10151 

2.26 

0  35 

2  21 

5  17 

9  23 

14  40 

2107 

28  45 

37  33 

47  31 

58  40 

70  59 

84  29 

99  09 

It 
2.20 

/     // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

2.15 

0  34 

2  14 

5  02 

8  58 

14  00 

20  10 

27  26 

35  50 

45  22 

56  00 

67  46 

80  38 

94  38 

II 
2.10 

0  33 

2  11 

4  55 

8  45 

13  40 

19  41 

26  47 

34  59 

44  17 

54  40 

66  09 

78  43 

92  23 

II 
2.05 

/     // 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

II 
2.00 

1     II 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

101  55 

1.95 

/     // 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

61  37 

73  21 

86  05 

99  49 

II 
1.91 

/     // 

0  30 

1  59 
4  28 
7  56 

12  24 
17  52 
24  18 
31  44 
40  11 
49  36 
60  01 
71  25 
83  49 
97  13 

II 
1.86 

0  29 

156 

4  22 

7  46 

12  08 

17  29 

23  47 

3103 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 
II 

1.82 

/     // 

0  28 

154 

4  17 

7  35 

11  52 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 

II 

1.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.363 
61 

0.354 
11 

0.342 
42 

0.332 
44 

0.322 
22 

0.311 
75 

0.301 
03 

0.290 
03 

0.281 
03 

0.269 
51 

0.260 
07 

0.250 
42 

Log. 

Limit 

45 

46 

47 

48 

48 

49 

50 

50 

51 

52 

53 

54 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  28 

152 

411 

7  25 

11  36 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

II 
1.74 

/     // 

0  27 

1  49 
4  05 
7  15 

11  20 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
II 

1.70 

0  27 

146 

3  59 

7  05 

11  04 

15  57 

21  41 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

86  46 

99  36 
II 

1.66 

/     // 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
II 

1.62 

/     // 

0  25 
141 

3  48 

6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/     // 

0  25 

1  39 
3  42 
6  34 

10  16 
14  47 
20  07 
26  17 
33  16 
41  04 
49  41 
59  08 
69  24 
80  29 
92  24 

1.54 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 
II 

1.50 

/     // 

0  23 

1  35 
3  32 
6  16 

9  48 

14  06 

19  13 

25  06 

3145 

39  12 

47  26 

56  27 

66  15 

76  50 

88  12 
II 

1.47 

/     // 

0  22 

1  32 
3  24 
6  06 
9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

/     // 

0  22 

1  30 
3  22 
5  58 
9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

1     II 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

8136 
II 

1.36 

0  21 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

51  04 

59  56 

69  31 

79  48 
II 

1.33 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.240 
55 

0.230 
45 

0.220 
11 

0.209 
52 

0.198 
66 

0.187 
52 

0.176 
09 

0.167 
32 

0.155 
34 

0.146 
13 

0.133 
54 

0.123 

85 

Log. 

Limit 

55 

56 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

Min- 
utes 

Merid- 
ian 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

Alti- 
tudes 

Latitude  22°  Declination  Contrary  Name. 


loo 


Declination's. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55°      56°  1    57° 

58° 

59° 

Hour 
Angles 

Min. 

/       " 

/      // 

/     // 

/      // 

/      // 

/      /' 

/      // 

/       II  y       II  \,       II 

/     // 

/      // 

Min. 

4 

0  21 

0  20 

0  19 

0  19 

0  19 

0  18 

0  18 

0  17|     0  17     0  16 

0  15 

0  15 

4 

8 

123 

121 

1  19 

1  17 

1  15 

1  12 

1  10      1  08      1  07      1  04 

1  02      1  01 

8 

12 

3  07 

3  02 

2  57 

2  53 

2  48 

2  42 

2  38     2  34     2  30     2  25 

2  22 

2  17 

12 

16 

5  33 

5  22 

5  15 

5  07     5  00 

4  50 

4  42j     4  34,     4  26,     4  19 

4  10 

4  03 

16 

20 

8  40 

8  24 

8  12 

8  00     7  48 

7  32 

7  20     7  08|     6  561     6  44 

6  32 

6  20 

20 

24 

12  29 

12  06    1148 

11  31    11  14 

10  51 

10  34    10  16     9  59     9  42 

9  24 

9  07 

24 

28 

16  59 

16  28    16  05 

15  411  15  17 

14  46 

14  22    13  59    13  35 

13  12 

12  49 

12  25 

28 

32 

22  11 

21  30   21  00 

2029;  19  58 

19  17 

18  46    18  16    17  45 

17  14 

16  44 

16  13 

32 

36 

28  05 

27  13    26  34 

25  55 

25  17 

24  25 

23  46    23  07'  22  28    21  49 

21  10 

20  31 

36 

40 

34  40 

33  36    32  48 

32  00 

31  12 

30  08 

29  20;  28  321  27  44!  26  56 

26  08 

25  20 

40 

44 

4157 

40  39    39  41 

38  43 

37  46 

36  28 

35  30!  34  32'  33  33!  32  35 

3127 

30  39 

44 

48 

49  55 

48  23!  47  14 

46  05    44  55 

43  23 

42  14   41  05   39  56 

38  47 

37  38 

36  29 

48 

52 

58  35 

56  47    55  26 

54  05'  52  43 

50  55 

49  34 

48  13i  46  52 

45  31 

44  10 

42  49 

52 

56 

67  57 

65  51    64  17 

62  43    61  10 

59  04 

57  30 

55  56   54  21 

52  47 

51  13 

49  39 

56 

60 

78  00 

75  361  73  48 

72  00    70  12 

67  48 

66  00 

64  12    62  24 

60  36 

58  48 

57  00 

60 

II 

//          // 

//          // 

II 

// 

//          // 

II 

// 

II 

Ajh 

1.30 

1.26  1  1.23 

1.20      1.17 

1.13 

1.10 

1.07      1.04 

1.01 

0.98 

0.95 

A,h 

Log. 

0.113 

0.100   0.089 

0.079   0.068 

0.053 

0.041 

0.029    0.017 

0.004 

9.991 

9.977 

Log. 

94 

37 

91 

18 

19 

08 

39 

38        03 

32 

23 

72 

Limit 

68 

69 

71 

72 

73 

74 

76 

77 

78 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60°  i    61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 
0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 

15  42 

19  52 

24  32 

29  41 

35  20 

4128 

48  05 

55  12 
II 

0.92 

/      // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 

/      // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

25  56 

27  45 

33  01 

38  45 

44  57 

5136 
II 

0.86 

/      // 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

/      // 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
2120 
25  49 
30  43 
36  03 
41  49 
48  00 

0.80 

/ 

// 

/      // 

/ 

// 

/      // 

/      // 

/ 

// 

// 

/      // 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.963!  9.949 

79        39 

9.934 
50 

9.919 
08 

9.903 
09 

Log. 

Limit 

82 

83 

84 

85 

86 

Min- 
utes 

Merid- 
ian 

8° 

7°        6° 

50        40 

3° 

2°         1°    1    0° 

1° 

2° 

3° 

Alti- 
tudea 

136 


Latitude  23°  Declination  Same  Name. 


Declinations. 


Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

IP 

Hour 
Angles 

Min. 

/       // 

/     // 

/     // 

/     // 

/     // 

1     II 

/     // 

/     // 

/     /' 

/     // 

1      II 

/         // 

Min. 

4 

1  14 

1  17 

121 

124 

1  29 

133 

1  39 

144 

1  50 

158 

2  06 

2  16 

4 

8 

4  56 

5  08 

5  23 

5  38 

5  55 

6  13 

6  33 

6  57 

7  22 

7  52 

8  26 

9  06 

8 

12 

1106 

11  34 

12  06 

12  41 

13  18 

13  59 

14  45 

15  37 

16  37 

17  43 

18  58 

20  28 

12 

16 

19  46 

20  34 

21  30 

22  31 

23  38 

24  53 

26  15 

27  47 

29  31 

3129 

33  45 

36  24 

16 

20 

30  52 

32  08 

33  36 

35  12 

36  56 

38  52 

41  00 

43  24 

46  08 

49  12 

52  44 

56  52 

20 

24 

44  27 

46  17 

48  23 

50  41 

53  11 

55  58 

59  03 

62  30 

66  26 

24 

28 

60  30 

62  59 

65  51 

69  00 

72  23 

76  11 

80  21 

28 

32 

79  01 

82  15 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

4.63 

4.82 

5.04 

5.28 

5.54 

5.83 

6.15 

6.51 

6.92 

7.38 

7.91 

8.53 

A,h 

0.665 

0.683 

0.702 

0.722 

0.743 

0.765 

0.788 

0.813 

0.840 

0.868 

0.898 

0.930 

Log. 

58 

05 

43 

63 

51 

67 

88 

58 

11 

06 

18 

95 

Limit 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

Min- 
utes 

Merid- 
ian 

QT 

) 

68' 

> 

69° 

70 

3 

71° 

72< 

3 

73° 

74 

3 

75 

3 

76 

3 

77 

3 

78 

3 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20^ 

>      21< 

'      22< 

'      23< 

3      Hour 
Angles 

1     II 

/     /' 

/      // 

/      // 

/      // 

/      // 

1 

//    / 

//    / 

//    / 

//     

Min. 

Min. 

4 

2  28 

2  42 

2  59 

3  21      3  48 

4  25 

5  15 

4 

8 

9  54 

10  49 

11  58    13  23i  15  13 

17  39 

21  02 

8 

12 

22  15 

24  20 

26  54 

30  06    34  14 

39  42 

12 

16 

39  33 

43  16 

_. . . 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

// 

// 

II 

II 

II 

II 

// 

II 

II 

II 

A,h 

9.27 

10.14 

11.21 

12.54 

14.26 

16.54 

19.72 

A,h 

Log. 

0.967 

1.006 

1.049 

1.098 

1.154 

1.218 

1.294 

Log. 

08 

04 

61 

30 

12 

54 

91 

Limit 

15 

14 

13 

12 

11 

10 

9 

8 

5 

3 

1 

0 

Min- 
utes 

Merid- 
ian 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87 

=      88 

=      89 

=      90 

3      Alti- 
tudes 

Latitude  23°  Declination  Same  Name* 

Declinations. 


137 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

// 

If 

1 
II 

// 

1 

// 

r 

4 
19 

II 
18.3 

n 

53 
32 

I 

4 
16 
36 

II 
15.1i 

02 
07 
17 

J 

/     // 

3  26 
13  42 
30  49 

II 
12.84 

2  58 
1152 
26  42 
47  30 

11.13 

/      // 

2  37 
10  27 
23  31 

41  49 

II 
9.80 

2  20 

9  19 

20  57 

37  15 

58  12 

8.73 

/     // 

2  06 

8  23 

18  51 

33  30 

52  20 

II 
7.85 

154 

7  36 

17  05 

30  23 

47  28 

7.12 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.262 
69 

1.179 
55 

1.108 
57 

1.046 
50 

0.991 
23 

0.941 
01 

0.894 
87 

0.852 

48 

Log. 

Limit 

2 

4 

5 

6 

7 

9 

11 

13 

14 

15 

17 

19 

Min- 
utes 

Merid-.     qqo 
ian        °^ 

88° 

87°      86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/     // 

/     // 

/     II 

/      // 

/      // 

/      // 

/     II 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

144 

136 

128 

122 

1  16 

110 

106 

102 

0  58 

0  55 

0  51 

0  48 

4 

8 

6  56 

6  22 

5  52 

5  26 

5  04 

4  43 

4  24 

4  07 

3  52 

3  38 

3  26 

3  14 

8 

12 

15  36 

14  20 

13  12 

12  14 

1123 

10  36 

9  54 

9  16 

8  42 

8  11 

7  43 

7  16 

12 

16 

27  44 

25  27 

23  28 

2145 

20  13 

18  50 

17  38 

16  29 

15  30 

14  33 

13  42 

12  55 

16 

20 

43  20 

39  48 

36  40 

34  00 

3136 

29  25 

27  32 

25  45 

24  12 

22  44 

21  24 

20  12 

20 

24 

62  24 

57  18 

52  48 

48  58 

45  30 

42  20 

39  39 

37  04 

34  51 

32  44 

30  49 

29  04 

24 

28 

78  01 

7152 

66  38 

61  54 

57  38 

53  58 

50  26 

47  26 

44  34 

4157 

39  36 

28 

32 

80  54 

75  16 

70  29 

65  52 

6157 

58  12 

54  47 

5143 

32 

36 

78  25 

73  39 

69  20 

65  27 

36 

40 

85  36 

80  48 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

A,h 

6.50 

5.97 

5.50 

5.10 

4.74 

4.41 

4.13 

3.86 

3.63 

3.41 

3.21 

3.03 

A,h 

0.812 

0.775 

0.740 

0.707 

0.675 

0.644 

0.615 

0.586 

0.559 

0.532 

0.506 

0.481 

Log. 

91 

97 

36 

57 

78 

44 

95 

59 

91 

75 

51 

44 

Log. 

Limit 

21 

23 

24 

25 

26 

27 

28 

29 

30 

32 

33 

34 

Min- 
utes 

Merid- 
ian 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

Alti- 
tudes 

138 


Latitude  23°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/       // 

1     II 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

/      // 

/     /' 

1     II 

/     " 

Min. 

4 

0  46 

0  43 

0  41 

0  39 

0  37 

0  35 

0  33 

0  31 

0  30 

0  28 

0  27 

0  25 

4 

8 

3  03 

2  53 

2  44 

2  35 

2  27 

2  19 

2  12 

2  05 

159 

153 

1  47 

141 

8 

12 

6  52 

6  29 

6  08 

5  49 

5  31 

5  14 

4  57 

4  43 

4  28 

4  14 

4  00 

3  48 

12 

16 

12  13 

11  32 

10  55 

10  20 

9  49 

9  18 

8  47 

8  21 

7  56 

7  30 

7  08 

6  44 

16 

20 

19  04 

18  01 

17  03 

16  09 

15  20 

14  32 

13  44 

13  04 

12  24 

11  44 

11  08 

10  32 

20 

24 

27  27 

25  57 

24  35 

23  14 

22  05 

20  56 

19  47 

18  49 

17  52 

16  54 

16  02 

15  10 

24 

28 

37  22 

35  18 

33  27 

31  38 

30  03 

28  29 

26  55 

25  37 

24  18 

23  00 

21  49 

20  39 

28 

32 

48  48 

46  05 

43  41 

41  17 

39  15 

37  12 

35  09 

33  27 

3144 

30  02 

28  30 

26  58 

32 

36 

61  47 

58  19 

55  18 

52  16 

49  41 

47  06 

44  30 

42  20 

40  11 

38  01 

36  05 

34  08 

36 

40 

76  16 

72  00 

68  16 

64  32 

61  20 

58  08 

54  56 

52  16 

49  36 

46  56 

44  32 

42  08 

40 

44 

87  07 

82  36 

78  05 

74  13 

70  21 

66  28 

63  14 

60  01 

56  47 

53  54 

50  59 

44 

48 

92  56 

88  19 

83  42 

79  06 

75  16 

71  25 

67  33 

64  07 

60  40 

48 

52 

92  50 

88  20 

83  49 

79  19 

75  15 

71  12 

52 

56 

97  13 

9159 

87  18 

82  35 

56 

60 

94  48 

60 

If 

II 

" 

" 

II 

II 

II 

II 

II 

II 

II 

" 

A,h 

2.86 

2.70 

2.56 

2.42 

2.30 

2.18 

2.06 

1.96 

1.86 

1.76 

1.67 

1.58 

A,h 

Log. 

0.456 

0.431 

0.408 

0.383 

0.361 

0.338 

0.313 

0.292 

0.269 

0.245 

0.222 

0.198 

Log. 

37 

36 

24 

82 

73 

46 

87 

26 

51 

51 

72 

66 

Limit 

35 

36 

37 

39 

40 

41 

43 

44 

45 

46 

48 

50 

Min- 
utes 

Merid- 
ian 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/      // 

/     // 

/      // 

/      // 

/     // 

/      // 

/     // 

/     // 

/      // 

Min. 

4 

0  24 

0  22 

0  22 

0  20 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  14 

0  12 

4 

8 

136 

1  31 

126 

1  22 

1  17 

1  13 

109 

105 

101 

0  57 

0  54 

0  50 

8 

12 

3  36 

3  25 

3  14 

3  05 

2  54 

2  44 

2  36 

2  27 

2  19 

2  10 

2  01 

1  52 

12 

16 

6  24 

6  03 

5  46 

5  27 

5  10 

4  52 

4  36 

4  21 

4  05 

3  50 

3  35 

3  19 

16 

20 

10  00 

9  28 

9  00 

8  32 

8  04 

7  36 

7  12 

6  48 

6  24 

6  00 

5  36 

5  12 

20 

24 

14  24 

13  38 

12  58 

12  17 

1137 

10  57 

10  22 

9  48 

9  13 

8  38 

8  04 

7  29 

24 

28 

19  36 

18  34 

17  38 

16  44 

15  49 

14  53 

14  07 

13  20 

12  33 

1146 

10  58 

10  12 

28 

32 

25  36 

24  14 

23  02 

21  51 

20  39 

19  27 

18  26 

17  24 

16  23 

15  22 

14  20 

13  19 

32 

36 

32  24 

30  40 

29  10 

27  39 

26  08 

24  38 

23  20 

22  02 

20  44 

19  26 

18  09 

16  51 

36 

40 

40  00 

37  52 

36  00 

34  08 

32  16 

30  24 

28  48 

27  12 

25  36 

24  00 

22  24 

20  48 

40 

44 

48  24 

45  49 

43  34 

41  18 

39  02 

36  47 

34  51 

32  55 

30  58 

29  02 

27  06 

25  10 

44 

48 

57  36 

54  32 

51  50 

49  09 

46  28 

43  46 

4128 

39  10 

36  52 

34  34 

32  15 

29  55 

48 

52 

67  36 

64  00 

60  50 

57  41 

54  32 

5122 

48  40 

45  58 

43  16 

40  34 

37  51 

35  09 

52 

56 

78  24 

74  13 

70  34 

66  54 

63  14 

59  35 

56  27 

53  19 

50  10 

47  02 

43  54 

40  46 

56 

60 

90  00 

85  12 

8100 

76  48 

72  36 
II 

68  24 

64  48 

61  12 

II 

57  36 
II 

54  00 
II 

50  24 
II 

46  48 
II 

60 

Ajh 

1.50 

1.42 

1.35 

1.28 

1.21 

1.14 

1.08 

1.02 

0.96 

0.90 

0.84 

0.78 

A,h 

Log. 

0.176 

0.152 

0.130 

0.107 

0.082 

0.056 

0.033 

i_0.008 

9.982 

9.954 

9.924 

9.892 

Log. 

09 

29 

33 

21 

79 

90 

42 

60 

27 

24 

28 

09 

Limit 

52 

54 

56 

58 

60 

61 

62 

64 

66 

68 

70 

72 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

Latitude  23°  Declination  Contrary  Name. 


139 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

4 
11 
19 
30. 
44 
60 
79 

II 
4.6. 

// 

14 
56 
36 
16 
52 
27 
JO 
31 

\ 

1 
4 
10 
18 
29 
42 
58 
75 

II 
4.4 

// 

11 

45 
40 
56 
36 
37 
31 
i7 

1 

1 

4 

10 

18 
28 
40 
55 
72 

4.2 

// 

08 
34 
15 
13 
28 
59 
48 
53 

r 

1 

1 

4 

9 
17 
27 
39 
53 
70 

II 
4.L 

II 

06 
23 
53 

35 
28 
34 
50 
18 

I 

/     // 

103 
4  14 
9  32 
16  56 
26  28 
38  06 
51  53 
67  46 

II 
3.97 

/     // 

1  02 
4  06 
9  13 
16  23 
25  36 
36  52 
50  10 
65  32 

II 
3.84 

0 
3 
8 
15 
24 
35 
48 
63 
80 

II 
3.7 

59 
58 
54 
50 
14 
37 
29 
19 
38 

/     // 

0  57 
3  50 
8  37 
15  19 
23  56 
34  28 
46  55 
61  16 
77  33 

II 
3.59 

/      // 

0  55 
3  43 
8  22 
14  50 
23  12 
33  24 
45  29 
59  24 
75  10 

II 
3.48 

/     // 

0  54 
3  36 
8  05 
14  23 
22  28 
32  21 
44  02 
57  31 
72  48 
89  52 

II 
3.37 

/     // 

0  52 
3  30 
7  51 
13  57 
21  48 
31  23 
42  44 
55  49 
70  38 
87  12 

II 
3.27 

/      II 

0  51 
3  23 
7  36 
13  32 
21  08 
30  26 
41  25 
54  06 
68  29 
84  32 

II 
3.17 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.665 
58 

0.647 
38 

0.6. 

JO 
13 

0.614 
90 

0.598 
79 

0.584 
33 

0.569 
37 

0.555 
09 

0.541 
58 

0.527 
63 

0.514 
55 

0.501 
06 

Log. 

Limit 

27 

28 

29 

30 

31 

31 

32 

32 

33 

34 

34 

35 

Min- 
utes 

Merid- 
ian 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

/     // 

/     // 

ff 

Min. 

Min. 

4 

0  49 

0  48 

0  46 

0  46 

0  44 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

0  37 

4 

8 

3  17 

3  12 

3  06 

3  02 

2  57 

2  52 

2  47 

2  43 

2  40 

2  36     2  32 

2  28 

8 

12 

7  24 

7  12 

6  59 

6  49 

6  38 

6  27 

6  17 

6  07 

5  59 

5  50 

5  41 

5  32 

12 

16 

13  08 

12  48 

12  25 

12  07 

1146 

11  29 

11  11 

10  53 

10  37 

10  22 

10  07 

9  52 

16 

20 

20  32 

20  00 

19  24 

18  56 

18  24 

17  56 

17  28 

17  00 

16  36 

16  12 

15  48 

15  24 

20 

24 

29  34 

28  48 

27  56 

27  16 

26  30 

25  50 

25  10 

24  29 

23  54 

23  19 

22  45 

22  11 

24 

28 

40  15 

39  12 

38  02 

37  06 

36  04 

35  09 

34  14 

33  19 

32  33 

3146 

30  58 

30  11 

28 

32 

52  34 

51  12 

49  40 

48  28 

47  06 

45  54 

44  42 

43  31 

42  30 

41  29 

40  27 

39  25 

32 

36 

66  32 

64  48 

62  51 

6121 

59  37 

58  07 

56  36 

55  05 

53  47 

52  29 

51  12 

49  54 

36 

40 

82  08 

80  00 

77  36 

75  44 

73  36 

7144 

69  52 

68  00 

66  24 

64  48 

63  12 

61  36 

40 

44 

86  48 

84  33 

82  17 

80  20 

78  24 

76  39 

74  32 

44 

48 

95  37 

93  19 

9100 

88  42 

48 

52 

106  48 

104  06 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.08 

3.00 

2.91 

2.84 

2.76 

2.69 

2.62 

2.55 

2.49 

2.43 

2.37 

2.31 

Ajh 

Log. 

0.488 

0.477 

0.463 

0.453 

0.440 

0.429 

0.418 

0.406 

0.396 

0.385 

0.374 

0.363 

Log. 

55 

12 

89 

32 

91 

75 

30 

54 

20 

61 

75 

61 

Limit 

36 

36 

37 

38 

39 

39 

40 

41 

42 

43 

44 

45 

Min- 
utes 

Merid- 
ian 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

140 


Latitude  23°  Declination  Contrary  Name. 
Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  36 

2  25 

5  26 

9  38 

15  04 

2142 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

101  51 

II 
2.26 

/      // 

0  35 

2  21 

5  17 

9  23 

14  40 

2107 

28  45 

37  33 

47  31 

58  40 

70  59 

84  29 

99  09 

II 
2.20 

/      // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

/     II 

0  34 

2  14 

5  02 

8  58 

14  00 

20  10 

27  26 

35  50 

45  22 

56  00 

67  46 

80  38 

94  38 

109  46 

2.10 

/      // 

0  33 

2  11 

4  55 

8  45 

13  40 

19  41 

26  47 

34  59 

44  17 

54  40 

66  09 

78  43 

92  23 

107  09 

It 
2.05 

/      // 

0  32 

2  09 

4  49 

8  35 

13  24 

19  18 

26  16 

34  18 

43  25 

53  36 

64  51 

77  11 

90  35 

105  03 

II 
2.01 

/      // 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

117  36 
II 

1.96 

/      // 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

61  37 

73  21 

86  05 

99  49 

114  36 
II 

1.91 

/      // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

3155 

40  24 

49  52 

60  21 

7148 

84  16 

97  45 

112  12 

1.87 

/     // 

0  30 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  14 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 

1.83 

1       n 

0  28 

154 

4  17 

7  35 

1152 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 

II 

1.78 

/      // 

0  27 

1  52 
4  12 
7  28 

11  40 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 
91  28 

105  00 

II 

1.75 

Min. 
4 

>^ 

16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.354 
11 

0.342 
42 

0.332 
44 

0.322 
22 

0311 
75 

0.303 
20 

0.292 
26 

0.281 
03 

0.271 
84 

0.262 
45 

0.250 
42 

0.243 
04 

Log. 

Limit 

46 

47 

48 

49 

50 

50 

51 

51 

52 

53 

54 

55 

Min- 
utes 

Merid- 
ian 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35°  i   34° 

33° 

32° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

1      II 

/     // 

/     // 

/     // 

/      " 

/      // 

/     // 

/      // 

/      // 

/      // 

/     // 

/      " 

Min. 

4 

0  27 

0  27 

0  26 

0  25 

0  25 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  21 

4 

8 

150 

147 

144 

142 

139 

137 

135 

133 

1  31 

128 

126 

1  24 

8 

12 

4  06 

4  00 

3  54 

3  49 

3  43 

3  37 

3  34 

3  28 

3  23 

3  19 

3  13 

3  08 

12 

16 

7  18 

7  08 

6  58 

6  47 

6  37 

6  27 

6  18 

6  08 

6  01 

5  53 

5  43 

5  36 

16 

20 

1124 

1108 

10  52 

10  36 

10  20 

10  04 

9  52 

9  36 

9  24 

9  12 

8  56 

8  44 

20 

24 

16  25 

1«02 

15  39 

15  16 

14  53 

14  30 

14  12 

13  49 

13  32 

13  15 

12  52 

12  35 

24 

28 

22  21 

2149 

21  18 

20  47 

20  15 

19  44 

19  21 

18  49 

18  26 

18  02 

17  30 

17  07 

28 

32 

29  11 

28  30 

27  49 

27  08 

26  27 

25  46 

25  16 

24  35 

24  04 

23  33 

22  52 

22  21 

32 

36 

36  56 

36  05 

35  13 

34  21 

33  29 

32  37 

3158 

31  06 

30  27 

29  49 

28  57 

28  18 

36 

40 

45  36 

44  32 

43  28 

42  24 

41  20 

40  16 

39  28 

38  24 

37  36 

36  48 

35  44 

34  56 

40 

44 

55  10 

53  54 

52  36 

51  18 

50  01 

48  43 

47  45 

46  27 

45  29 

44  32 

43  14 

42  16 

44 

48 

65  38 

64  07 

62  35 

6103 

59  31 

57  59 

56  50 

55  18 

54  09 

52  59 

5127 

50  18 

48 

52 

77  04 

75  15 

73  27 

7139 

69  51 

68  03 

66  42 

64  54 

63  33 

62  11 

60  23 

59  02 

52 

56 

89  22 

87  18 

85  12 

83  06 

8101 

78  55 

77  21 

75  15 

73  41 

72  08 

70  02 

68  28 

56 

60 

102  36 

100  12 

97  48 
II 

95  24 

93  00 

II 

90  36 
II 

88  48 
II 

86  24 
II 

84  36 
II 

82  48 
II 

80  24 
II 

78  26 
II 

60 

A,h 

1.71 

1.67 

1.63 

1.59 

1.55 

1.51 

1.48 

1.44 

1.41 

1.38 

1.34 

1.31 

A,h 

Log. 

0.233 

0.222 

0.212 

0.201 

0.190 

0.178 

0.170 

0.158 

0.149 

0.139 

0.127 

0.117 

Log. 

00 
55 

72 

19 

40 

33 

98 

26 

36 

22 

88 

10 

27 

Limit 

56 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

Alti- 
tudes 

Latitude  23°  Decimation  Contrary  Name. 


141 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Anglos 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/     // 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 
16  44 
2151 
27  39 
34  08 
41  18 
49  09 
57  41 
66  54 
76  48 

1.28 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 

1.25 

/     // 

0  19 

1  18 

2  54 
5  10 
8  04 

1137 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 
72  36 

1.21 

/     // 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
3128 
38  05 
45  18 
53  10 
6141 
70  48 

1.18 

/     // 

0  18 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  08 
5149 
60  07 
69  00 

1.15 

/     // 

0  17 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

1.12 

/     // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

II 

1.09 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

1     II 

0  16 
105 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 

17  04 

2136 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
II 

1.00 

/     // 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

/     // 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

II 

0.94 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.107 
21 

0.096 
91 

0.082 
79 

0.071 

88 

0.060 
70 

0.049 
22 

0.037 
43 

0.025 
31 

0.012 

84 

0.00 

9.986 

77 

9.973 
13 

Log. 

Limit 

67 

68 

70 

71 

72 

74 

76 

77 

78 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 
15  32 
19  39 
24  16 
29  21 
34  57 
41  01 
47  33 

54  36 

II 

0.91 

/     // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

/     // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  36 

5100 
II 

0.85 

II 

1 

II 

// 

/ 

// 

/ 

// 

II 

// 

II 

// 

1 

II 

// 

/ 

II 

// 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.959 
04 

9.944 

48 

9.929 
42 

Log. 

Limit 

82 

83 

84 

Min- 
utes 

Merid- 
ian 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

Alti- 
tudes 

142 


Latitude  24°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
86 
40 
44 
48 
52 
56 
60 

/      -11 

1  10 
4  43 
10  35 
18  49 
29  24 
42  20 
57  38 
75  16 

4.41 

1  13 
4  54 
11  01 
19  35 
30  36 
44  04 
59  59 
78  20 

II 
4.59 

/ 

1 

5( 
11 
20 
31 
45 
62 
81 

II 
4.7 

// 

16 
37 
30 
26 
56 
59 
34 
15 

9 

/     // 

120 
5  20 
12  00 
21  20 
33  20 
48  00 
65  20 

II 
5.00 

1 

1  . 

5. 
12 
22 
34 
50 
68 

II 
5.2 

// 

23 
35 
33 
19 
52 
12 
21 

3 

1  i 
5. 

13 

23. 

36 

52' 

71 

II 
5.4 

// 

27 
52 
11 
25 
36 
12 
15 

3 

1 

1. 

6 

13. 
24 
38 
55. 
75 

II 
5.7 

32 
10 
51 
37 
28 
23 
24 

1 ; 
6: 

14  > 
25. 
40. 
58. 
79. 

II 
6.0 

// 

37 
30 
37 
59 
36 
28 
55 

3 

143 
6  53 
15  28 
27  28 
42  56 
61  49 
84  09 

II 
6.44 

150 
7  18 
16  26 
29  14 
45  40 
65  46 

II 
6.85 

/     // 

157 

7  47 

17  31 

31  09 

48  40 

II 
7.30 

2  05 

8  21 

18  47 

33  25 

52  12 

7.83 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.644 
44 

0.661 
81 

0.680 
34 

0.698 
97 

0.718 
50 

0.739 
57 

0.761 
18 

0.784 
62 

0.808 
89 

0.835 
69 

0.863 
32 

0.893 
76 

Log. 

Limit 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

Min- 
utes 

Merid- 
ian 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23 

0      Hour 
Angles 

Min. 

1       II 

1      II 

/       n . 

1     II 

1     II 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

1 

"      Min. 

4 

2  15 

2  27 

2  40 

2  57 

3  18 

3  45 

4  21 

5  11 

4 

8 

9  01 

9  46 

10  41 

11  49 

13  13 

15  01 

17  24 

20  46 

8 

12 

20  16 

2159 

24  03 

26  36 

29  44 

33  48 

39  10 

12 

16 

36  00 

39  05 

42  45 

16 

20 

56  16 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

.     60 

60 

// 

II 

II 

" 

II 

II 

II 

II 

II 

II 

" 

// 

A,h 

8.44 

9.16 

10.02 

11.08 

12.39 

14.08 

16.32 

19.46 

A,h 

0.926 

0.961 

1.000 

1.044 

1.093 

1.148 

1.212 

1.289 

Log. 

Log. 

34 

90 

87 

54 

07 

60 

72 

14 

Limit 

16 

15 

14 

13 

12 

11 

10 

8 

7 

5 

3 

1 

Min- 
utes 

Merid- 
ian 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89' 

)      Alti- 
tudes 

Latitude  24°  Declination  Same  Name, 
Declinations. 


143 


Hour 
Anglee 

24° 

25°  1   26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

n 

/ 

n 

1 

n 
n 

1 

H 

/ 

II 

4 
19 

II 
18.0( 

48 
12 

) 

/ 

3 

15 
35 

II 
14.8( 

n 

58 
51 
40 

5 

/     II 

3  22 
13  27 
30  17 

II 
12.62 

/      // 

2  55 
11  40 
26  15 
46  38 

II 
10.93 

/     II 

2  34 
10  16 
23  04 
4103 

II 
9.62 

/      // 

2  17 

9  08 

20  33 

36  31 

57  04 

II 
8.56 

/      // 

2  03 

8  13 

18  28 

32  50 

51  20 

II 
7.70 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.255 
37 

1.172 
02 

1.101 
06 

1.038 
62 

0.983 
18 

0.932 
47 

0.886 
49 

Log. 

Limit 

0 

2 

4 

5 

6 

7 

9 

11 

13 

15 

16 

17 

Min- 
utes 

Merid- 
ian 

90° 

89° 

88° 

87° 

86°  1 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

151 

142 

/      II 
1  33 

126 

/      // 
1  19 

1  14 

108 

104 

/      // 
100 

0  57 

1     II 
0  53 

/      // 
0  50 

Min. 
4 

8 

7  26 

6  47 

6  13 

5  45 

5  19 

4  56 

4  36 

4  18 

4  01 

3  47 

3  33 

3  20 

8 

12 

16  46 

15  17 

13  58 

12  56 

1159 

1106 

10  20 

9  40 

9  03 

8  30 

7  59 

7  30 

12 

16 

29  46 

27  11 

24  54 

23  00 

21  17 

19  46 

18  24 

17  12 

16  04 

15  06 

14  12 

13  22 

16 

20 

46  32 

42  28 

38  56 

35  56 

33  16 

30  52 

28  44 

26  52 

25  06 

23  36 

22  12 

20  52 

20 

24 

6109 

56  04 

5145 

47  54 

44  27 

41  23 

38  41 

36  11 

33  59 

31  58 

30  03 

24 

28 

76  18 

70  26 

65  11 

60  30 

56  19 

52  40 

49  16 

46  15 

43  31 

40  54 

28 

32 

79  01 

73  33 

68  47 

64  21 

60  25 

56  50 

53  25 

32 

36 

76  28 

71  56 

67  37 

36 

40 
44 
48 
52 
56 
60 

II 

II 

//  ■ 

II 

II 

II 

II 

II 

II 

II 

83  28 
II 

40 
44 
48 
52 
56 
60 

Aih 

6.98 

6.37 

5.84 

5.39 

4.99 

4.63 

4.31 

4.03 

z.n 

0.576 

3.54 

3.33 

3.13 

A,h 

Log. 

0.843 

0.804 

0.766 

0.731 

0.698 

0.665 

0.634 

0.605 

0.549 

0.522 

0.495 

86 

14 

41 

59 

10 

58 

48 

31 

34 

00 

44 

54 

Log. 

Limit 

19 

21 

23 

24 

25 

26 

27 

28 

29 

31 

32 

33 

Min- 
utes 

Merid- 
ian 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

Alti- 
tudes 

144 


Latitude  24°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Augles 

/       n 

/      /' 

/     II 

/     // 

/      // 

/      // 

1     II 

/       n 

/       n 

Min. 

Min. 

4 

0  47 

0  45 

0  42 

0  40 

0  38 

0  36 

0  34 

0  32 

0  30 

0  28 

0  28 

0  26 

4 

8 

3  09 

2  58 

2  48 

2  39 

2  31 

2  23 

2  15 

2  08 

2  01 

155 

149 

143 

8 

12 

7  05 

6  40 

6  18 

5  58 

5  39 

5  21 

5  04 

4  48 

4  32 

4  18 

4  05 

3  51 

12 

16 

12  36 

11  52 

11  14 

10  36 

10  02 

9  31 

9  01 

8  32 

8  04 

7  38 

7  15 

6  53 

16 

20 

19  40 

18  32 

17  32 

16  34 

15  41 

14  53    14  04 

13  20 

12  36    1156 

11  20    10  44 

20 

24 

28  20 

26  41 

25  15 

23  54 

22  34 

21  25*  20  14 

19  12 

18  09    17  11 

16  19    15  28 

24 

28 

38  32    36  20 

34  22 

32  33 

30  43 

29  09    27  32 

26  08 

24  42   23  24 

22  13    21  02 

28 

32 

50  20    47  27 

44  53 

42  30 

40  06 

38  03    36  00 

34  08 

32  15    30  33 

29  01    27  28 

32 

36 

63  43 

60  03 

56  49 

53  47 

50  46 

48  08    45  35 

43  12 

40  50    38  40 

36  43    34  47 

36 

40 

78  40 

74  08 

70  08 

66  24 

62  40 

59  28   56  16 

53  20 

50  24    47  44 

45  20    42  56 

40 

44 

84  52 

80  20 

75  50 

7157 

68  05 

64  32 

60  59    57  45 

54  51    5157 

44 

48 

95  37 

90  14 

85  38 

8101 

76  48 

72  34,  68  42 

65  15 

6149 

48 

52 

90  08 

85  10 

80  40 

76  37 

72  33 

52 

56 

88  51 

84  09 

56 

60 

60 

It 

II 

II 

" 

II 

II 

II 

" 

II 

II 

II 

II 

Ajh 

2.95 

2.78 

2.63 

2.49 

2.35 

2.23 

2.11 

2.00 

1.89 

1.79 

1.70 

1.61 

A,h 

0.469 

0.444 

0.419 

0.396 

0.371 

0.348 

0.324 

0.301 

0.276 

0.252 

0.230 

0.206 

Log. 

Log. 

82 

04 

96 

20 

07 

30 

28 

03 

46 

85 

45 

83 

Limit 

34 

35 

37 

39 

40 

41 

;  42 

43 

44 

45 

47 

49 

Min- 
utes ' 

Merid- 
ian 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

/      // 

/      // 

1     II 

/      // 

/      // 

/      // 

/      /' 

/      // 

/      /' 

1     II 

/      // 

Min. 

4 

0  25 

0  24 

0  22 

0  20 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  14 

0  12 

4 

8 

138 

133 

128 

123 

1  18 

1  13 

1  10 

105 

101 

0  58 

0  54 

0  51 

8 

12 

3  40 

3  29 

3  17 

3  06 

2  56 

2  45 

2  37 

2  27 

2  19 

2  11 

2  02 

154 

12 

16 

6  32 

6  12 

5  51 

5  30 

5  12 

'    4  55 

4  39 

4  21 

4  05 

3  53 

3  38 

3  22 

16 

20 

10  12 

9  41 

9  08 

8  36 

8  08 

7  40 

7  16 

6  48 

6  24 

6  04 

5  40 

5  16 

20 

24 

14  41 

13  57 

13  09 

12  23 

1143 

1103 

10  28 

9  48 

9  13 

8  44 

8  10 

7  35 

24 

28 

20  00 

18  59 

17  54 

16  52 

15  57 

15  01 

14  15 

13  20 

12  33 

11  54 

1106 

10  20 

28 

32 

26  07 

24  47 

23  23 

22  01 

20  49 

19  37 

18  36 

17  24 

16  23 

15  32 

14  30 

13  29 

32 

36 

33  03 

3121 

29  36 

27  52 

26  21 

24  51 

23  33 

22  02 

20  44 

19  39 

18  22 

17  04 

36 

40 

40  48 

38  41 

36  32 

34  24 

32  32 

30  40 

29  04 

27  12 

25  36 

24  16 

22  40 

2104 

40 

44 

49  22 

46  47 

44  13 

41  37 

39  12 

37  07 

35  10 

32  55 

30  58 

29  21 

27  26 

25  29 

44 

48 

58  45 

55  39 

52  36 

49  32 

46  51 

44  09 

41  51 

39  10 

36  52 

34  57 

32  38 

30  18 

48 

52 

68  57 

65  21 

6144 

58  08 

54  59 

51  49 

49  07 

45  58 

43  16 

4101 

38  18 

35  36 

52 

56 

79  58 

75  37 

7137 

67  25 

63  46 

60  07 

56  58 

53  19 

50  10 

47  33 

44  26 

41  17 

56 

60 

9148 

87  00 

32  12 

77  24 

73  12 

69  00 

65  24 

61  12 

57  36 

54  36 

5100 

47  24 

60 

II 

II 

II 

II 

II 

II 

" 

" 

II 

II 

II 

II 

A,h 

1.53 

1.45 

1.37 

1.29 

1.22 

1.15 

1.09 

1.02 

0.96 

0.91 

0.85 

0.79 

A,h 

0.184 

0.161 

0.136 

0.110 

0.086 

0.060 

0.037 

0.008 

9.982 

9.959 

9.929 

9.897 

Log. 

Log. 

69 

37 

72 

59 
58 

36 

70 

43 

60 

27 

04 

42 

63 

Limit 

52 

54 

56 

60 

61 

62 

64 

66 

68 

70 

72 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

Latitude  24°  Declination  Contrary  Name. 

Declinations. 


145 


Hour 
Angles 

0° 

1° 

2° 

3° 

4'^ 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/      /' 

/     // 

1     II 

/     // 

/     // 

/     // 

/     // 

/      II 

/     // 

/     // 

/      // 

/      // 

Min. 

Min. 

4 

1  10 

108 

105 

103 

101 

0  59 

0  57 

0  55 

0  54 

0  52 

0  51 

0  49 

4 

8 

4  43 

4  32 

4  22 

4  12 

4  04 

3  56 

3  49 

3  42 

3  34 

3  28 

3  22 

3  17 

8 

12 

10  35 

10  11 

9  49 

9  29 

9  08 

8  51 

8  34 

8  19 

8  02 

7  48 

7  35 

7  22 

12 

16 

18  49 

18  05 

17  27 

16  51 

16  16 

15  45 

15  14 

14  45 

14  18 

13  52 

13  29 

13  06 

16 

20 

29  24 

28  16 

27  16 

26  20 

25  24 

24  36 

23  48 

23  04 

22  20 

21  40 

2104 

20  28 

20 

24 

42  20 

40  42 

39  16 

37  55 

36  35 

35  26 

34  16 

33  13 

32  10 

31  12 

30  21 

29  28 

24 

28 

57  38 

55  24 

53  27 

5137 

49  47 

48  13 

46  39 

45  13 

43  46 

42  28 

41  17 

40  07 

28 

32 

75  16 

72  22 

69  48 

67  25 

65  01 

62  58 

60  56 

59  03 

57  10 

55  28 

53  55 

52  24 

32 

36 

79  43 

77  07 

74  44 

72  22 

70  12 

68  16 

66  19 

36 

40 

92  16 

89  20 

86  40 

84  16 

8152 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

n 

II 

II 

>i 

II 

II 

II 

II 

II 

II 

II 

A,h 

4.41 

4.24 

4.09 

3.95 

3.81 

3.69 

3.57 

3.46 

3.35 

3.25 

3.16 

3.07 

A,h 

Log. 

0.644 

0.627 

0.611 

0.596 

0.580 

0.567 

0.552 

0.539 

0.525 

0.511 

0.499 

0.487 

Log. 

44 

37 

72 

60 

92 

03 

67 

08 

04 

88 

69 

14 

Limit 

28 

29 

30 

31 

32 

32 

33 

33 

34 

35 

35 

36 

Min- 
utes 

Merid- 
ian 

66' 

) 

65' 

64' 

> 

63' 

} 

62< 

3 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

/      // 

/     // 

/     // 

/     // 

/     /' 

/     /' 

1     II 

Min. 

Min. 

4 

0  47 

0  46 

0  45 

0  44 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

0  37 

0  36 

4 

8 

3  11 

3  05 

3  01 

2  56 

2  51 

2  47 

2  43 

2  40 

2  36 

2  32 

2  28 

2  25 

8 

12 

7  11 

6  58 

6  47 

6  36 

6  26 

6  15 

6  07 

5  59 

5  50 

5  41 

5  32 

5  26 

12 

16 

12  45 

12  22 

12  05 

1144 

1126 

1109 

10  53 

10  37 

10  22 

10  07 

9  52 

9  38 

16 

20 

19  56 

19  20 

18  52 

18  20 

17  52 

17  24 

17  00 

16  36 

16  12 

15  48 

15  24 

15  04 

20 

24 

28  42 

27  50 

27  10 

26  24 

25  44 

25  04 

24  29 

23  54 

23  19 

22  45 

22  11 

21  42 

24 

28 

39  05 

37  54 

36  59 

35  56 

35  01 

34  06 

33  19 

32  33 

3146 

30  58 

30  11 

29  32 

28 

32 

5102 

49  30 

48  18 

46  56 

45  44 

44  32 

43  31 

42  30 

4129 

40  27 

39  25 

38  34 

32 

36 

64  35 

62  38 

6108 

59  24 

57  54 

56  23 

55  05 

53  47 

52  29 

51  12 

49  54 

48  49 

36 

40 

79  44 

77  20 

75  28 

73  20 

7128 

69  36 

68  00 

66  24 

64  48 

63  12 

61  36 

60  16 

40 

44 

88  44 

86  29 

84  13 

82  17 

80  20 

78  24 

76  39 

74  32 

72  55 

44 

48 

95  37 

93  19 

91  00 

88  42 

86  47 

48 

52 

106  48 

104  06 

101  51 

52 

56 

56 

60 

60 

II 

II 

II 

II 

ir 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.99 

2.90 

2.83 

2.75 

2.68 

2.61 

2.55 

2.49 

2.43 

2.37 

2.31 

2.26 

A,h 

Log. 

0.475 

0.462 

0.451 

0.439 

0.428 

0.416 

0.406 

0.396 

0.385 

0.374 

0.363 

0.354 

Log. 

67 

40 

79 

33 

13 

64 

54 

20 

61 

75 

61 

11 

Limit 

36 

37 

38 

39 

39 

40 

41 

42 

42 

43 

44 

45 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

146 


Latitude  24°  Declination  Contrary  Name. 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33°  1   34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  35 

2  22 

5  18 

9  26 

14  44 

21  13 

28  53 

37  43 

47  44 

58  56 

71  18 

84  52 

2.21 

/      // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

2.15 

/      // 

0  34 
2  14 
5  02 

8  58 
14  00 
20  10 
27  26 
35  50 
45  22 
56  00 
67  46 
80  38 

2.10 

0  33 

2  12 

4  57 

8  47 

13  44 

19  47 

26  55 

35  09 

44  30 

54  56 

66  28 

79  06 

II 
2.06 
0.313 

87 

0  32 

2  09 

4  49 

8  35 

13  24 

19  18 

26  16 

34  18 

43  25 

53  36 

64  51 

77  11 

II 
2.01 

/      // 

0  31 

2  05 
4  43 
8  21 
13  04 
18  49 
25  37 
33  27 
42  20 
52  16 
63  14 
75  16 

II 
1.96 

/      // 

0  31 
2  02 
4  37 
8  11 

12  48 
18  26 
25  06 
32  46 
41  28 
51  12 
61  57 
73  44 

1.92 

/      // 

0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

1.88 

/     // 

0  30 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  14 

39  32 

48  48 

59  03 

70  16 

82  28 

II 
1.83 

/     II 

0  28 

1  55 
4  18 
7  38 

11  56 
17  11 
23  24 
30  33 
38  40 
47  44 
57  45 
68  42 
80  40 

1.79 

/        n 

0  27 

1  52 
4  12 

7  28 
11  40 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 

II 
1.75 

/      // 

0  27 

1  50 
4  06 

7  18 
11  24 
16  25 
22  21 
29  11 
36  56 
45  36 
55  10 
65  38 
77  04 

II 
1.71 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.344 
39 

0.332 
44 

0.322 
22 

0.303 
20 

0.292 
26 

0.283 
30 

0.274 
16 

0.262 
45 

0.252 
85 

0.243 
04 

0.233 
00 

Log. 

Limit 

46 

47 

48 

49 

50 

51 

52 

53 

54 

54 

55 

56 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

4^170    1  Hour 
^'      'Angles 

Min. 

/      // 

/      // 

/     // 

/      // 

1     II 

/      // 

/      // 

/      /' 

/      // 

/      // 

/      '/ 

,    Mm. 

4 

0  27 

0  27 

0  26 

0  25 

0  25 

0  23 

0  23 

0  22 

0  22 

0  22 

0  21 

0  20        4 

8 

147 

145 

142 

139 

138 

136 

1  34 

131 

129 

127 

125 

123       8 

12 

4  01 

3  56 

3  50 

3  44 

3  40 

3  35 

3  31 

3  25 

3  20 

3  16 

3  11 

3  06      12 

16 

7  10 

7  00 

6  50 

6  39 

6  32 

6  21 

6  13 

6  03 

5  56 

5  48 

5  41 

5  30      16 

20 

11  12 

10  56 

10  40 

10  24 

10  12 

9  56 

9  44 

9  28 

9  16 

9  04 

8  52 

8  36|     20 

24 

16  08 

15  45 

15  22 

14  59 

14  41 

14  18 

14  01 

13  38 

13  21 

13  04 

12  46 

12  23,     24 

28 

2157 

21  25 

20  54 

20  23 

20  00 

19  29 

19  05 

18  34 

18  10 

17  46 

17  23 

16  52'     28 

32 

28  40 

27  59 

27  18 

26  27 

26  07 

25  26 

24  55 

24  14 

23  43 

23  12 

22  42 

22  01 i     32 

36 

36  18 

35  26 

34  34 

33  42 

33  03 

32  11 

31  32 

30  40 

30  02 

29  23 

28  44 

27  52,     36 

40 

44  48 

43  44 

42  40 

4136 

40  48 

39  44 

38  56 

37  52 

37  04 

36  16 

35  28 

34  241     40 

44 

54  13 

52  55 

51  38 

50  20 

49  22 

48  04 

47  06 

45  49 

44  51 

43  53 

42  55 

41  37,     44 

48 

64  30 

62  58 

61  26 

59  54 

58  45 

57  13 

56  04 

54  32 

53  22 

52  13 

5104 

49  32     48 

52 

75  42 

73  54 

72  06 

70  18 

68  57 

67  09 

65  48 

64  00 

62  38 

61  17 

59  56 

58  08'     52 

56 

87  49 

85  43 

83  38 

8132 

79  58 

77  52 

76  18 

74  13 

72  39 

7105 

69  31 

67  25     56 

60 

100  48 

98  24 

96  00 

93  36 

91  48 

89  24 

87  36 

85  12 

83  24 

8136 

79  48 

77  24     60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

"     1 

A,h 

1.68 

1.64 

1.60 

1.56 

1.53 

1.49 

1.46 

1.42 

1.39 

1.36 

1.33 

1.29 

A,h 

Log. 

0.225 

0.214 

0.204 

0.193 

0.184 

0.173 

0.164 

0.152 

0.143 

0.133 

0.123 

0.110 

Log. 

31 

84 

12 

12 

69 

19 

35 

29 

01 

54 

85 

59 

Limit 

56 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

07     i   Miu- 
*>'        utes 

Merid- 
ian 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21°- 

20° 

iQo    1  Alti- 
■'•''     1  tudes 

Latitude  24**  Declination  Contrary  Namc« 


147 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/       n 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  38 

48  23 

56  47 

65  51 

75  36 

1.26 

0  19 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

/      // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

II 

1.20 

I  II 

0  19 

1  15 

2  48 
5  00 
7  48 

II  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/      // 

0  18 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
5122 
59  35 

68  24 

II 

1.14 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

/      II 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 

II 

1.08 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

1.05 

1     II 

0  16 
105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
II 

1.02 

/      // 

0  15 

1  03 

2  23 
4  13 
6  36 
9  30 

12  57 

16  54 

21  23 

26  24 

31  56 

38  01 

44  37 

51  44 

59  24 
II 

0.99 

0  15 

1  01 

2  19 
4  05 
6  24 
9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 
II 

0.96 

0  15 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 

55  48 

II 

0.93 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.100 
37 

0.089 
91 

0.079 

18 

0.068 
19 

0.056 
90 

0.045 
32 

0.033 
42 

0.021 
19 

0.008 
60 

9.995 
64 

9.982 
27 

9.968 
48 

Log. 

Limit 

68 

69 

71 

72 

73 

74 

76 

78 

79 

80 

81 

82 

Min- 
utes 

Merid-      -i  qo 
ian        ^° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

Alti- 
tudes 

Declinations.  - 

-Inferior  Meridian. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

/      // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 

15  22 

19  26 

24  00 

29  02 

34  34 

40  34 

47  02 

54  00 
II 

0.90 

0  14 
0  56 

2  05 

3  43 
5  48 
8  21 

11  22 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  29 

52  12 
II 

0.87 

/      // 

II 

// 

r 

II 

1 
II 

1 
II 

II 

/ 

// 

1 

II 
II 

/ 

II 
II 

/      // 

0  09 
0  37 
124 

2  28 

3  52 
5  32 
7  35 
9  54 

12  32 
15  28 
18  43 
22  16 
26  09 
30  19 
34  48 

0.58 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.954 

24 

9.939 
52 

9.763 
43 

Log. 

Limit 

83 

84 

92 

Min- 
utes 

Merid- 
ian 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

Alti- 
tudes 

148 


Latitude  25°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5°        6° 

7° 

8° 

9° 

10° 

IP 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

4 
10 
17 
28 
40 
55 
71 

It 
4.2 

D7 
30 
[)6 
58 
D4 
25 
31 
51 

I 

1 

4 
10 
18 
29 
41 
57 
74 

II 
4.3* 

10 
iO 
29 
39 
D8 
57 
36 
34 

1 

4 

10 
19 
30 
43 
59 
77 

II 
4.5. 

13 
51 
55 
25 
20 
41 
27 
39 

3 

1 

5 
11 
20 
31 
45 
61 
80 

4.7' 

16 
34 
23 
13 
36 
30 
54 
54 

1 

/ 

1 

5 
11 
21 
33 
47 
64 

II 
4.9. 

19 
16 
53 
37 
30 
31 
41 

3 

1 

5 
12 
22 
34 
49 
67 

// 
5.1i 

23 
31 
26 
36 
32 
44 
11 

1 

1 

5 
13 
23 
36 
52 
71 

II 
5.4' 

27 
49 
04 
12 
16 
13 
35 

1 

/     // 

131 
6  06 
13  44 
24  24 
38  08 
54  55 
74  45 

II 
5.72 

/       n 

136 
6  26 
14  28 
25  44 
40  12 
57  54 
78  48 

II 
6.03 

/       n 

142 
6  48 
15  19 
27  13 
42  32 
61  15 
83  23 

II 
6.38 

/     // 

1  49 
7  14 
16  15 
28  53 
45  08 
64  59 

II 
6.77 

/     // 

155 
7  42 
17  20 
30  48 
48  08 
69  19 

II 
7.22 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.624 
28 

0.640 
48 

0.658 
01 

0.675 
78 

0.694 
61 

0.714 
33 

0.735 
60 

0.757 
40 

0.780 
32 

0.804 
82 

0.830    0.858 
59        54 

Log. 

Limit 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19        18 

Min- 
utes 

Merid- 
ian 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

f     II 

/     // 

/     // 

/     // 

/     '/ 

/     '/ 

Min. 

Min. 

4 

2  04 

2  13 

2  25 

2  38 

2  55 

3  16 

3  42 

4  18 

5  07 

4 

8 

8  16 

8  54 

9  39 

10  33 

1139 

13  03 

14  49 

17  10 

20  28 

8 

12 

18  35 

20  01 

21  43 

23  46 

26  14 

29  21 

33  20 

38  38 

12 

16 

33  01 

35  35 

38  37 

42  14 

46  38 

16 

20 

5136 

55  36 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

" 

" 

II 

II 

II 

II 

Ajh 

i:i^ 

8.34 

9.05 

9.90 

10.93 

12.23 

13.89 

16.10 

19.19 

A.h 

Log. 

0.888 

0.921 

0.956 

0.995 

1.038 

1.087 

1.142 

1.206 

1.283     . . 

Log. 

74 

17 

65 

64 

62 

43 

70 

83 

07 

Limit 

18 

17 

16 

15 

14 

13 

12 

11 

10 

8 

6 

4 

Min- 
utes 

Merid- 
ian 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

Alti- 
tudes 

Latitude  25°  Declination  Same  Name. 
Declinations. 


149 


Hour" 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

11 

1 

II 

/ 

II 

II 

// 

1 

// 

// 

1 

// 

4 
18 
42 

II 
17.6i 

n 

44 
51 
26 

1 

3 

15 
35 

II 
14.5< 

54 
34 
31 

) 

/     // 

3  18 
13  12 
29  43 

II 
12.38 

/     // 

2  51 
11  26 
25  44 
45  44 

II 
10.72 

/     II 

2  31 
10  04 
22  38 
40  14 

9.43 

/      // 

2  14 

8  57 
20  07 
35  48 
55  56 

II 
8.39 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.247 
48 

1.164 
09 

1.092 
72 

1.030 
19 

0.974 
51 

0.923 
76 

Log. 

Limit 

2 

0 

2 

4 

6 

7 

8 

10 

12 

14 

15 

16 

Min- 
utes 

Merid- 
ian 

89 

3 

90 

-> 

89= 

3 

88' 

> 

{ 

I7< 

3 

J 

6' 

) 

85' 

) 

84' 

) 

83' 

82' 

) 

81"= 

80= 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/     /' 

/     // 

/     /' 

1     II 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

2  00 

150 

1  40 

132 

124 

1  18 

1  12 

107 

103 

0  59 

0  55 

0  52 

4 

8 

8  03 

7  17 

6  39 

6  06 

5  37 

5  12 

4  49 

4  29 

4  12 

3  56 

3  41 

3  28 

8 

12 

18  06 

16  25 

14  57 

13  43 

12  40 

1141 

10  51 

10  06 

9  25 

8  50 

8  17 

7  48 

12 

16 

32  10 

29  11 

26  35 

24  23 

22  29 

20  47 

19  17 

17  58 

16  45 

15  42 

14  43 

13  52 

16 

20 

50  16 

45  36 

4132 

38  08 

35  08 

32  27 

30  08 

28  03 

26  12 

24  32 

23  00 

21  40 

20 

24 

65  40 

59  48 

54  55 

50  35 

46  45 

43  22 

40  25 

37  43 

35  19 

33  07 

31  12 

24 

28 

74  45 

68  52 

63  38 

59  04 

55  01 

5122 

48  05 

45  04 

42  27 

28 

32 

83  07 

77  08 

7151 

67  05 

62  48 

58  53 

55  28 

32 

36 

79  30 

74  31 

70  12 

36 

40 

86  40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

7.54 

6.84 

6.23 

5.72 

5.27 

4.87 

4.52 

4.21 

3.93 

3.68 

3.45 

3.25 

Ajh 

Log. 

0.877 

0.835 

0.794 

0.757 

0.721 

0.687 

0.655 

0.624 

0.594 

0.565 

0.537 

0.511 

Log. 

37 

06 

49 

40 

81 

53 

14 

28 

39 

85 

82 

88 

Limit 

17 

19 

21 

23 

24 

25 

26 

27 

28 

30 

31 

32 

Min- 
utes 

Merid- 
ian 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

160 


Latitude  25°  Declination  Same  Name* 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/     // 

/      '/ 

/      // 

/     // 

/     '/ 

/      // 

/     // 

/      // 

/     // 

1     II 

/     // 

/     /' 

Min. 

4 

0  49 

0  46 

0  43 

0  40 

0  39 

0  36 

0  34 

0  32 

0  31 

0  30 

0  28 

0  25 

4 

8 

3  15 

3  04 

2  53 

2  44 

2  34 

2  25 

2  18 

2  09 

2  03 

157 

150 

1  44 

8 

12 

7  19 

6  54 

6  30 

6  08 

5  47 

5  27 

5  10 

4  52 

4  38 

4  22 

4  08 

3  55 

12 

16 

13  01 

12  17 

11  34 

10  55 

10  17 

9  40 

9  12 

8  38 

8  13 

7  46 

7  22 

6  57 

16 

20 

20  20 

19  11 

18  03 

17  04 

16  04 

15  08 

14  23 

13  31 

12  51 

12  08 

11  32 

10  52 

20 

24 

29  17 

27  37 

26  01 

24  35 

23  08 

2147 

20  45 

19  29 

18  30 

17  28 

16  36 

15  38 

24 

28 

39  51 

37  38 

35  25 

33  27 

3129 

29  40 

28  13 

26  32 

25  14 

23  46 

22  37 

21  17 

28 

32 

52  03 

49  09 

46  14 

43  41 

4108 

38  45 

36  51 

34  39 

32  57 

3103 

29  32 

27  49 

32 

36 

65  53 

62  13 

58  32 

55  18 

52  03 

49  02 

46  40 

43  51 

41  41 

39  19 

37  22 

35  13 

36 

40 

8120 

76  48 

72  16 

68  16 

64  16 

60  32 

57  36 

54  08 

51  28 

48  32 

46  08 

43  28 

40 

44 

87  26 

82  36 

77  45 

73  15 

69  42 

65  30 

62  16 

58  44 

55  49 

52  36 

44 

48 

92  33 

87  10 

82  56 

77  57 

74  07 

69  53 

66  24 

62  35 

48 

52 

9129 

86  59 

82  01 

77  58 

73  27 

52 

56 

90  25 

85  12 

56 

60 

60 

// 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.05 

2.88 

2.71 

2.56 

2.41 

2.27 

2.16 

2.03 

1.93 

1.82 

1.73 

1.63 

A,h 

0.484 

0.459 

0.432 

0.408 

0.382 

0.356 

0.334 

0.307 

0.285 

0.260 

0.238 

0.212 

Log. 

Log. 

30 

39 

97 

24 

02 

03 

45 

50 

56 

07 

05 

19 

Limit 

34 

35 

36 

37 

39 

40 

41 

42 

43 

44 

46 

48 

Min- 
utes 

Merid- 
ian 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/     // 

/      // 

/     // 

/     // 

/     // 

/      // 

Min. 

Min. 

4 

0  25 

0  23 

0  22 

0  21 

0  20 

0  19 

0  18 

0  17 

0  15 

0  14 

0  14 

0  13 

4 

8 

139 

134 

1  29 

124 

120 

1  15 

1  10 

1  05 

1  02 

0  58 

0  55 

0  51 

8 

12 

3  43 

3  31 

3  20 

3  08 

2  59 

2  48 

2  38 

2  28 

2  20 

2  13 

2  04 

155 

12 

16 

6  36 

6  13 

5  56 

5  36 

5  17 

5  00 

4  42 

4  24 

4  08 

3  55 

3  40 

3  25 

16 

20 

10  20 

9  44 

9  16 

8  44 

8  16 

7  48 

7  20 

6  52 

6  28 

6  08 

5  44 

5  20 

20 

24 

14  53 

14  01 

13  21 

12  35 

1154 

11  14 

10  34 

9  53 

9  18 

8  50 

8  16 

7  41 

24 

28 

20  15 

19  05 

18  10 

17  07 

16  12 

15  17 

14  22 

13  28 

12  41 

12  02 

11  14 

10  27 

28 

32 

26  27 

24  55 

23  43 

22  21 

21  10 

19  58 

18  46 

17  35 

16  34 

15  42 

14  40 

13  39 

32 

36 

33  29 

31  32 

30  02 

28  18 

26  47 

25  17 

23  46 

22  15 

20  57 

19  52 

18  35 

17  17 

36 

40 

4120 

38  56 

37  04 

34  56 

33  04 

31  12 

29  20 

27  28 

25  52 

24  32 

22  56 

21  20 

40 

44 

50  01 

47  06 

44  51 

42  16 

40  00 

37  46 

35  30 

33  14 

31  18 

29  40 

27  45 

25  49 

44 

48 

59  31 

56  04 

53  22 

50  18 

47  37 

44  55 

42  14 

39  33 

37  15 

35  20 

33  01 

30  43 

48 

52 

69  51 

65  48 

62  38 

59  02 

55  53 

52  43 

49  34 

46  25 

43  43 

41  28 

38  45    36  03 

52 

56 

8101 

76  18 

72  39 

68  28 

64  48 

61  10 

57  30 

53  50 

50  42 

48  05 

44  57 

4149 

56 

60 

93  00 

87  36 

83  24 

78  36 

74  24 

70  12 

66  00 

6148 

58  12 

55  12 

51  36 

48  00 

60 

II 

II 

II 

" 

II 

II 

II 

II 

If 

II 

II 

" 

A,h 

1.55 

1.46 

1.39 

1.31 

1.24 

1.17 

1.10 

1.03 

0.97 

0.92 

0.86 

0.80 

A,li 

Log. 

0.190 

0.164 

0.143 

0.117 

0.093 

0.068 

0.041 

0.012 

0.986 

0.963 

0.934 

0.903 

Log. 

33 

35 

01 

27 

42 

19 

39 

84 

77 

79 

50 

09 

Limit 

51 

53 

55 

57 

59 

60 

61 

63 

65 

67 

69 

71 

Min- 
utes 

Merid- 
ian 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

Latitude  25°  Declination  Contrary  Name. 
Declinations. 


161 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       II 

/     // 

1      II 

1     II 

/     // 

1     II 

/      // 

/      // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

107 

105 

102 

100 

0  59 

0  57 

0  55 

0  53 

0  52 

0  51 

0  49 

0  47 

4 

8 

4  30 

4  20 

4  10 

4  03 

3  54 

3  47 

3  41 

3  33 

3  28 

3  21 

3  16 

3  10 

8 

12 

10  06 

9  45 

9  25 

9  06 

8  47 

8  31 

8  16 

7  59 

7  47 

7  32 

7  21 

,  7  08 

12 

16 

17  58 

17  19 

16  43 

16  10 

15  37 

15  09 

14  40 

14  13 

13  49 

13  24 

13  03 

12  40 

16 

20 

28  04 

27  04 

26  08 

25  16 

24  24 

23  40 

22  56 

22  12 

21  36 

20  56 

20  24 

19  48 

20 

24 

40  25 

38  59 

37  38 

36  23 

35  09 

34  05 

33  01 

31  58 

3106 

30  09 

29  23 

28  30 

24 

28 

55  01 

53  03 

51  14 

49  32 

47  49 

46  23 

44  57 

43  31 

42  20 

4101 

39  59 

38  49 

28 

32 

71  51 

69  17 

66  54 

64  41 

62  27 

60  35 

58  43 

56  50 

55  18 

53  35 

52  13 

50  42 

32 

36 

79  04 

76  41 

74  18 

71  56 

69  59 

67  50 

66  06 

64  09 

36 

40 

9144 

88  48 

86  24 

83  44 

81  36 

79  12 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

" 

II 

II 

II 

II 

II 

II 

II 

" 

'1 

II 

A,h 

4.21 

4.06 

3.92 

3.79 

3.66 

3.55 

3.44 

3.33 

3.24 

3.14 

3.06 

2.97 

A,h 

Log. 

0.624 

0.608 

0.593 

0.578 

0.563 

0.550 

0.536 

0.522 

0.510 

0.496 

0.485 

0.472 

Log. 

28 

53 

29 

64 

48 

23 

56 

44 

55 

93 

72 

76 

Limit 

29 

30 

31 

32 

32 

33 

33 

34 

34 

35 

36 

36 

Min- 
utes 

Merid-I 

ian     1 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      II 

/     // 

/      // 

/     // 

/     // 

/     /' 

/     // 

/      // 

/     // 

/     // 

II 

/      // 

Min. 

4 

0  46 

0  45 

0  44 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

4 

8 

3  05 

3  00 

2  56 

2  51 

2  47 

2  43 

2  39 

2  35 

2  31 

2  28 

2  25 

2  21 

8 

12 

6  56 

6  46 

6  35 

6  24 

6  15 

6  06 

5  58 

5  49 

5  40 

5  32 

5  26 

5  17 

12 

16 

12  20 

12  02 

1141 

11  24 

11  09 

10  50 

10  34 

10  19 

10  04 

9  52 

9  38 

9  23 

16 

20 

19  16 

18  48 

18  16 

17  48 

17  24 

16  56 

16  32 

16  08 

15  44 

15  24 

15  04 

14  40 

20 

24 

27  45 

27  05 

26  18 

25  38 

25  04 

24  23 

23  48 

23  14 

22  40 

22  11 

2142 

2107 

24 

28 

37  46 

36  51 

35  48 

34  53 

34  06 

33  11 

32  25 

31  38 

30  50 

30  11 

29  32 

28  45 

28 

32 

49  19 

48  07 

46  46 

45  34 

44  32 

43  2ll  42  20 

41  18 

40  16 

39  25 

38  34 

37  33 

32 

36 

62  26 

60  55 

59  11 

57  41 

56  23 

54  52 

53  34 

52  16 

50  59 

49  54 

48  49 

47  31 

36 

40 

77  04 

75  12 

73  04 

71  12 

69  36 

67  44 

66  08 

64  32 

62  56 

6136 

60  16 

58  40 

40 

44 

88  24 

86  10 

84  13 

8157 

80  01 

78  05 

76  09 

74  32 

72  55 

70  59 

44 

48 

95  14 

92  56 

90  37 

88  42 

86  47 

84  29 

48 

52 

106  21 

104  06 

101  51 

99  09 

52 

56 

56 

60 

60 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.89 

2.82 

2.74 

2.67 

2.61 

2.54 

2.48 

2.42 

2.36 

2.31 

2.26 

2.20 

A,h 

Log. 

0.460 

0.450 

0.437 

0.426 

0.416 

0.404 

0.394 

0.383 

0.372 

0.363 

0.354 

0.342 

Log. 

90 

25 

75 

51 

64 

83 

45 
42 

82 
43 

91 

61 

11 

42 

Limit 

37 

38 

39 

40 

40 

41 

43 

44 

45 

46 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

152 


Latitude  25°  Declination  Qjntrary  Name. 
Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

/     // 

/     /' 

/          H 

/      // 

/     II 

/     // 

/     // 

/        n 

/      // 

/       n 

Min. 

4 

0  35 

0  34     0  33 

0  32 

0  32 

0  31 

0  30|    0  30 

0  28 

0  28 

0  27 

0  27 

4 

8 

2  17 

2  15 

2  11 

2  09 

2  06 

2  02 

2  00 

1  58 

155 

153 

1  50 

147 

8 

12 

5  09 

5  03 

4  55 

4  49 

4  44 

4  37 

4  31 

4  25 

4  19 

4  14 

4  08 

4  01 

12 

16 

9  11 

9  01 

8  45 

8  35 

8  24 

811 

8  01 

7  51 

7  41 

7  30 

7  20 

7  10 

16 

20 

14  20 

14  04 

13  40 

13  24 

13  08 

12  48 

12  32 

12  14 

12  00 

11  44 

11  28 

11  12 

20 

24 

20  39 

20  16 

19  41 

19  18 

18  44 

18  26 

18  03 

17  40 

17  17 

16  54 

16  31 

16  08 

24 

28 

28  05 

27  34 

26  47 

26  16 

25  45 

25  06 

24  34 

24  02 

23  31 

23  00 

22  29 

21  57 

28 

32 

36  41 

36  00 

34  59 

34  18 

33  38 

32  46 

32  05 

31  24 

30  43 

30  02 

29  21 

28  40 

32 

36 

46  27 

45  35 

44  17 

43  25 

42  33 

41  28 

40  37 

39  45 

38  53 

38  01 

37  09 

36  18 

36 

40 

57  20 

56  16 

54  40 

53  36 

52  32 

51  12 

50  08 

49  04 

48  00 

46  56 

45  52 

44  48 

40 

44 

69  23 

68  05 

66  09 

64  51 

63  34 

6157 

60  40 

59  22 

58  05 

56  47 

55  30 

54  13 

44 

48 

82  33 

8101 

78  43 

77  11 

75  39 

73  44 

72  11 

70  39 

69  07 

67  33 

66  01 

64  30 

48 

52 

96  53 

95  05 

92  23 

90  35 

88  47 

86  32 

84  43 

82  55 

8107 

79  19 

77  31 

75  42 

52 

56 

105  03 

102  57 

100  21 

98  15 

96  10 

94  05 

9159 

89  54 

87  49 

56 

60 

* 

110  24 

108  00 

105  36 

103  12 

100  48 

60 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.15 

2.11 

2.05 

2.01 

1.97 

1.92 

1.88 

1.84 

1.80 

1.76 

1.72 

1.68 

A,h 

0.332 

0.324 

0.311 

0.303 

'0.294 

0.283 

0.274 

0.264 

0.255 

0.245 

0.235 

0.225 

Log, 

Log. 

44 

28 

75 

20 

47 

30 

16 

82 

27 

51 

53 

31 

Limit 

47 

48 

49 

50 

51 

52 

53 

53 

54 

55 

56 

57 

Min- 
utes 

Merid- 
ian 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

/      // 
0  27 

/     // 
0  26 

0  25 

/     // 
0  25 

/      II 
0  24 

/      // 
0  23 

/     // 
0  23 

/      // 
0  22 

/     // 
0  22 

/      // 
0  22 

1     II 
0  21 

0  20 

Min. 
4 

8 

1  45 

142 

1  41 

1  39 

136 

1  35 

1  33 

130 

128 

126 

1  24 

1  22 

8 

12 

3  56 

3  50 

3  48 

3  42 

3  36 

3  32 

3  28 

3  22 

3  17 

3  13 

3  08 

3  05 

12 

16 

7  00 

6  50 

6  44 

6  34 

6  24 

6  16 

6  08 

5  58 

5  51 

5  43 

5  36 

5  27 

16 

20 

10  56 

10  40 

10  32 

10  16 

10  00 

9  48 

9  36 

9  20 

9  08 

8  56 

8  44 

8  32 

20 

24 

15  45 

15  22 

15  10 

14  47 

14  24 

14  06 

13  49 

13  26 

13  09 

12  52 

12  35 

12  17 

24 

28 

21  25 

20  54 

20  39 

20  07 

19  36 

19  13 

18  49 

18  18 

17  54 

17  30 

17  07 

16  44 

28 

32 

27  59 

27  18 

26  58 

26  17 

25  36 

25  06 

24  35 

23  54 

23  23 

22  52 

22  21 

21  51 

32 

36 

35  26 

34  34 

34  08 

33  16 

32  24 

3145 

31  06 

30  14 

29  36 

28  57 

28  18 

27  39 

36 

40 

43  44 

42  40 

42  08 

41  04 

40  00 

39  12 

38  24 

37  20 

36  32 

35  44 

34  56 

34  08 

40 

44 

52  55 

51  38 

50  59 

49  41 

48  24 

47  26 

46  27 

45  10 

44  13 

43  14 

42  16 

41  18 

44 

48 

62  58 

6126 

60  40 

59  08 

57  36 

56  27 

55  18 

53  46 

52  36 

51  27 

50  18 

49  09 

48 

52 

73  54 

72  06 

71  12 

69  24 

67  36 

66  15 

64  54 

63  06 

6144 

60  23 

59  02 

57  41 

52 

56 

85  43 

83  38 

82  35 

80  29 

78  24 

76  50 

75  15 

73  10 

71  37 

70  02 

68  28 

66  54 

56 

60. 

98  24 

96  00 

94  48 

92  24 

90  00 

88  12 

86  24 

84  00 

82  12 

80  24 

78  36 

76  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.64 

1.60 

1.58 

1.54 

1.50 

1.47 

1.44 

1.40 

1.37 

1.34 

1.31 

1.28 

A,h 

0.214 

0.204 

0.198 

0.187 

0.176 

0.167 

0.158 

0.146 

0.136 

0.127 

0.117 

0.107 

Log. 

Log. 

84 

12 

66 

52 

09 

32 

36 

13 

72 

10 

27 
67 

21 

Limit 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

68 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

Latitude  25°  Decimation  Contrary  Name. 


153 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Anglos 

Min. 

/      // 

/     /' 

/      // 

/      // 

1     It 

/        n 

/       n 

/      // 

/     // 

/        n 

/     // 

/     // 

Min. 

4 

0  20 

0  19 

0  19 

0  19 

0  19 

0  18 

0  17 

0  17 

0  16 

0  15 

0  15 

0  14 

4 

8 

120 

1  18 

1  16 

1  14 

1  12 

1  10 

1  09 

1  07 

105 

102 

1  00 

0  58 

8 

12 

2  59 

2  56 

2  51 

2  47 

2  42 

2  38 

2  34 

2  30 

2  25 

2  22 

2  17 

2  13 

12 

16 

5  17 

5  12 

5  05 

4  57 

4  50 

4  42 

4  34 

4  26 

4  19 

4  10 

4  03 

3  55 

16 

20 

8  16 

8  08 

7  56 

7  44 

7  32 

7  20 

7  08 

6  56 

6  44 

6  32 

6  20 

6  08 

20 

24 

11  54 

11  43 

11  26 

1109 

10  51 

10  34 

10  16 

9  59 

9  42 

9  24 

9  07 

8  50 

24 

28 

16  12 

15  57 

15  33 

15  09 

14  46 

14  22 

13  59 

13  35 

13  12 

12  49 

12  25 

12  02 

28 

32 

21  10 

20  49 

20  18 

19  47 

19  17 

18  46 

18  16 

17  45 

17  14 

16  44 

16  13 

15  52 

32 

36 

26  47 

26  21 

25  43 

25  04 

24  25 

23  46 

23  07 

22  28 

21  49i  21  10 

20  31 

19  52 

36 

40 

33  04 

32  32 

3144 

30  56 

30  08 

29  20 

28  32 

27  44 

26  56 

26  08 

25  20 

24  32 

40 

44 

40  00 

39  22 

38  24 

37  26 

36  28 

35  30 

34  32 

33  33 

32  35 

31  37 

30  39 

29  41 

44 

48 

47  37 

46  51 

45  41 

44  32 

43  23 

42  14 

4105 

39  56 

38  47 

37  38 

36  29 

35  20 

48 

52 

55  53 

54  59 

53  37 

52  16 

50  55 

49  34 

48  13 

46  52 

45  31 

44  10 

42  49 

4128 

52 

56 

64  48 

63  46 

62  12 

60  38 

59  04 

57  30 

55  56 

54  21 

52  47 

51  13 

49  39 

48  05 

56 

60 

74  24 

73  12 

7124 

69  36 

67  48 

66  00 

64  12 

62  24 

60  36 

.58  48 

57  00 

55  12 

60 

It 

" 

// 

// 

// 

// 

If 

II 

II 

// 

II 

II 

A,h 

1.24 

1.22 

1.19 

1.16 

1.13 

1.10 

1.07 

1.04 

1.01 

0.98 

0.95 

0.92 

A,h 

Log. 

0.093 

0.086 

0.075 

0.064 

0.053 

0.041 

0.029 

0.017 

0.004 

9.991 

9.977 

9.963 

Log. 

42 

36 

55 

46 

08 

39 

38 

03 

32 

23 

72 

79 

Limit 

69 

70 

72 

73 

74 

75 

76 

78 

79 

80 

81 

82 

Min- 
utes 

Merid- 
ian 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

Alti- 
tudes 

Declinations. 

—  Inferior  Meridlajj. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

S 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/        n 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

II 

0.89 
9.949 
39 

II 

// 

II 

// 

II 

// 

1 
II 

// 

/ 

II 

II 

II 

/ 

1 

II 

1 

1 

// 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 

36  36 

II 

0.61 

/      // 

0  09 

0  37 

1  24 

2  28 

3  52 
5  32 
7  35 
9  54 

12  32 

15  28 

18  43 

22  16 

26  09 

30  19 

34  48 
II 

0.58 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

9.785 
33 

9.763 
43 

Log. 

Limit 

83 

92 

92 

Min- 
utes 

Merid- ,      co 
ian     1      ^ 

4° 

3° 

2° 

1° 

0°    i     1° 

2° 

3° 

4° 

5° 

6° 

Alti- 
tudes 

154 


Latitude  26°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

1 1o    1  Hour 
•■•■'•      lAngles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1  ( 

4 

9  ' 
17 
26  > 
38 
52 
68 
87 

4.0 

)4 
18 
10 
12 
52 
11 
10 
17 
33 

i 

1 
4 
10 
17 
27 
40 
54 
71 
90 

II 
4.1 

// 

D7 
27 
D2 
50 
52 
08 
37 
20 
18 

3 

/     // 

1  10 
4  38 
10  25 
18  31 
28  56 
41  40 
56  42 
74  04 

II 
4.34 

1 
4 
10 
19 
30 
43 
58 
76 

II 
4.5 

// 

12 
49 
49 
15 
04 
18 
56 
58 

1 

1 
1 
5 
11 
20 
31 
45 
61 
80 

II 
4.7 

// 

15 
01 
17 
03 
20 
07 
25 
13 

0 

1 
5 
11 
20 
32 
47 
64 

II 
4.9 

// 

18 
14 
47 
57 
44 
08 
10 

I 

1 
5 

12 
21 
34 
49 
67 

II 
5.1 

22 
28 
18 
54 
12 
15 
02 

3 

/ 

1 
5 
12 
22 
35 
51 
70 

II 
5.3 

// 

26 
44 
55 
57 
52 
39 
18 

3 

/ 

1 
6 
13 
24 
37 
54 
73 

II 
5.6 

// 

31 
02 
35 
09 
44 
21 
57 

5 

t     II 

1  35 
6  21 
14  19 
25  25 
39  44 
57  13 
77  53 

II 
5.96 

/     II 

1  41 
6  44 
15  08 
26  56 
42  04 
60  35 
82  27 

II 
6.31 

1  47 
7  08 
16  03 
28  33 
44  36 
64  14 

II 
6.69 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.605 
31 

0.621 
18 

0.637 
49 

0.654 
18 

0.672 
10 

0.691 
08 

0.710 
12 

0.730 
78 

0.752 
82 

0.775 
25 

0.800 
03 

0.825 
43 

Log. 

Limit 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

21 

20 

Min- 
utes 

Merid- 
ian 

64° 

65° 

66° 

67° 

68° 

69° 

,  70° 

71° 

72° 

73° 

74° 

75° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18°  1   19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      II 

1     II 

/      // 

1     II 

1     II 

1     II 

/     // 

f          ff 

/      // 

/      II 

/      // 

/      // 

Min. 

4 

1  55 

2  03 

2  12 

2  22 

2  36 

2  52 

3  13 

3  39 

4  14 

5  02 

4 

8 

7  37 

8  09 

8  48 

9  31 

10  26 

11  31 

12  52 

14  36 

16  56 

20  09 

8 

12 

17  08 

18  20 

19  47 

21  26 

23  27 

25  54 

28  57 

32  51 

38  05 

12 

16 

30  28 

32  36 

35  09 

38  06 

41  41 

46  02 

16 

20 

47  36 

50  56 

54  56 

20 

24 

68  33 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

.  ^ 

60 

" 

II 

II 

II 

II 

11 

II 

n 

II 

II 

II 

// 

A,h 

7.14 

7.64 

8.24 

8.93 

^.11 

10.79 

12.06 

13.69 

15.87 

18.90 

A,h 

Log. 

0.853 

0.883 

0.915 

0.950 

0.989 

1.033 

1.081 

1.136 

1.200 

1.276 

Log. 

70 
19 

09 

93 

85 

89 

02 

35 

40 

58 

46 

Limit 

18 

17 

16 

15 

14 

13 

12 

11 

10 

8 

6 

Min- 
utes 

Merid- 
ian 

76^ 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

Alti- 
tudes 

Latitude  26°  Declination  Same  Name. 


155 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

II 

// 

1 

II 

// 

1 

II 

// 

II 

// 

/ 

II 

II 

// 

4 
18 
41 

II 
17.3 

38 
31 
iO 

3 

3  49 
15  16 
34  22 

II 
14.32 

3  15 
12  57 
29  08 

12.14 

2  48 
11  13 
25  13 
44  51 

10.51 

2  28 

9  51 

22  10 

39  24 

61  36 

II 
9.24 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.239 
55 

1.155 
94 

1.084 
22 

1.021 
60 

0.965 
67 

Log. 

Limit 

4 

2 

0 

2 

4 

6 

7 

8 

10 

12 

13 

15 

Min- 
utes 

Merid- 
ian 

8i 

}° 

89 

o 

90 

o 

89' 

■> 

88' 

5 

i 

\7 

3 

86 

3 

85 

5 

84 

} 

83 

3 

82 

} 

81 

3 

Alti- 
tudes 

Declinations. 


Hour       Q/ 
Angles     "^^ 

5° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min.      ' 

// 

/     II 

/      // 

/      // 

/     // 

/      // 

/     // 

/      /' 

/      // 

/      // 

/      // 

/      // 

Min. 

4          2 

11 

158 

147 

1  38 

129 

123 

1  16 

1  10 

106 

1  01 

0  57 

0  54 

4 

8         8 

46 

7  53 

7  08 

6  30 

5  58 

5  29 

5  05 

4  42 

4  23 

4  05 

3  49 

3  35 

8 

12       19 

44 

17  44 

16  03 

14  38 

13  25 

12  21 

11  26 

10  35 

9  51 

9  11 

8  36 

8  04 

12 

16       35 

04 

31  32 

28  33 

26  02 

23  51 

21  59 

20  18 

18  49 

17  33 

16  21 

15  16 

14  20 

16 

20       54 

48 

49  16 

44  36 

40  40 

37  16 

34  20 

3144 

29  24 

27  24 

25  32 

23  52 

22  24 

20 

24 

64  14 

58  34 

53  40 

49  27 

45  42 

42  20 

39  28 

36  46 

34  22 

32  16 

24 

28 

73  01 

67  17 

62  10 

57  38 

53  42 

50  03 

46  47 

43  54 

28 

32 

75  16 

70  08 

65  22 

6106 

57  20 

32 

36 

77  20 

72  35 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

It 

II 

II 

" 

II 

II 

A,h     8. 

22 

7.39 

6.69 

6.10 

5.59 

5.15 

4.76 

4.41 

4.11 

3.83 

3.58 

3.36 

A,h 

Log.      0- 

)14 

0.868 

0.825 

0.785 

0.747 

0.711 

0.677 

0.644 

0.613 

0.583 

0.553 

0.526 

87 

64 

43 

33 

41 

81 

61 

44 

84 

20 

88 

34 

Log. 

Limit       1 

6 

18 

20 

22 

23 

24 

25 

26 

27 

29 

30 

31 

Min- 
utes 

Merid-      q, 
ian         °^ 

)° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71 

o 

70° 

69° 

Alti- 
tudes 

156 


Latitude  26°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/       " 

/       n 

/     // 

/     // 

/      // 

/      // 

/      //■ 

/           // 

/     // 

/     // 

/      /' 

/      // 

Min. 

4 

0  50 

0  47 

0  44 

0  42 

0  40 

0  38 

0  35 

0  33 

0  31 

0  30 

0  28 

0  27 

4 

8 

3  21 

3  10 

2  59 

2  48 

2  39 

2  30 

2  22 

2  14 

2  05 

2  00 

153 

147 

8 

12 

7  33 

7  08 

6  42 

6  18 

5  58 

5  37 

5  18 

5  01 

4  44 

4  29 

4  14 

4  00 

12 

16 

13  27 

12  40 

1154 

11  14 

10  34 

10  00 

9  26 

8  55 

8  24 

8  00 

7  30 

7  08 

16 

20 

2100 

19  48 

18  36 

17  32 

16  32 

15  36 

14  44 

13  56 

13  08 

12  28 

1144 

1108 

20 

24 

30  15 

28  30 

26  47 

25  15 

23  48 

22  28 

21  13 

20  04 

18  44 

17  57 

16  54 

16  02 

24 

28 

4109 

38  49 

36  28 

34  22 

32  25 

30  34 

28  53 

27  19 

25  48 

24  26 

22  59 

2149 

28 

32 

53  45 

50  42 

47  37 

44  53 

42  20 

39  56 

37  43 

35  40 

33  38 

31  55 

30  02 

28  30 

32 

36 

68  03 

64  09 

60  16 

56  49 

53  34 

50  33 

47  44 

45  09 

42  33 

40  24 

38  01 

36  05 

36 

40 

84  00 

79  12 

74  24 

70  08 

66  08 

62  24 

58  56 

55  44 

52  32 

49  52 

46  56 

44  32 

40 

44 

84  52 

80  01 

75  30 

71  18 

67  26 

63  34 

60  21 

56  47 

53  54 

44 

48 

89  51 

84  52 

80  15 

75  39 

7148 

67  33 

64  07 

48 

52 

88  47 

84  16 

79  19 

75  15 

52 

56 

9159 

87  18 

56 

60 

60 

" 

n 

// 

If 

II 

II 

II 

" 

" 

II 

" 

II 

A,h 

3.15 

2.97 

2.79 

2.63 

2.48 

2.34 

2.21 

2.09 

1.97 

1.87 

1.76 

1.67 

A,h 

Log. 

0.498 

0.472 

0.445 

0.419 

0.394 

0.369 

0.344 

0.320 

0.294 

0.271 

0.245 

0.222 

Log. 

31 

76 

60 

96 

45 

22 

39 

15 

47 

84 

51 

72 

Limit 

33 

34 

35 

36 

38 

39 

40 

42 

43 

44 

46 

48 

Min- 
utes 

Merid- 
ian 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/      /' 

/      // 

1     II 

/     II 

/     II 

f     II 

Min. 

Min. 

4 

0  25 

0  23 

0  22 

0  21 

0  20 

0  19 

0  18 

0  17 

0  15 

0  15 

0  14 

0  13 

4 

8 

141 

136 

130 

125 

1  21 

1  16 

1  11 

107 

102 

0  59 

0  55 

0  51 

8 

12 

3  48 

3  35 

3  23 

3  11 

3  02 

2  51 

2  41 

2  31 

2  22 

2  14 

2  05 

156 

12 

16 

6  44 

6  21 

6  01 

5  41 

5  22 

5  05 

4  47 

4  29 

4  10 

3  58 

3  43 

3  28 

16 

20 

10  32 

9  56 

9  24 

8  52 

8  24 

7  56 

7  28 

7  00 

6  32 

6  12 

5  48 

5  24 

20 

24 

15  10 

14  18 

13  32 

12  46 

12  06 

1126 

10  46 

10  05 

9  24 

8  55 

8  21 

7  47 

24 

28 

20  39 

19  29 

18  26 

17  23 

16  28 

15  33 

14  38 

13  43 

12  49 

12  10 

1122 

10  35 

28 

32 

26  58 

25  26 

24  04 

22  42 

2130 

20  18 

19  06 

17  55 

16  44 

15  53 

14  51 

13  49 

32 

36 

34  08 

32  11 

30  27 

28  44 

27  13 

25  43 

24  12 

22  41 

21  10 

20  05 

18  48 

17  30 

36 

40 

42  08 

39  44 

37  36 

35  28 

33  36 

31  44 

29  52 

28  00 

26  08 

24  48 

23  12 

2136 

40 

44 

50  59 

48  04 

45  29 

42  55 

40  39 

38  24 

36  09 

33  53 

3137 

30  00 

28  05 

26  08 

44 

48 

60  40 

57  13 

54  09 

51  04 

48  23 

45  41 

43  00 

40  19 

37  38 

35  43 

33  24 

3106 

48 

52 

71  12 

67  09 

63  33 

59  56 

56  47 

53  37 

50  28 

47  19 

44  10 

4155 

39  12 

36  30 

52 

56 

82  35 

77  52 

73  41 

69  31 

65  51 

62  12 

58  33 

54  53 

51  13 

48  36 

45  29 

42  20 

56 

60 

94  48 

89  24 

84  36 

79  48 

75  36 

7124 

6712 

63  00 

58  48 

55  48 

52  12 

48  36 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

A,h 

1.58 

1.49 

1.41 

1.33 

1.26 

1.19 

1.12 

1.05 

0.98 

0.93 

0.87 

0.81 

A,h 

Log. 

0.198 

0.173 

0.149 

0.123 

0.100 

0.075 

0.049 

0.021 

9.991 

9.968 

9.939 

9.908 

Log. 

66 

19 

22 

85 

37 

55 

22 

19 

23 

48 

52 

49 

Limit 

50 

52 

54 

56 

58 

59 

60 

62 

64 

66 

68 

70 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

Alti- 
tudes 

Latitude  26°  Decimation  Contrary  Name. 


157 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

>        n 

/     // 

/     // 

/     // 

/      // 

f     II 

/     // 

1     II 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

104 

1  02 

1  00 

0  59 

0  56 

0  54 

0  53 

0  51 

0  50 

0  49 

0  47 

0  46 

4 

8 

4  18 

4  09 

4  01 

3  53 

3  45 

3  39 

3  32 

3  26 

3  20 

3  15 

3  09 

3  04 

8 

12 

9  40 

9  20 

9  02 

8  44 

8  27 

8  11 

7  56 

7  44 

7  30 

7  18 

7  07 

6  55 

12 

16 

17  12 

16  36 

16  02 

15  32 

15  01 

14  33 

14  08 

13  44 

13  22 

12  58 

12  37 

12  17 

16 

20 

26  52 

25  56 

25  04 

24  16 

23  28 

22  44 

22  04 

21  28 

20  52 

20  16 

19  44 

19  12 

20 

24 

38  41 

37  21 

36  06 

34  57 

33  48 

32  44 

3147 

30  55 

30  03 

29  11 

28  25 

27  39 

24 

28 

52  40 

50  50 

49  08 

47  33 

46  00 

44  34 

43  15 

42  05 

40  54 

39  43 

38  41 

37  38 

28 

32 

68  47 

66  23 

64  10 

62  07 

60  04 

58  12 

56  29 

54  57 

53  25 

51  53 

50  31 

49  09 

32 

36 

78  38 

76  02 

73  39 

7130 

69  33 

67  37 

65  40 

63  56 

62  13 

36 

40 

90  56 

88  16 

85  52 

83  28 

8104 

78  56 

76  48 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

" 

II 

" 

" 

II 

II 

II 

II 

II 

II 

A,h 

4.03 

3.89 

3.76 

3.64 

3.52 

3.41 

3.31 

3.22 

3.13 

3.04 

2.96 

2.88 

A,h 

Log. 

0.605 

0.589 

0.575 

0.561 

0.546 

0.532 

0.519 

0.507 

0.495 

0.482 

0.471 

0.459 

Log. 

31 

95 

19 

10 

54 

75 

83 

86 

54 

87 

29 

39 

Limit 

30 

31 

32 

33 

34 

34 

35 

35 

'36 

38 

37 

37 

Min- 
utes 

Merid- 
ian 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/     // 

/     // 

/     // 

/     // 

/      II 

/     // 

1     II 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  45 

0  43 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

4 

8 

2  59 

2  55 

2  50 

2  46 

2  43 

2  39 

2  35 

2  31 

2  28 

2  24 

2  21 

2  17 

8 

12 

6  43 

6  33 

6  23 

6  14 

6  06 

5  56 

5  49 

5  40 

5  32 

5  24 

5  17 

5  09 

12 

16 

1157 

1139 

1121 

1106 

10  50 

10  32 

10  19 

10  04 

9  52 

9  36 

9  23 

9  11 

16 

20 

18  40 

18  12 

17  44 

17  20 

16  56 

16  28 

16  08 

15  44 

15  24 

15  00 

14  40 

14  20 

20 

24 

26  53 

26  12 

25  33 

24  58 

24  23 

23  42 

23  14 

22  40 

22  11 

2136 

2107 

20  39 

24 

28 

36  35 

35  41 

34  45 

33  58 

33  1] 

32  17 

3138 

30  50 

30  11 

29  24 

28  45 

28  05 

28 

32 

47  47 

46  36 

45  23 

44  22 

43  21 

42  10 

41  18 

40  16 

39  25 

38  24 

37  33 

36  41 

32 

36 

60  29 

58  58 

57  28 

56  10 

54  52 

53  21 

52  16 

50  59 

49  54 

48  36 

47  31 

46  27 

36 

40 

74  40 

72  48 

70  56 

69  20 

67  44 

65  52 

64  32 

62  56 

6136 

60  00 

58  40 

57  20 

40 

44 

88  05 

85  50 

83  54 

8157 

79  42 

78  05 

76  09 

74  32 

72  36 

70  59 

69  23 

44 

48 

99  50 

97  32 

94  51 

92  56 

90  37 

88  42 

86  24 

84  29 

82  33 

48 

52 

106  21 

104  06 

101  24 

99  09 

96  53 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.80 

2.73 

2.66 

2.60 

2.54 

2.47 

2.42 

2.36 

2.31 

2.25 

2.20 

2.15 

Ajh 

Log. 

0.447 

0.436 

0.424 

0.414 

0.404 

0.392 

0.383 

0.372 

0.363 

0.352 

0.342 

0.332 

Log. 

16 

16 

88 

97 

83 

70 

82 

91 

61 

18 

42 

44 

Limit 

38 

39 

40 

41 

41 

42 

43 

43 

44 

45 

46 

47 

Min- 
utes 

Merid- 
ian 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

Alti- 
tudes 

158 


Latitude  26°  Declination  Contrary  Nanie« 


Dkclinatioxs. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      " 

/      '/ 

/      // 

/      // 

/      II 

/      /' 

/      II 

/     // 

/     // 

/     // 

/      // 

/     // 

Min. 

4 

0  34 

0  33 

0  32 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

0  27 

4 

8 

2  14 

2  12 

2  09 

2  05 

2  03 

2  00 

158 

1  56 

1  53 

1  50 

148 

145 

8 

12 

5  02 

4  57 

4  49 

4  44 

4  38 

4  31 

4  26 

4  20 

4  14 

4  08 

4  03 

3  57 

12 

16 

8  58 

8  47 

8  35 

8  24 

8  14 

8  01 

7  54 

7  44 

7  30 

7  20 

7  13 

7  03 

16 

20 

14  00 

13  44 

13  24 

13  08 

12  52 

12  32 

12  20 

12  04 

11  44 

11  28 

11  16 

1100 

20 

24 

20  10 

19  47 

19  18 

18  44 

18  31 

18  03 

17  46 

17  23 

16  54 

16  31    16  14 

15  51 

24 

28 

27  26 

26  55 

26  16 

25  45 

25  14 

24  34 

24  10 

23  39 

23  00 

22  29;  22  05 

21  33 

28 

32 

35  50 

35  09 

34  18 

33  38 

32  57 

32  05 

31  34 

30  53 

30  02 

29  21'  28  50 

28  09 

32 

36 

45  22 

44  30 

43  25 

42  33 

41  41 

40  37 

39  58 

39  06 

38  01 

37  09    36  31 

35  39 

36 

40 

56  00 

54  56 

53  36 

52  32 

51  28 

50  08 

49  20 

48  16 

46  56 

45  52    45  04 

44  00 

40 

44 

67  46 

66  28 

64  51 

63  34 

62  16 

60  40 

59  42 

58  24 

56  47 

55  30l  54  32 

53  15 

44 

48 

80  38 

79  06 

77  11 

75  39 

74  07 

72  11 

71  02 

69  30 

67  33 

66  01,  64  53 

63  21 

48 

52 

94  38 

92  50 

90  35 

88  47 

86  59 

84  43 

83  22 

81  34 

79  19 

77  31 

76  09 

74  21 

52 

56 

109  46 

107  40 

105  03 

102  58 

100  52 

98  15 

96  42 

94  36 

91  59 

89  54 

88  20 

86  15 

56 

60 

118  12 

115  48 

II 

112  48 

111  00 

108  36 
II 

105  36 

II 

103  12 

101  24 

II 

99  00 
II 

60 

A,h 

2.10 

2.06 

2.01 

1.97 

1.93 

1.88 

1.85 

1.81 

1.76 

1.72 

1.69 

1.65 

A,h 

Log. 

0.323 

0.313 

0.303 

0.294 

0.285 

0.274 

0.267 

0.257 

0.245 

0.235 

0.227 

0.217 

Log. 

22 

87 

20 

47 

56 

16 

17 

68 

51 

53 

89 

48 

Limit 

48 

49 

50 

51 

51 

52 

53 

53 

54 

55 

56 

57 

Min- 
utes 

Merid- 
ian 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/      // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  26 

0  25 

0  25 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

4 

8 

1  42 

141 

139 

136 

1  35 

133 

130 

1  28 

126 

1  24 

123 

121 

8 

12 

3  51 

3  48 

3  43 

3  37 

3  34 

3  29 

3  23 

3  19 

3  14 

3  10 

3  06 

3  02 

12 

16 

6  53 

6  44 

.    6  37 

6  27 

6  18 

6  11 

6  01 

5  53 

5  46 

5  38 

5  30 

5  22 

16 

20 

10  44 

10  32 

10  20 

10  04 

9  52 

9  40 

9  24 

9  12 

9  00 

8  48 

8  36 

8  24 

20 

24 

15  28 

15  10 

14  53 

14  30 

14  12 

13  55 

13  32 

13  15 

12  58 

12  41 

12  23 

12  06 

24 

28 

2102 

20  39 

20  15 

19  44 

19  21 

18  57 

18  26 

18  02 

17  38 

17  15 

16  52 

16  28 

28 

32 

27  28 

26  58 

26  27 

25  46 

25  16 

24  45 

24  04 

23  33 

23  02 

22  31 

22  01 

2130 

32 

36 

34  47 

34  08 

33  29 

32  37 

3158 

31  19 

30  27 

29  49 

29  10 

28  31 

27  52 

27  13 

36 

40 

42  56 

42  08 

41  20 

40  16 

39  28 

38  40 

37  36 

36  48 

36  00 

35  12 

34  24 

33  36 

40 

44 

5157 

50  59 

50  01 

48  43 

47  45 

46  47 

45  29 

44  32 

43  34 

42  36 

4137 

40  39 

44 

48 

6149 

60  40 

59  31 

57  59 

56  50 

55  41 

54  09 

52  59 

5150 

50  41 

49  32 

48  23 

48 

52 

72  33 

71  12 

69  51 

68  03 

66  42 

65  21 

63  33 

62  11 

60  50 

59  29 

58  08 

56  47 

52 

56 

84  09    82  35 

8101 

78  55 

77  21 

75  47 

73  41 

72  08 

70  34 

69  00 

67  25 

65  51 

56 

60 

96  36 

94  48 

93  00 

90  36 

88  48 

87  00 

84  36 

82  48 

8100 

79  12 

77  24 

75  36 

60 

// 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

1.61 

1.58 

1.55 

1.51 

1.48 

1.45 

1.41 

1.38 

1.35 

1.32 

1.29 

1.26 

A,h 

0.206 

0.198 

0.190 

0.178 

0.170 

0.161 

0.149 

0.139 

0.130 

0.120 

0.110 

0.100 

Log. 

Log. 

83 

66 

33 

98 

26 

37 

22 

88 

33 

57 

59 

37 

Limit 

58 

59 

60 

61 

62 

63 

64 

65 

66 

66 

67 

68 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

Alti- 
tudes 

Latitude  26''  Declination  Contrary  Name. 


159 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Anglea 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/  // 

0  20 

1  19 

2  57 
5  15 
8  12 

11  48 
16  05 
21  00 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 
73  48 

1.23 

/   // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
II 

1.20 

/  // 

0  19 
115 

2  48 
5  00 
7  48 
11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

II 

1.17 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
II 

1.14 

0  18 

1  11 

2  39 
4  45 

7  24 
10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

/  // 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 
II 

1.08 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 
II 

1.05 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

II 

1.02 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

II 

1.00 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

/  II 

0  15 

1  00 

2  16 
4  00 
6  16 
9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
II 

0.94 

/  // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 
15  32 
19  39 
24  16 
29  21 
34  57 
41  01 
47  33 
54  36 

0.91 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.089 
91 

0.079 
18 

0.068 
19 

0.056 
90 

0.045 
32 

0.033 
42 

0.021 
19 

0.008 
60 

0.00 

9.986 
77 

9:973 
13 

9.959 
04 

Log. 

Limit 

69 

70 

72 

73 

74 

75 

76 

78 

79 

80 

81 

82 

Min- 
utes 

Merid- 
ian 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridlajj. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

/ 

// 

II 

1 

// 

1 

II 

1 

1 

// 

II 

// 

1 

II 

1 

II 

/  // 

0  10 

0  40 

1  30 

2  42 
4  12 
6  03 
8  14 

10  45 
13  37 
16  48 
20  20 
24  11 
28  23 
32  56 
37  48 

0.63 

/  // 

0  10 

0  39 

1  27 

2  37 

4  04 

5  52 
7  58 

10  24 

13  11 

16  16 

19  41 

23  25 

27  29 

31  53 

36  36 
II 

0.61 

/  // 

0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 
35  24 

0.59 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.799 
34 

9.785 
33 

92 

9.770 
85 

Log. 

Limit 

91 

93 

Min- 
utes 

Merid- 
ian 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

Alti- 
tudes 

160 


Latitude  27°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angle? 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

102 
4  06 
9  14 
16  26 
25  40 
36  58 
50  18 
65  42 

II 
3.85 

1 
4 
9 
1-7 
26 
38 
52 
68 

II 
3.9 

// 

03 
15 
35 
01 
36 
18 
09 
06 

1 

1 

4 

9 
17 
27 
39 
54 
70 

II 
4.1^ 

// 

37 
25 
56 
iO 
36 
i5 
35 
39 

I 

/ 

1 

4 
10 
18 
28 
41 
56 
73 

II 
4.3{ 

09 
35 
19 
21 
iO 
17 
11 
23 

) 

1 

1 
4 
10 
19 
29 
42 
58 
76 

4.4 

// 

11 

47 
44 
04 
48 
53 
25 
18 

r 

1 

4 
11 
19 
31 
44 
60 
79 

II 
4.6. 

// 

15 
57 
09 
51 
00 
39 
45 
21 

5 

1 

1 

5 
11 
20 
32 
46 
63 
82 

4.8( 

// 

18 
11 
40 
44 
24 
40 
30 
56 

5 

/ 

1 

5 
12 
21 
33 
48 
66 

II 
5.0i 

// 

21 
25 
12 
40 
52 
46 
23 

3 

125 
5  40 
12  46 
22  42 
35  28 
5105 
69  31 

II 
5.32 

/     // 

1  29 
5  58 
13  25 
23  51 
37  16 
53  40 
73  01 

II 
5.59 

1     II 

134 
6  17 
14  08 
25  08 
39  16 
56  33 
76  58 

II 
5.89 

/      // 

1  39 
6  39 
14  57 
26  35 
4132 
59  48 
8125 

II 
6.23 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.585 
46 

0.600 
97 

0.617 
00 

0.633 

47 

0.650 
31 

0.667 
45 

0.686 
64 

0.705 
86 

0.725 
91 

0.747 
41 

0.770 
12 

0.794 
49 

Log. 

Limit 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

22 

21 

Min- 
utes 

Merid- 
ian 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     /' 

/     // 

Min. 

Min. 

4 

146 

153 

2  01 

2  10 

2  21 

2  34 

2  51 

3  10 

3  35 

4  11 

4  58 

4 

8 

7  03 

7  31 

8  03 

8  40 

9  24 

10  16 

1121 

12  41 

14  24 

16  40 

19  51 

8 

12 

15  51 

16  55 

18  07 

19  30 

2108 

23  06 

25  32 

28  32 

32  23 

37  30 

12 

16 

28  13 

30  05 

32  13 

34  42 

37  36 

41  06 

45  24 

16 

20 

44  04 

47  00 

50  20 

54  12 

20 

24 

63  28 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

" 

" 

n 

" 

II 

II 

II 

A,h 

6.61 

7.05 

7.55 

8.13 

8.81 

9.63 

10.64 

11.89 

13.49 

15.63 

18.61 

A,h 

Log. 

0.820 

0.848 

0.877 

0.910 

0.944 

0..983 

1.026 

1.075 

1.130 

1.193 

1.269 

Log. 

20 

19 

95 

09 

98 

63 

94 

18 

01 

96 

75 

Limit 

20 

19 

18 

17 

16 

15 

14 

13 

11 

10 

9 

8 

Min- 
utes 

Merid- 
ian 

75 

0 

76 

0 

77 

0 

78 

3 

79 

0 

80 

3 

81 

3 

82 

3 

83° 

84 

3 

85 

3 

86 

3 

Alti- 
tudes 

Latitude  27°  Declination  Same  Name. 

Declinations. 


161 


"Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

II 

// 

/ 

// 

// 

II 

// 

II 

// 

1 

II 
II 

II 

// 

II 

// 

II 

// 

/     // 

4  32 
18  09 
40  51 

II 
17.02 

/       n 

3  44 
14  59 
33  42 

II 
14.04 

3  10 
12  41 
28  34 

II 
11.90 

/      // 

2  45 
10  59 
24  43 
43  57 

II 
10.30 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.230 
96 

1.147 
37 

1.075 
55 

1.012 
84 

Log. 

Limit 

6 

4 

2 

0 

2 

4 

5 

7 

9 

11 

12 

13 

Min- 
utes 

Merid- 
ian 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/     // 

/      // 

/     // 

/     // 

/      // 

/      // 

Min. 

Min. 

4 

2  25 

2  09 

155 

145 

135 

127 

120 

1  15 

109 

104 

100 

0  55 

4 

8 

9  39 

8  35 

7  43 

6  59 

6  21 

5  50 

5  21 

4  57 

4  35 

6  16 

4  00 

3  44 

8 

12 

2143 

19  19 

17  21 

15  42 

14  19 

13  07 

12  03 

1108 

10  19 

9  36 

8  57 

8  23 

12 

16 

38  37 

34  21 

30  51 

27  54 

25  25 

23  17 

2125 

19  48 

18  21 

17  04 

15  55 

14  53 

16 

20 

48  12 

43  36 

39  44 

36  24 

33  28 

30  56 

28  40 

26  40 

24  52 

23  16 

20 

24 

62  47 

5713 

52  25 

48  12 

44  33 

41  17 

38  24 

35  48 

33  30 

24 

28 

7121 

65  36 

60  37 

56  11 

52  16 

48  45 

45  37 

28 

32 

73  23 

68  16 

63  40 

59  34 

32 

36 

75  23 

36 

40 

. . 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

9.05 

8.05 

7.23 

6.54 

5.96 

5.46 

5.02 

4.6 

t 

4.30 

4.00 

3.73 

3.49 

A,h 

Log. 

0.956 

0.905 

0.859 

0.815 

0.775 

0.737 

0.700 

0.6 

56 

0.633 

0.602 

0.571 

0.542 

Log. 

65 

80 

14 

58 

25 

19 

70 

52 

47 

06 

71 

83 

Limit 

14 

15 

17 

19 

21 

23 

24 

25 

26 

28 

29 

30 

Min- 
utes 

Merid- 
ian 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

Alti- 
tudes 

162 


Latitude  27°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/       // 

/     // 

/      // 

/      // 

/     // 

/      // 

1     II 

/      // 

Min. 

4 

0  52 

0  49 

0  46 

0  43 

0  41 

0  38 

0  36 

0  35 

0  32 

0  30 

0  29 

0  27 

4 

8 

3  30 

3  16 

3  04 

2  54 

2  43 

2  34 

2  26 

2  17 

2  09 

2  02 

155 

149 

8 

12 

7  51 

7  21 

6  55 

6  30 

6  07 

5  46 

5  27 

5  08 

4  51 

4  35 

4  19 

4  05 

12 

16 

13  57 

13  03 

12  17 

11  34 

10  53 

10  14 

9  41 

9  08 

8  37 

8  09 

7  41 

7  15 

16 

20 

2148 

20  24 

19  12 

18  64 

17  00 

16  00 

15  08 

14  16 

13  28 

12  44 

12  00 

11  20 

20 

24 

31  23 

29  23 

27  39 

26  01 

24  29 

23  02 

21  47 

20  33 

19  24 

18  20 

17  17 

16  19 

24 

28 

42  44 

39  59 

37  38 

35  25 

33  19 

31  22 

29  40 

27  57 

26  24 

24  58 

23  31 

22  13 

28 

32 

55  49 

52  13 

49  09 

46  15 

43  31 

40  58 

38  45 

36  31 

34  28 

32  36 

30  43 

29  01 

32 

36 

70  38 

66  06 

62  13 

58  32 

55  05 

51  50 

49  02 

46  14 

43  38 

41  15 

38  53 

36  43 

36 

40 

81  36 

76  48 

72  16 

68  00 

64  00 

60  32 

57  04 

53  52 

50  56 

48  00 

45  20 

40 

44 

82  17 

77  26 

73  15 

69  03 

65  11 

6137 

58  05 

54  51 

44 

48 

87  10 

82  10 

77  34 

73  21 

69  07 

65  15 

48 

52 

86  05 

8107 

76  37 

52 

56 

88  51 

56 

60 

60 

ti 

II 

" 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.27 

3.06 

2.88 

2.71 

2.55 

2.40 

2.27 

2.14 

2.02 

1.91 

1.80 

1.70 

A,h 

Log. 

0.514 

0.485 

0.459 

0.432 

0.406 

0.380 

0.356 

0.33i 

0.305 

0.281 

0.255 

0.230 

Log. 

55 

72 

39 

97 

54 

21 

03 

41 

35 

03 

27 

45 

Limit 

32 

33 

34 

35 

37 

38 

39 

41 

42 

43 

45 

47 

Min- 
utes 

Merid- 
ian 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  26 

142 

3  51 

6  53 

10  44 

15  28 

21  02 

27  28 

34  47 

42  56 

51  57 

61  49 

72  33 

84  09 

96  36 
II 

1.61 

/     // 

0  24 

138 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 

II 

1.52 

/      // 

0  22 

132 

3  24 

6  11 

9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

/     // 

0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

81  00 
II 

1.35 

0  20 
121 
3  03 
5  25 

8  28 
12  11 
16  36 
21  41 
27  26 
33  52 
40  59 
48  46 
57  14 
66  23 

76  12 

II 

1.27 

/     // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
II 

1.20 

/      // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 
67  48 

1.13 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
II 

1.06 

/      // 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
II 

1.00 

/      // 

0  15 

1  00 

2  16 
4  00 
6  16 
9  01 

12  17 
16  03 
20  18 
25  04 
30  19 
36  06 
42  22 
49  07 

56  24 

II 

0.94 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 
II 

0.82 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.206 
83 

0.181 
84 

51 

0.155 
34 

0.130 
33 

0.103 
80 

0.079 
18 

0.053 
08 

0.025 
31 

0.00 

9.973 
13 

9.944 
48 

9.913 
81 

Log. 

Limit 

49 

53 

55 

57 

58 

59 

61 

63 

65 

67 

69 

Min- 
utes 

Merid- 
ian 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

Latitude  27°  Declination  Contrary  Name. 


163 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/   n 

/   // 

1      " 

t     II 

Min. 

Min. 

4 

102 

0  59 

0  58 

0  55 

0  54 

0  52 

0  51 

0  50 

0  48 

0  47 

0  46 

0  44 

4 

8 

4  06 

4  00 

3  51 

3  44 

3  37 

3  31 

3  24 

3  19 

3  13 

3  08 

3  03 

2  59 

8 

12 

9  14 

8  57 

8  39 

8  23 

8  08 

7  54 

7  39 

7  27 

7  15 

7  04 

6  52 

6  42 

12 

16 

16  26 

15  55 

15  25 

14  53 

14  28 

14  02 

13  37 

13  17 

12  53 

12  32 

12  12 

11  54 

16 

20 

25  40 

24  52 

24  04 

23  16 

22  36 

2156 

21  16 

20  44 

20  08 

19  36 

19  04 

18  36 

20 

24 

36  58 

35  48 

34  40 

33  30 

32  33 

31  35 

30  38  29  52 

29  00 

28  13 

27  28 

26  47 

24 

28 

50  18 

48  45 

47  10 

45  37 

44  18 

43  00 

41  41 

40  38 

39  28 

38  25 

37  22 

36  28 

28 

32 

65  42 

63  40 

61  36 

59  34 

57  51 

56  09 

54  26 

53  04 

51  32 

50  11 

48  48 

47  37 

32 

36 

77  59 

75  23 

73  14 

7104 

68  55 

67  11 

65  14 

63  30 

61  47 

60  16 

36 

40 

90  24 

87  44 

85  04 

82  56 

80  32 

78  24 

76  16 

74  24 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

It 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.85 

3.73 

3.61 

3.49 

3.39 

3.29 

3.19 

3.11 

3.02 

2.94 

2.86 

2.79 

A,h 

Log. 

0.585 

0.571 

0.557 

0.542 

0.530 

0.517 

0.503 

0.492 

0.480 

0.468 

0.456 

0.445 

Log. 

46 

71 

51 

83 

20 

20 

79 

76 

01 

35 

37 

60 

Limit 

30 

31 

32 

33 

34 

35 

35 

36 

37 

38 

38 

39 

Min- 
utes 

Merid- 
ian 

63= 

62^ 

) 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

Alti- 
tudes 

Decx,inations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  /' 

/  // 

1     II 

1     II 

/  II 

/  // 

/  // 

/  // 

1     II 

Min. 

4 

0  43 

0  43 

0  41 

0  40 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  34 

4 

8 

2  54 

2  49 

2  46 

2  42 

2  39 

2  35 

2  30 

2  27 

2  24 

2  21 

2  17 

2  14 

8 

12 

6  32 

6  21 

6  13 

6  04 

5  56 

5  47 

5  38 

5  31 

5  24 

5  17 

5  09 

5  02 

12 

16 

11  36 

11  19 

11  03 

10  48 

10  32 

10  17 

10  02 

9  49 

9  36 

9  23 

9  11 

8  58 

16 

20 

18  08 

17  40 

17  16 

16  52 

16  28 

16  04 

15  40 

15  20 

15  00 

14  40 

14  20 

14  00 

20 

24 

26  07 

25  27 

24  52 

24  17 

23  42 

23  08 

22  34 

22  05 

2136 

2107 

20  39 

20  10 

24 

28 

35  33 

34  37 

33  51 

33  04 

32  17 

3130 

30  42 

30  03 

29  24 

28  45 

28  05 

27  26 

28 

32 

46  25 

45  13 

44  12 

43  11 

42  10 

41  08 

40  06 

39  15 

38  24 

37  33 

36  41 

35  50 

32 

36 

58  45 

57  15 

55  57 

54  39 

53  21 

52  03 

50  46 

49  41 

48  36 

47  31 

46  27 

45  22 

36 

40 

72  32 

70  40 

69  04 

67  28 

65  52 

64  16 

62  40 

61  20 

60  00 

58  40 

57  20 

56  00 

40 

44 

87  46 

85  31 

83  34 

8138 

79  42 

77  45 

75  50 

74  13 

72  36 

70  59 

69  23 

67  46 

44 

48 

94  51 

92  33 

90  14 

88  19 

86  24 

84  29 

82  33 

80  38 

48 

52 
56 

105  54 

103  39 

10124 

99  09 

96  53 

94  38 

52 

60 

II 

II 

II 

II 

II 

If 

II 

II 

II 

II 

II 

II 

A,h 

2.72 

2.65 

2.59 

2.53 

2.47 

2.41 

2.35 

2.30 

2.25 

2.20 

2.15 

2.10 

A 

Log. 

0.434 

0.423 

0.413 

0.403 

0.392 

0.382 

0.371 

0.361 

0.352 

0.342 

0.332 

0.322 

57 

25 

30 

12 

70 

02 

07 

73 

18 

42 

44 

22 

Log. 

Limit 

39 

40 

41 

42 

42 

43 

44 

45 

45 

46 

47 

48 

Min- 
utes 

Merid- 
ian 

51« 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

Alti- 
tudes 

164 


Latitude  27°  Declination  Contrary  Name* 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/       n 

/          H 

/       n 

/     II 

'         H 

/     II 

/     // 

/       n 

/       n 

/       n 

/       n 

/     It 

Min. 

4 

0  33 

0  32]     0  31 

0  30 

0  30'    0  30 

0  29 

0  28 

0  27 

0  27 

0  27 

0  26 

4 

8 

2  12 

2  09 

2  05 

2  03 

2  01      158 

1  56 

1  54 

151 

148 

1  46 

143 

8 

12 

4  57 

4  49 

4  44 

4  38 

4  32     4  26 

4  20 

4  16 

4  09 

,     4  03 

3  59 

3  53 

12 

16 

8  47 

8  35 

8  24 

8  14 

8  04!     7  54 

7  44 

7  33 

7  23 

1     7  13 

7  05 

6  55 

16 

20 

13  44 

13  24 

13  08 

12  52 

12  36    12  20 

12  04 

11  48 

11  32 

11  16 

11  04 

10  48 

20 

24 

19  47 

19  18 

18  44 

18  31 

18  09    17  46 

17  23 

16  59 

16  36 

16  14 

15  57 

15  34 

24 

28 

26  55 

26  16 

25  45 

25  14 

24  42    24  10 

23  39 

23  08 

22  37 

22  05 

21  41 

21  10 

28 

32 

35  09 

34  18 

33  38 

32  57 

32  15    31  34 

30  53 

30  13 

29  32 

28  50 

28  19 

27  38 

32 

36 

44  30 

43  25 1  42  33 

41  41 

40  50'  39  58 

39  06 

38  14 

37  22 

36  31 

35  52 

35  00 

36 

40 

54  56 

53  36 

52  32 

5128 

50  24    49  20 

48  16 

47  12 

46  08 

45  04 

44  16 

43  12 

40 

44 

66  28 

64  51 

63  34 

62  16 

60  59    59  42 

58  24 

59  07 

55  49 

54  32 

53  34 

52  17 

44 

48 

79  06 

77  11 

75  39 

74  07 

72  34    71  02 

69  30 

67  56 

66  24 

64  53 

63  44 

62  12 

48 

52 

92  50 

90  35 

88  47 

86  59 

85  10    83  22 

81  34 

79  46 

77  58 

76  09 

74  48 

73  00 

52 

56 

98  47    96  42 

94  36 

92  31 

90  25 

88  20 

86  46 

84  11 

56 

60 

103  48 

101  24 

99  36 

97  12 

60 

" 

// 

// 

II 

// 

II 

II 

II 

II 

n 

II 

II 

A,h 

2.06 

2.01 

1.97 

1.93 

1.89 

1.85 

1.81 

1.77 

1.73 

1.69 

1.66 

1.62 

A,h 

Log. 

0.313 

0.303    0.294 

0.285   0.276 

0.267 

0.257 

0.247 

0.238 

0.227 

0.220 

0.209 

Log. 

87 

20 

47 

56 

46 

17 

68 

97 

05 

89 

11 

52 

Limit 

49 

50 

51 

52 

53 

53 

54 

54 

55 

56 

57 

58 

Min- 
utes 

Merid- 
ian 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  25 

0  25 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

0  20 

4 

8 

141 

139 

137 

136 

134 

1  31 

129 

127 

125 

123 

1  21 

120 

8 

12 

3  48 

3  43 

3  39 

3  35 

3  31 

3  25 

3  20 

3  16 

3  11 

3  07 

3  03 

2  59 

12 

16 

6  44 

6  37 

6  29 

6  21 

6  13 

6  03 

5  56 

5  48 

5  41 

5  33 

5  25 

5  17 

16 

20 

10  32 

10  20 

10  08 

9  56 

9  44 

9  28 

9  16 

9  04 

8  52 

8  40 

8  28 

8  16 

20 

24 

15  10 

14  53 

14  36 

14  18 

14  01 

13  38 

13  21 

13  04 

12  46 

12  29 

12  11 

1154 

24 

28 

20  39 

20  15 

19  52 

19  29 

19  05 

18  34 

18  10 

17  46 

17  23 

16  59 

16  36 

16  12 

28 

32 

26  58 

26  27 

25  56 

25  26 

24  55 

24  14 

23  43 

23  12 

22  42 

22  11 

21  41 

21  10 

32 

36 

34  08 

33  29 

32  50 

32  11 

3132 

30  40 

30  02 

29  23 

28  44 

28  05 

27  26 

26  47 

36 

40 

42  08 

41  20 

40  32 

39  44 

38  56 

37  52 

37  04 

36  16 

35  28 

34  40 

33  52 

33  04 

40 

44 

50  59 

50  01 

49  03 

48  04 

47  06 

45  49 

44  51 

43  53 

42  55 

41  57 

40  59 

40  00 

44 

48 

60  40 

59  31 

58  22 

57  13 

56  04 

54  32 

53  22 

52  13 

51  04 

49  55 

48  46 

47  37 

48 

52 

71  12 

69  51 

68  30 

67  09 

65  48 

64  00 

62  38 

61  17 

59  56 

58  35 

57  14 

55  53 

52 

56 

82  35 

81  01 

79  27 

77  52 

76  18 

74  13 

72  39 

7105 

69  31 

67  57 

66  23 

64  48 

56 

60 

94  48 

93  00 

91  12 

89  24 

87  36 

85  12 

83  24 

8136 

79  48 

78  00 

76  12 

74  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

" 

" 

II 

II 

A,h 

1.58 

1.55 

1.52 

1.49 

1.46 

1.42 

1.39 

1.36 

1.33 

1.30 

1.27 

1.24 

A,h 

Log. 

0.198 

0.190 

0.181 

0.173 

0.164 

0.152 

0.143 

0.133 

0.123 

0.113 

0.103 

0.093 

Log. 

66 

33 

84 

19 

35 

29 

01 

54 

85 

94 

80 

42 

Limit 

59 

60 

61 

62 

63 

64 

65 

66 

67 

67 

68 

69 

Min- 
utes 

Merid- 
iao 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

Alti- 
tudes 

Latitude  27°  Declination  Contrary  Name. 


165 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/     // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
// 

1.21 

/     // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
// 

1.18 

/     // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  52 
52  16 
60  38 

69  36 

// 

1.16 

/      // 

0  19 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

/     // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

/     // 

0  17 
108 
2  34 
4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 
II 

1.07 

/     II 

^11 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

II 

1.04 

/     // 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

II 

1.01 

/     // 

0  15 

1  03 

2  23 
4  13 
6  36 
9  30 

12  57 
16  54 
21  23 
26  24 
31  56 
38  01 
44  37 
51  44 

59  24 

II 

0.99 

/      // 

0  15 

1  01 

2  19 
4  05 
6  24 
9  13 

12  33 
16  23 
20  44 
25  36 
30  58 
36  52 
43  16 
50  10 

57  36 

II 

0.96 

/     // 

0  15 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 

55  48 

II 

0.93 

1 
II 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.082 
79 

0.071 
88 

0.064 
46 

0.053 
08 

0.041 
39 

0.029 
38 

0.017 
03 

0.004 
32 

9.995 
64 

9.982 
27 

9.968 
48 

Log. 

Limit 

70 

71 

73 

74 

75 

76 

77 

78 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

Alti- 
tudes 

Declinations.  — Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

II 
II 

/      // 
If 

II 

II 

// 

II 

// 

II 

// 

/ 

// 

II 

Oil 

0  41 

133 

2  47 

4  20 

6  15 

8  29 

1105 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 
II 

0.65 

/      // 

0  10 
0  39 
129 
2  39 

4  08 

5  58 
8  06 

10  34 

13  24 

16  32 

20  01 

23  48 

27  56 

32  25 

37  12 
II 

0.62 

/      // 

0  10 

0  38 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 

12  58 

16  00 

19  22 

23  02 

27  02 

31  22 

36  00 
II 

0.60 

/     // 

0  09 

0  37 

1  24 

2  28 

3  52 
5  32 
7  35 
9  54 

12  32 

15  28 

18  43 

22  16 

26  09 

30  19 

34  48 
II 

0.58 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.812 
91 

9.792 
39 

9.778 
15 

9.763 
43 

Log. 

Limit 

90 

91 

91 

92 

Min- 
utes 

Merid- 
ian 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

Alti- 
tudes 

166 


Latitude  28°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

go           70 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  59 
3  56 
8  51 
15  45 
24  36 
35  26 
48  13 
62  58 
79  43 

3.69 

1      II 

101 
4  05 
9  10 
16  18 
25  28 
36  41 
49  55 
65  11 

3.82 

1 

4 

9 
16 
26 
37 
51 
67 

II 
3.9. 

// 

03 
12 

29 
51 
20 
55 
37 
25 

5 

1 

4 

9 
17 
27 
39 
53 
69 

II 
4.1( 

// 

06 
22 
50 
30 
20 
22 
34 
58 

) 

1 
4 
10 
18 
28 
40 
55 
72 

4.2 

// 

08 
32 
12 
08 
20 
48 
32 
32 

5 

1 

1 
4 
10 
18 
29 
42 
57 
75 

II 
4.4 

10 
43 
37 
51 
28 
26 
46 
26 

2 

1 

4 
11 
19 
30 
44 
60 
78 

// 
4.6( 

14 
54 
02 
38 
40 
10 
06 
30 

3 

/ 

1 
5 
11 
20 
32 
46 
62 
81 

II 
4.8 

// 

17 
07 
31 
29 
00 
05 
43 
55 

3 

/     // 

1  20 
5  21 
12  03 
21  25 
33  28 
48  12 
65  36 

II 
5.02 

/      // 

1  24 
5  37 
12  38 
22  26 
35  04 
50  30 
68  44 

II 
5.26 

/      // 

1  28 
5  54 
13  16 
23  36 
36  52 
53  05 
72  16 

5.53 

/     // 

133 
6  12 

13  58 
24  50 
38  48 
55  53 
76  03 

// 
5.82 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.567 
03 

0.582 
06 

0.596 
60 

0.612 

78 

0.628 
39 

0.645 
42 

0.662 
76 

0.681 
24 

0.700 
70 

0.720 
99 

0.742 
73 

0.764 
92 

Log. 

Limit 

31 

31 

30 

29 

28 

28 

27 

26 

25 

24 

23 

22 

Min- 
utes 

Merid- 
ian 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

700      Alti- 
"^        tui^es 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

/      // 

/      // 

1     II 

1     II 

1     II 

/     // 

/      // 

/     // 

1     II 

;3  52 

/      // 

/      II 

Min. 

4 

139 

144 

151 

1  59 

2  08 

2  19 

2  32 

2  47 

3  07 

)   4  06 

4  53 

4 

8 

6  33 

6  58 

7  24 

7  57 

8  33 

9  16 

10  08 

11  11 

12  30 

14T0 

16  24 

19  32 

8 

12 

14  45 

15  40 

16  41 

17  52 

19  13 

20  51 

22  48 

25  10 

28  06 

3153 

36  55 

12 

16 

26  15 

27  52 

29  39 

31  44 

34  13 

37  05 

40  32 

44  42 

16 

20 

41  00 

43  32 

46  20 

49  36 

53  28 

57  56 

20 

24 

59  03 

62  41 

66  43 

24 

28 

80  21 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

6.15 

6.53 

6.95 

7.44 

8.02 

8.69 

9.50 

10.48 

11.71 

13.28 

15.38 

18.31 

A,h 

Log. 

0.788 

0.814 

0.841 

0.871 

0.904 

0.939 

0.977 

1.020 

1.068 

1.123 

1.186 

1.262 

Log. 

88 

91 

98 

57 

17 

02 

72 

36 

56 

20 

96 

69 

Limit 

21 

20 

19 

18 

17 

16 

15 

14 

12 

11 

10 

9 

Min- 
utes 

Merid- 
ian 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

Alti- 
tudes 

Latitude  28°  Decimation  Same  Name. 

Declinations. 


167 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

35° 

35° 

Hour 
Angles 

iMiu. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A  jh 

1 

1 

// 

/ 

// 

1 

n 

/ 

II 

// 

II 

// 

II 

/ 

II 

1     II 

4  27 
17  24 
40  02 

II 
16.68 

3  40 
14  40 
33  00 

II 
13.75 

1     II 

3  06 

12  25 
27  57 
49  43 

II 
11.65 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.222 
20 

1.138 
30 

1.066 
33 

Log. 

Limit 

7 

5 

4 

2 

0 

2 

3 

5 

7 

9 

11 

12 

Min- 
utes 

Merid- 
ian 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/     /' 

1     II 

/     // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

2  41 

2  22 

2  06 

153 

142 

133 

125 

1  18 

1  12 

107 

102 

0  58 

4 

8 

10  45 

9  26 

8  24 

7  32 

6  49 

6  12 

5  41 

5  13 

4  49 

4  29 

4  09 

3  52 

8 

12 

24  12 

21  14 

18  53 

16  57 

15  20 

13  58 

12  47 

11  46 

10  51 

10  05 

9  22 

8  42 

12 

16 

43  00 

37  46 

33  35 

30  07 

27  16 

24  50 

22  45 

20  54 

19  17 

17  55 

16  38 

15  30 

16 

20 

59  00 

52  28 

47  04 

42  36 

38  48 

35  32 

32  40 

30  08 

28  00 

26  00 

24  12 

20 

24 

67  47 

61  21 

55  53 

51  10 

47  02 

43  24 

40  19 

37  26 

34  51 

24 

28 

76  03 

69  39 

64  02 

59  04 

54  53 

50  58 

47  26 

28 

32 

77  08 

7141 

66  34 

61  57 

32 

36 

78  25 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

II 

II 

A,h 

10.08 

8.85 

7.87 

7.06 

6.39 

5.82 

5.33 

4.90 

4.52 

4.20 

3.90 

3.63 

Ajh 

Log. 

1.003 

0.946 

0.895 

0.848 

0.805 

0.764 

0.726 

0.690 

0.655 

0.623 

0.591 

0.559 

46 

94 

97 

80 

50 

62 

73 

20 

14 

25 

06 

91 

Log. 

Limit 

14 

16 

18 

19 

20 

22 

24 

25 

26 

27 

28 

29 

Min- 
utes 

Merid- 
ian 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

Alti- 
tudes 

168 


Latitude  28°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

5.2° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/     // 

/      // 

/      // 

/      // 

/      // 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

0  54 

0  51 

0  47 

0  44 

0  42 

0  39 

0  37 

0  35 

0  33 

0  31 

0  30 

0  27 

4 

8 

3  37 

3  23 

3  10 

2  59 

2  47 

2  39 

2  28 

2  20 

2  11 

2  04 

158 

151 

8 

12 

8  08 

7  36 

7  08 

6  42 

6  17 

5  56 

5  34 

5  15 

4  57 

4  41 

4  25 

4  09 

12 

16 

14  28 

13  32 

12  40 

11  54 

11  11 

10  32 

9  54 

9  21 

8  47 

8  19 

7  51 

7  23 

16 

20 

22  36 

21  08 

19  48 

18  36 

17  28 

16  28 

15  28 

14  36 

13  44 

13  00 

12  16 

11  32 

20 

24 

32  33 

30  26 

28  30 

26  47 

25  10 

23  42 

22  17 

21  02 

19  47 

18  43 

17  40 

16  36 

24 

28 

44  18 

41  25 

38  49 

36  28 

34  14 

32  17 

30  19 

28  37 

26  55 

25  29 

24  02 

22  37 

28 

32 

57  51 

54  06 

50  42 

47  37 

44  42 

42  10 

39  35 

37  22 

35  09 

33  17 

3124 

29  32 

32 

36 

73  14 

68  29 

64  09 

60  16 

56  36 

53  21 

50  07 

47  19 

44  30 

42  07 

39  45 

37  22 

36 

40 

79  12 

74  24 

69  52 

65  52 

6152 

58  24 

54  56 

52  00 

49  09 

46  08 

40 

44 

84  33 

79  42 

74  52 

70  40 

66  28 

62  55 

59  22 

55  49 

44 

48 

89  05 

84  05 

79  06 

74  53 

70  39 

66  24 

48 

52 

87  53 

82  55 

77  58 

52 

56 

90  25 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.39 

3.17 

2.97 

2.79 

2.62 

2.47 

2.32 

2.19 

2.06 

1.95 

1.84 

1.73 

A,h 

Log. 

0.530 

0.501 

0.472 

0.445 

0.418 

0.392 

0.365 

0.340 

0.313 

0.290 

0.264 

0.238 

Log. 

20 

06 

76 

60 

30 

70 

49 

44 

87 

03 

82 

05 

Limit 

31 

32 

33 

34 

36 

37 

39 

40 

41 

42 

44 

46 

Min- 
utes 

Merid- 
ian 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  27 

1  45 
3  56 
7  00 

10  56 
15  45 
21  25 
27  59 
35  26 
43  44 
52  55 
62  58 
73  54 
85  43 

II 
1.64 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

/      // 

0  23 

1  34 
3  31 
6  13 
9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

46  06 

56  04 

65  48 

78  18 

87  36 
II 

1.46 

/      // 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

71  37 

82  12 
II 

1.37 

/      // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 
II 

1.29 

/      // 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
II 

}.14 

/      // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 

II 

1.07 

1     II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
II 

1.01 

/      // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
II 

0.95 

/      // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 

/      // 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 
14  10 
17  56 
22  08 
26  47 
3152 
37  24 
43  23 

49  48 

II 

0.83 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.214 
84 

0.187 
52 

0.164 
35 

0.136 
72 

0.110 
59 

0.082 
79 

0.056 
90 

0.029 
38 

0.004 
32 

9.977 
72 

9.949 
39 

9.919 
08 

Log. 

Limit 

48 

50 

52 

54 

56 

57 

58 

60 

62 

64 

66 

68 

Min- 
utes 

Merid- 
ian 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

Alti- 
tudes 

Latitude  28°  Declination  Gjntrary  Name* 


169 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       // 

/      // 

/      // 

/     // 

/     // 

/     // 

1        n 

/     II 

/      // 

/     // 

/     // 

/     // 

Min. 

4 

0  59 

0  57 

0  55 

0  54 

0  52 

0  51 

0  49 

0  48 

0  46 

0  46 

0  44 

0  43 

4 

8 

3  56 

3  49 

3  43 

3  35 

3  29 

3  23 

3  17 

3  12 

3  06 

3  02 

2  58 

2  53 

8 

12 

8  51 

8  36 

8  20 

8  04 

7  50 

7  36 

7  24 

7  12 

7  01 

6  50 

6  39 

6  29 

12 

16 

15  45 

15  16 

14  48 

14  20 

13  54 

13  32 

13  08 

12  48 

12  27 

12  10 

1149 

11  31 

16 

20 

24  36 

23  52 

23  08 

22  24 

2144 

2108 

20  32 

20  00 

19  28 

19  00 

18  28 

18  00 

20 

24 

35  26 

34  22 

33  18 

32  16 

31  18 

30  26 

29  34 

28  48 

28  02 

27  22 

26  35 

25  55 

24 

28 

48  13 

46  47 

45  21 

43  54 

42  36 

41  25 

40  15 

39  12 

38  10 

37  14 

36  12 

35  17 

28 

32 

62  58 

61  06 

59  14 

57  20 

55  38 

54  06 

52  34 

51  12 

49  50 

48  38 

47  17 

46  05 

32 

36 

79  43 

77  20 

74  57 

72  35 

70  25 

68  29 

66  32 

64  48 

63  04 

61  34 

59  50 

58  19 

36 

40 

92  32 

89  36 

86  56 

84  32 

82  08 

80  00 

77  52 

76  00 

73  52 

72  00 

40 

44 

87  07 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

" 

" 

II 

" 

II 

II 

" 

II 

" 

II 

A,h 

3.69 

3.58 

3.47 

3.36 

3.26 

3.17 

3.08 

3.00 

2.92 

2.85 

2.77 

2.70 

A,h 

Log. 

0.567 

0.553 

0.540 

0.526 

0.513 

0.501 

0.488 

0.477 

0.465 

0.454 

0.442 

0.431 

Log. 

03 

88 

33 

34 

22 

06 

55 

12 

38 

84 

48 

36 

Limit 

31 

33 

33 

34 

35 

35 

36 

36 

37 

38 

38 

39 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  43 

0  41 

0  40 

0  39 

0  38 

0  38 

0  36 

0  36 

0  35 

0  35 

0  34 

0  33 

4 

8 

2  49 

2  45 

2  41 

2  38 

2  34 

2  30 

2  27 

2  24 

2  20 

2  17 

2  14 

2  11 

8 

12 

6  20 

6  10 

6  01 

5  55 

5  46 

5  37 

5  30 

5  23 

5  15 

5  08 

5  02 

4  55 

12 

16 

11  16 

10  58 

10  43 

10  29 

10  14 

9  59 

9  46 

9  33 

9  21 

9  08 

8  58 

8  45 

16 

20 

17  36 

17  08 

16  44 

16  24 

16  00 

15  36 

15  16 

14  56 

14  36 

14  16 

14  00 

13  40 

20 

24 

25  21 

24  40 

24  06 

23  37 

23  02 

22  28 

2159 

21  30 

2102 

20  33 

20  10 

19  41 

24 

28 

34  29 

33  35 

32  48 

32  09 

31  22 

30  34 

29  56 

29  16 

28  37 

27  57 

27  26 

26  47 

28 

32 

45  03 

43  52 

42  50 

4159 

40  58 

39  56 

39  05 

38  14 

37  22 

36  31 

35  50 

34  59 

32 

36 

57  02 

55  31 

54  13 

53  08 

5150 

50  33 

49  28 

48  23 

47  19 

46  14 

45  22 

44  17 

36 

40 

70  24 

68  32 

66  56 

65  36 

64  00 

62  24 

61  04 

59  44 

58  24 

57  04 

56  00 

54  40 

40 

44 

85  11 

82  56 

80  59 

79  22 

77  26 

75  30 

73  53 

72  16 

70  40 

69  03 

67  46 

66  09 

44 

48 

96  23 

94  28 

92  10 

89  51 

87  56 

86  01 

84  05 

82  10 

80  38 

78  43 

48 

52 

105  27 

103  12 

100  57 

98  41 

96  26 

94  38 

92  23 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

It 

II 

II 

II 

II 

II 

A,h 

2.64 

2.57 

2.51 

2.46 

2.40 

2.34 

2.29 

2.24 

2.19 

2.14 

2.10 

2.05 

A,h 

Log. 

0.421 

0.409 

0.399 

0.390 

0.380 

0.369 

0.359 

0.350 

0.340 

0.330 

0.322 

0.311 

Log. 

60 

93 

67 

94 

21 

22 

84 

25 

44 

41 

22 

75 

Limit 

40 

41 

42 

43 

43 

44 

44 

45 

46 

47 

48 

49 

Min- 
utes 

Merid- 
ian 

50° 

49° 

4-8° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tudes 

170 


Latitude  28°  Declination  Contrary  Name. 


Declixations. 


Hour 

Augles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

/  '/ 

/  // 

t     1 

/  // 

/  // 

/  // 

/  // 

/   // 

/  // 

/  // 

1     II 

Min. 

Min. 

4 

0  32 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

0  27 

0  27 

0  27 

0  26 

0  25 

4 

8 

2  09 

2  05 

2  02 

2  01 

158 

156 

154 

151 

149 

146 

142 

142 

8 

12 

4  49 

4  43 

4  37 

4  32 

4  26 

4  20 

4  16 

4  09 

4  05 

3  59 

3  54 

3  49 

12 

16 

8  35 

8  21 

8  11 

8  04 

7  54 

7  44 

7  33 

7  23 

7  15 

7  05 

6  58 

6  47 

16 

20 

13  24 

13  04 

12  48 

12  36 

12  20 

12  04 

1148 

1132 

11  20 

1104 

10  52 

10  36 

20 

24 

19  18 

18  49 

18  26 

18  09 

17  46 

17  23 

16  59 

16  36 

16  19 

15  57 

15  39 

15  16 

24 

28 

26  16 

25  37 

25  06 

24  42 

24  10 

23  39 

23  08 

22  37 

22  13 

21  41 

21  18 

20  47 

28 

32 

34  18 

33  27 

32  46 

32  15 

3134 

30  53 

30  13 

29  32 

29  01 

28  19 

27  49 

27  08 

32 

36 

43  25 

42  20 

4128 

40  50 

39  58 

39  06 

38  14 

37  22 

36  43 

35  52 

35  13 

34  21 

36 

40 

53  36 

52  16 

51  12 

50  24 

49  20 

48  16 

47  12 

46  08 

45  20 

44  16 

43  28 

42  24 

40 

44 

64  51 

63  14 

6157 

60  59 

59  42 

58  24 

57  07 

55  49 

54  51 

53  34 

52  36 

51  18 

44 

48 

77  11 

75  16 

73  44 

72  34 

71  02 

69  30 

67  56 

66  24 

65  15 

63  44 

62  35 

6103 

48 

52 

90  35 

88  20 

86  32 

85  10 

83  22 

81  34 

79  46 

77  58 

76  37 

74  48 

73  27 

7139 

52 

56 

105  03 

102  26 

100  21 

98  47 

96  42 

94  36 

92  31 

90  25 

88  51 

86  46 

85  12 

83  06 

56 

60 

120  36 

117  36 

115  12 

113  24 

11100 

108  36 

106  12 

103  48 

102  00 

99  36 

97  48 

95  24 

60 

// 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.01 

1.96 

1.92 

1.89 

1.85 

1.81 

1.77 

1.73 

1.70 

1.66 

1.63 

1.59 

A,h 

Log. 

0.303 

0.292 

0.283 

0.276 

0.267 

0.257 

0.247 

0.238 

0.230 

0.220 

0.212 

0.201 

Log. 

20 

26 

30 

46 

17 

68 

97 

05 

45 

11 

19 

40 

Limit 

49 

51 

52 

53 

53 

54 

55 

55 

56 

57 

58 

59 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

3P 

30° 

29° 

28° 

27° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  '/ 

/  /' 

/  // 

/  // 

/  // 

/  // 

/  /' 

/  // 

/  // 

/  /' 

Min. 

4 

0  25 

0  24 

0  24 

0  23 

0  22 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

4 

8 

140 

138 

136 

134 

1  32 

1  30 

1  28 

126 

124 

122 

120 

1  18 

8 

12 

3  45 

3  40 

3  36 

3  31 

3  24 

3  22 

3  17 

3  13 

3  08 

3  05 

3  00 

2  56 

12 

16 

6  39 

6  32 

6  24 

6  13 

6  06 

5  58 

5  51 

5  43 

5  36 

5  27 

5  20 

5  12 

16 

20 

10  24 

10  12 

10  00 

9  44 

9  32 

9  20 

9  08 

8  56 

8  44 

8  32 

8  20 

8  08 

20 

24 

14  59 

14  41 

14  24 

14  01 

13  43 

13  26 

13  09 

12  52 

12  35 

12  17 

12  00 

1143 

24 

28 

20  23 

20  00 

19  36 

19  05 

18  42 

18  18 

17  54 

17  30 

17  07 

16  44 

16  20 

15  57 

28 

32 

26  37 

26  07 

25  36 

24  55 

24  25 

23  54 

23  23 

22  52 

22  21 

2151 

21  20 

20  49 

32 

36 

33  42 

33  03 

32  24 

31  32 

30  53 

30  14 

29  36 

28  57 

28  18 

27  39 

27  00 

26  21 

36 

40 

41  36 

40  48 

40  00 

38  56 

38  08 

37  20 

36  32 

35  44 

34  56 

34  08 

33  20 

32  32 

40 

44 

50  20 

49  22 

48  24 

47  06 

46  08 

45  10 

44  13 

43  14 

42  16 

41  18 

40  20 

39  12 

44 

48 

59  24 

58  45 

57  36 

56  04 

54  55 

53  46 

52  36 

51  27 

50  18 

49  09 

48  00 

46  51 

48 

52 

70  18 

68  57 

67  36 

65  48 

64  27 

63  06 

61  44 

60  23 

59  02 

57  41 

56  20 

54  59 

52 

56 

81  32 

79  58 

78  24 

76  18 

74  44 

73  10 

7137 

70  02 

68  28 

66  54 

65  20 

63  46 

56 

60 

93  36 

91  48 

90  00 

87  36 

85  48 

84  00 

82  12 

80  24 

78  36 

76  48 

75  00 

73  12 

50 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

,  A,h 

1.56 

1.53 

1.50 

1.46 

1.43 

1.40 

1.37 

1.34 

1.31 

1.28 

1.25 

1.22 

A,h 

Log. 

0.193 

0.184 

0.176 

0.164 

0.155 

0.146 

0.136 

0.127 

0.117 

0.107 

0.096 

0.086 

Log. 

12 

69 

09 

35 

34 

13 

72 

10 

27 

21 

91 

36 

Limit 

60 

61 

62 

63 

64 

65 

66 

67 

68 

68 

69 

70 

Min- 
utes 

Merid- 
ian 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

Alti- 
tudes 

Latitude  28°  Declination  Contrary  Name. 


171 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/     // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

II 

1.20 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/     // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 
68  24 

1.14 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 

1      II 

0  17 

1  10 

2  37 
4  39 

7  16 
10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

II 

1.09 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

II 

1.06 

/     II 

0  17 
106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

/     // 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

1.00 

1     II 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

31  37 

37  38 

44  10 

51  13 

58  48 
II 

0.98 

/      // 

0  15 
101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  29 

36  29 

42  49 

49  39 

57  00 

0.95 

II 

// 

1 

1 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

0.079 
18 

0.068 
19 

0.056 
90 

0.045 
32 

0.037 
43 

0.025 
31 

0.012 

84 

0.00 

9.991 
20 

9.977 
72 

Log. 

Limit 

71 

72 

73 

74 

75 

76 

78 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

Alti- 
tudes 

Declinations.  - 

- 

[nferior  Meridian. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

II 

II 

// 

II 

// 

/ 

// 

1 

II 

// 

/ 

// 

/ 

0  11 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

21  57 

26  06 

30  38 

35  33 

40  48 
II 

0.68 

0  11 

0  41 

1  33 

2  47 
4  20 
6  15 
8  29 

11  05 
14  03 
17  20 
20  59 
24  57 
29  17 
33  59 

39  00 

II 

0.65 

/      // 

0  10 

0  39 

1  29 

2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

0.62 

0  10 

0  38 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 
12  58 
16  00 
19  22 
23  02 
27  02 
31  22 

36  00 

II 

0.60 

/      // 

0  09 

0  37 

1  24 

2  28 

3  52 
5  32 
7  35 
9  54 

12  32 
15  28 
18  43 
22  16 
26  09 
30  19 

34  48 

II 

0.58 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.832 
51 

9.812 
91 

9.792 
39 

9.778 
15 

9.763 
43 

Log. 

Limit 

89 

89 

90 

91 

92 

Min- 
utes 

Merid-I      no 
ian    1     ^ 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Alti- 
tudes 

172 


Latitude  29°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Miu. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

0, 
3' 
8 

15 

23 

33 

46 

60 

76 

3.5 

// 

57 
17 
50 
)6 
56 
59 
15 
25 
28 

1 

1      " 

0  59 
3  54 

8  47 
15  37 
24  24 
35  09 
47  49 
62  27 
79  04 

n 

3.66 

/      // 

100 
4  02 
9  05 
16  07 
25  12 
36  17 
49  24 
64  31 

n 

3.78 

1 

1 
4 
9 
16 
26 
37 
51 
66 

II 
3.9 

32 
10 
23 
11 
34 
32 
36 
14 

I 

1 
4 
9 

17 

27 

38 

52 

69 

II 
4.0 

35 
19 
13 
17 
30 
53 
55 
37 

5 

1 
4 
10 
17 
28 
40 
55 
71 

II 
4.2 

37 
30 
36 
58 
34 
25 
31 
51 

1 

1 

1 
4 
10 
18 
29 
41 
57 
74 

II 
4.3 

10 
40 

29 
39 
38 
57 
36 
34 

7 

1 

1 

4 
10 
19 
30 
43 
59 
77 

II 
4.5. 

13 
51 
55 
25 
20 
11 
27 
39 

5 

I  II 

1  16 
5  04 

II  24 
20  16 
31  40 
45  36 
62  02 
8104 

II 
4.75 

1           H 

1  19 
5  17 
1155 
21  09 
33  04 
47  37 
64  49 

II 
4.96 

/     // 

123 
5  32 
12  27 
22  09 
34  36 
49  50 
67  49 

II 
5.19 

127 
5  50 
13  07 
23  17 
36  24 
52  25 
7121 

II 
5.46 

Min. 
4 

.1 

16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.549 
00 

0.563 
48 

0.577 
49 

0.592 
18 

0.607 
46 

0.624 
28 

0.640 
48 

0.658 
01 

0.676 
69 

0.695 
48 

0.715 
17 

0.737 
19 

Log. 

Limit 

32 

31 

30 

29 

29 

28 

28 

27 

26 

25 

24 

24 

Min- 
utes 

Merid- 
ian 

61°      62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

/      // 

/      /' 

/     // 

/     // 

/     // 

/      // 

/      /' 

/     // 

Min. 

Min. 

4 

132 

137 

143 

150 

158 

2  06 

2  17 

2  30 

2  45 

3  04 

3  29 

4  02 

4 

8 

6  08 

6  29 

6  53 

7  19 

7  50 

8  25 

9  08 

9  58 

1100 

12  17 

13  57 

16  07 

8 

12 

13  48 

14  34 

15  28 

16  28 

17  37 

18  58 

20  23 

22  26 

24  46 

27  39 

31  22 

36  17 

12 

16 

24  32 

25  54 

27  28 

29  16 

31  19 

33  42 

36  31 

39  54 

44  02 

16 

20 

38  20 

40  28 

42  56 

45  44 

48  56 

52  40 

57  04 

20 

24 

55  12 

58  16 

6149 

65  52 

24 

28 

75  08 

79  19 

84  09 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

5.75 

6.07 

6.44 

6.86 

7.34 

7.90 

8.56 

9.35 

10.32 

11.52 

13.07 

15.12 

A,h 

Log. 

0.759 

0.783 

0.808 

0.836 

0.865 

0.897 

0.932 

0.970 

1.013 

1.061 

1.116 

1.179 

Log. 

67 

19 

89 

32 

70 

63 

47 

81 

68 

45 

28 

55 

Limit 

23 

22 

21 

20 

19 

18 

17 

16 

14 

13 

12 

10 

Min- 
utes 

Merid- 
ian 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

Alti- 
tudes 

Latitude  29°  Declination  Same  Name. 

Declinations. 


173 


Honr 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

4 
19 

18.0( 

18 
12 

) 

1 

// 

/ 

II 

II 

// 

/ 

/ 

1 

II 

// 

1 

II 

// 

II 

// 

/     // 

4  22 
17  26 
39  51 

16.34 

/      II 

3  35 
14  21 
32  17 

13.45 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

1.255 
27 

1.213 
25 

1.128 
72 

Log. 

Limit 

8 

6 

5 

4 

2 

0 

2 

4 

6 

8 

9 

10 

Min- 
utes 

Merid- 
ian 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

Min. 

4 

3  02 

2  28 

2  19 

2  03 

1  50 

1  39 

131 

123 

1  16 

1  10 

105 

100 

4 

8 

12  10 

10  30 

9  13 

8  12 

7  21 

6  39 

6  03 

5  32 

5  06 

4  43 

4  21 

4  03 

8 

12 

27  22 

23  38 

20  45 

18  27 

16  34 

14  57 

13  36 

12  27 

11  27 

10  35 

9  48 

9  06 

12 

16 

28  06 

42  02 

36  55 

32  49 

29  26 

26  35 

24  12 

22  09 

20  21 

18  49 

17  24 

16  10 

16 

20 

51  16 

46  00 

4132 

37  48 

34  36 

3148 

29  24 

27  12 

25  16 

20 

24 

59  48 

54  26 

49  50 

45  47 

42  20 

39  10 

36  23 

24 

28 

67  49 

62  18 

57  38 

53  19 

49  32 

28 

32 

75  16 

69  38 

64  41 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

H 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

Aih 

11.40 

9.85 

8.65 

7.69 

6.90 

6.23 

5.67 

5.19 

4.77 

4.41 

4.08 

3.79 

A,h 

Log. 

1.056 

0.993 

0.937 

0.885 

0.838 

0.794 

0.753 

0.715 

0.678 

0.644 

0.610 

0.578 

Log. 

90 

44 

02 

93 

85 

49 

58 

17 

52 

44 

66 

64 

Limit 

12 

14 

15 

16 

18 

20 

21 

23 

25 

26 

27 

28 

Min- 
utes 

Merid- 
ian 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

Alti- 
tudes 

•P  THE 

UNiVPDCi-rv 


174 


Latitude  29°  Declination  Same  Name.' 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hoar 
Angles 

/     // 

/     " 

/     // 

/     // 

t     II 

/     II 

/     // 

/     " 

/     /' 

/     // 

Min. 

Min. 

4 

0  56 

0  52 

0  49 

0  46 

0  43 

0  41 

0  38 

0  36 

0  34 

0  31 

0  30 

0  28 

4 

8 

3  46 

3  31 

3  17 

3  05 

2  54 

2  43 

2  33 

2  24 

2  15 

2  07 

2  00 

1  54 

8 

12 

8  28 

7  54 

7  24 

6  56 

6  30 

6  06 

5  44 

5  24 

5  03 

4  47 

4  31 

4  16 

12 

16 

15  04 

14  02 

13  08 

12  20 

11  34 

10  50 

10  12 

9  36 

9  01 

8  29 

8  01 

7  33 

16 

20 

23  32 

21  56 

20  32 

19  16 

18  04 

16  56 

15  56 

15  00 

14  04 

13  16 

12  32 

11  48 

20 

24 

33  53 

31  35 

29  34 

27  45 

26  01 

24  23 

22  57 

21  36 

21  16 

19  06 

18  03 

16  59 

24 

28 

46  08 

43  00 

40  15 

37  46 

35  25 

33  11 

31  14 

29  24 

27  34 

26  01 

24  34 

23  08 

28 

32 

60  15 

56  09 

52  34 

49  19 

46  15 

43  21 

40  47 

38  24 

36  00 

33  58 

32  05 

30  13 

32 

36 

76  15 

7104 

66  32 

62  26 

58  22 

54  52 

5138 

48  36 

45  35 

42  59 

40  37 

38  14 

36 

40 

77  04 

72  16 

67  44 

63  44 

60  00 

56  16 

53  04 

50  08 

47  12 

40 

44 

8157 

77  07 

72  36 

68  05 

64  12 

60  40 

57  07 

44 

48 

8101 

76  25 

72  11 

67  56 

48 

52 

84  43 

79  46 

52 

56 

92  31 

56 

60 

60 

/' 

It 

II 

" 

" 

" 

II 

II 

II 

II 

II 

" 

A,h 

3.53 

3.29 

3.08 

2.89 

2.71 

2.54 

2.39 

2.25 

2.11 

1.99 

1.88 

1.77 

A,h 

Log. 

0.547 

0.517 

0.488 

0.460 

0.432 

0.404 

0.378 

0.352 

0.324 

0.298 

0.274 

0.247 

Log. 

77 

20 

55 

90 

97 

83 

40 

18 

28 

85 

16 

97 

Limit 

30 

31 

32 

33 

35 

36 

37 

38 

39 

41 

43 

45 

Min- 
utes 

Merid- 
ian 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

/     // 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     // 

1     II 

/     // 

1     II 

/     // 

/     // 

/      /' 

/      // 

/      // 

/     // 

Min. 

4 

0  27 

0  25 

0  23 

0  22 

0  21 

0  19 

0  19 

0  17 

0  16 

0  15 

0  14 

0  13 

4 

8 

147 

141 

135 

129 

123 

1  19 

1  14 

1  10 

105 

101 

0  57 

0  52 

8 

12 

4  00 

3  46 

3  34 

3  20 

3  08 

2  57 

2  47 

2  37 

2  27 

2  19 

2  08 

158 

12 

16 

7  08 

6  42 

6  18 

5  56 

5  36 

5  15 

4  57 

4  39 

4  21 

4  05 

3  48 

3  30 

16 

20 

1108 

10  28 

9  52 

9  16 

8  44 

8  12 

7  44 

7  16 

6  48 

6  24 

5  56 

5  28 

20 

24 

16  02 

15  04 

14  12 

13  21 

12  35 

1148 

1109 

10  28 

9  48 

9  13 

8  33 

7  53 

24 

28 

21  49 

20  31 

19  21 

18  10 

17  07 

16  05 

15  09 

14  15 

13  20 

12  33 

11  38 

10  43 

28 

32 

28  30 

26  48 

25  16 

23  43 

22  21 

2100 

19  47 

18  36 

17  24 

16  23 

15  11 

13  59 

32 

36 

36  05 

33  55 

3158 

30  02 

28  18 

26  34 

25  04 

23  33 

22  02 

20  44 

19  14 

17  43 

36 

40 

44  32 

4152 

39  28 

37  04 

34  56 

32  48 

30  56 

29  04 

27  12 

25  36 

23  44 

21  52 

40 

44 

53  54 

50  40 

47  45 

44  51 

42  16 

39  41 

37  26 

35  10 

32  55 

30  58 

28  43 

26  28 

44 

48 

64  07 

60  17 

56  50 

53  22 

50  18 

47  14 

44  32 

4151 

39  10 

36  52 

34  10 

31  29 

48 

52 

75  15 

70  45 

66  42 

62  38 

59  02 

55  26 

52  16 

49  07 

45  58 

43  16 

40  06 

36  57 

52 

56 

87  18 

82  04 

77  21 

72  39 

68  28 

64  17 

60  38 

56  58 

53  19 

50  10 

46  31 

42  52 

56 

60 

88  48 

83  24 

78  36 

73  48 

69  36 

65  24 

61  12 

57  36 

53  24 

49  12 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

A,h 

1.67 

1.57 

1.48 

1.39 

1.31 

1.23 

1.16 

1.09 

1.02 

0.96 

0.89 

0.82 

A,h 

Log. 

0.222 

0.195 

0.170 

0.143 

0.117 

0.089 

0.064 

0.037 

0.008 

9.982 

9.949 

9.913 

Log, 

72 

90 

26 

01 

27 

91 

46 

43 

60 

27 

39 

•     81 

Limit 

47 

49 

50 

52 

54 

56 

58 

60 

62 

64 

66 

68 

Min- 
utes 

Merid- 
ian 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

Latitude  29°  Decimation  Contrary  Name. 


175 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

0 

3 

8 
15 
23 
33 
46 
60 
76 

n 

3.5' 

// 

57 
47 
30 
[)6 
36 
59 
15 
25 
28 

1 

/ 

0 
3 

8 
14 
22 
32 
44 
58 
74 
91 

II 
3.4. 

54 
40 
14 
38 
52 
55 
50 
33 
35 
28 

3 

1 

0 
3 

7 

14 
22 
31 
43 
56 
71 
88 

II 
3.3 

// 

53 
33 

59 
31 
12 
58 
31 
50 
56 
i8 

3 

1 

0 
3 

7 

13 
21 
31 
42 
55 
69 
86 

3.2 

// 

52 

28 
47 
49 
36 
06 
20 
18 
59 
24 

i 

0 
3 

7 
13 
21 
30 
41 
53 
68 
84 

II 
3.1 

51 
21 
33 

27 
00 
15 
09 
i5 
33 
30 

5 

0 
3 

7 
13 
20 
29 
39 
52 
66 
81 

II 
3.0 

// 

49 
16 
21 
03 
24 
23 
59 
13 
36 
36 

5 

0 
3 

7 
12 
19 
28 
38 
50 
64 
79 

II 
2.9 

// 

47 
10 
10 
42 
52 
36 
57 
52 
22 
28 

3 

0 

3 

6 

12 

19 
27 
37 
49 
62 
77 

II 
2.9 

// 

46 
05 
58 
22 
20 
50 
54 
30 
38 
20 

0 

/     // 

0  45 
3  01 

6  47 
12  05 
18  52 
27  10 
36  59 
48  18 
61  08 
75  28 

II 
2.83 

/     // 

0  44 
2  57 
6  38 
11  46 
18  24 
26  30 
36  04 
47  06 
59  37 
73  36 

II 
2.76 

I  II 

0  43 
2  52 
6  27 

II  29 
17  56 
25  50 
35  09 
45  54 
58  07 
7144 
86  48 

II 
2.69 

'      II 

0  42 

2  47 

6  17 

11  11 

17  28 

25  10 

34  14 

44  42 

56  36 

69  52 

84  33 

II 
2.62 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.549 
00 

0.535 
29 

0.522 
44 

0.510 
55 

0.498 
31 

0.485 
72 

0.474 
22 

0.462 
40 

0.451 
79 

0.440 
91 

0.429 
75 

0.418 
30 

Log. 

Limit 

32 

33 

33 

34 

35 

36 

37 

37 

38 

39 

39 

40 

Min- 
utes 

Merid- 
ian 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

1      II 

1     II 

1     II 

/     // 

/      /' 

/     // 

/     // 

Min. 

Min. 

4 

0  41 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  35 

0  35 

0  33 

0  33 

0  32 

4 

8 

2  44 

2  40 

2  37 

2  33 

2  29 

2  26 

2  23 

2  19 

2  17 

2  14 

2  11 

2  09 

8 

12 

6  09 

6  00 

5  52 

5  44 

5  35 

5  29 

5  21 

5  14 

5  08 

5  01 

4  55 

4  49 

12 

16 

10  55 

10  40 

10  24 

10  12 

9  57 

9  43 

9  31 

9  18 

9  08 

8  55 

8  45 

8  35 

16 

20 

17  04 

16  40 

16  16 

15  56 

15  32 

15  12 

14  52 

14  32 

14  16 

13  56 

13  40 

13  24 

20 

24 

24  35 

24  00 

23  25 

22  57 

22  22 

2153 

21  24 

20  56 

20  33 

20  04 

19  41 

19  18 

24 

28 

33  27 

32  40 

3153 

31  14 

30  27 

29  48 

29  09 

28  29 

27  57 

27  19 

26  47 

26  16 

28 

32 

43  41 

42  40 

4139 

40  47 

39  46 

38  55 

38  04 

37  12 

36  31 

35  40 

34  59 

34  18 

32 

36 

55  18 

54  00 

52  42 

5138 

50  20 

49  15 

48  10 

47  06 

46  14 

45  09 

44  17 

43  25 

36 

40 

68  16 

66  40 

65  04 

63  44 

62  08 

60  48 

59  28 

58  08 

57  04 

55  44 

54  40 

53  36 

40 

44 

82  36 

80  40 

78  43 

77  07 

75  11 

73  34 

7157 

70  21 

69  03 

67  26 

66  09 

64  51 

44 

48 

96  00 

93  42 

91  46 

89  28 

87  33 

85  38 

83  42 

82  10 

80  15 

78  43 

77  11 

48 

52 

107  42 

105  00 

102  45 

100  30 

98  14 

96  26 

94  11 

92  23 

90  35 

52 

56 

56 

60 

60 

II 

" 

II 

II 

II 

>' 

II 

II 

II 

II 

II 

II 

A,h 

2.56 

2.50 

2.44 

2.39 

2.33 

2.28 

2.23 

2.18 

2.14 

2.09 

2.05 

2.01 

Ajh 

Log. 

0.408 

0.397 

0.387 

0.378 

0.367 

0.357 

0.348 

0.338 

0.330 

0.320 

0.311 

0.303 

24 

94 

39 

40 

36 

93 

30 

46 

41 

15 

75 

20 

Log. 

Limit 

40 

41 

42 

43 

43 

44 

45 

46 

47 

48 

49 

50 

Min- 
utes 

Merid- 
ian 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

Alti- 
tudes 

176 


Latitude  29°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

117  36 

n 

1.96 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

6137 

73  21 

86  05 

99  49 

114  36 

// 

1.91 

0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

98  15 

112  48 
II 

1.88 

/     // 

0  30 

1  58 
4  26 
7  54 

12  20 
17  46 
24  10 
31  34 
39  58 
49  20 
59  42 
7102 
83  22 
96  42 

11100 

II 

1.85 

/     // 

0  29 

1  56 
4  20 
7  44 

12  04 
17  23 
23  39 
30  53 
39  06 
48  16 
58  24 
69  30 
8134 
94  36 

108  36 

II 

1.81 

/      II 

0  28 

154 

4  16 

7  33 

11  48 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 

II 

1.77 

/     // 

0  28 

1  52 
4  11 
7  25 

11  36 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 
90  56 
104  24 

1.74 

/     // 

0  27 

1  49 
4  05 
7  15 

11  20 
16  19 
22  13 
29  01 
36  43 
45  20 
54  51 
65  15 
76  37 
88  51 
102  00 

1.70 

/     // 

0  27 

147 

4  00 

7  08 

11  08 

16  02 

2149 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

II 

1.67 

/     // 

0  26 

1  44 
3  54 
6  58 

10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 

97  48 

II 

1.63 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
5138 
61  26 
72  06 
83  38 

96  00 

II 

1.60 

/       n 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 

94  12 

II 

1.57 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.292 
26 

0.281 
03 

0.274 
16 

0.267 
17 

0.257 
68 

0.247 
97 

0.240 
55 

0.230 
45 

0.222 
72 

0.212 
19 

0.204 
12 

0.195 
90 

Log. 

Limit 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

59 

60 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       II 

/      // 

/      // 

/      // 

/      // 

/      // 

/     // 

/     // 

/      // 

/     // 

/      // 

/     // 

Min. 

4 

0  25 

0  24 

0  23 

0  22 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  19 

0  19 

4 

8 

1  38 

1  36 

134 

133 

1  30 

1  28 

126 

124 

1  23 

121 

1  19 

1  17 

8 

12 

3  40 

3  36 

3  32 

3  28 

3  23 

3  19 

3  14 

3  10 

3  06 

3  02 

2  57 

2  54 

12 

16 

6  32 

6  24 

6  16 

6  08 

6  01 

5  53 

5  46 

5  38 

5  30 

5  22 

5  15 

5  10 

16 

20 

10  12 

10  00 

9  48 

9  36 

9  24 

9  12 

9  00 

8  48 

8  36 

8  24 

8  12 

8  04 

20 

24 

14  41 

14  24 

14  06 

13  49 

13  32 

13  15 

12  58 

12  41 

12  23 

12  06 

11  48 

11  37 

24 

28 

20  00 

19  36 

19  13 

IS  49 

18  26 

18  02 

17  38 

17  15 

16  52 

16  28 

16  05 

15  49 

28 

32 

26  07 

25  36 

25  06 

24  35 

24  04 

23  33 

23  02 

22  31 

22  01 

21  30 

21  00 

20  39 

32 

36 

33  03 

32  24 

3145 

3106 

30  27 

29  49 

29  10 

28  31 

27  52 

27  13 

26  34 

26  08 

36 

40 

40  48 

40  00 

39  12 

38  24 

37  36 

36  48 

36  00 

35  12 

34  24 

33  36 

32  48 

32  16 

40 

44 

49  22 

48  24 

47  26 

46  27 

45  29 

44  32 

43  34 

42  36 

4137 

40  39 

39  41 

39  02 

44 

48 

58  45 

57  36 

56  27 

55  18 

54  09 

52  59 

51  50 

50  41 

49  32 

48  23 

47  14 

46  28 

48 

52 

68  57 

67  36 

66  15 

64  54 

63  33 

62  11 

60  50 

59  29 

58  08 

56  47 

55  26 

54  32 

52 

56 

79  58 

78  24 

76  50 

75  15 

73  41 

72  08 

70  34 

69  00 

67  25 

65  51 

64  17 

63  14 

56 

60 

9148 

90  00 

88  12 

86  24 

84  36 

82  48 

8100 

79  12 

77  24 

75  36 

73  48 

72  36 

60 

II 

" 

II 

II 

II 

II 

" 

II 

II 

" 

II 

II 

Ajh 

1.53 

1.50 

1.47 

1.44 

1.41 

1.38 

1.35 

1.32 

1.29 

1.26 

1.23 

1.21 

A,h 

0.184 

0.176 

0.167 

0.158 

0.149 

0.139 

0.130 

0.120 

0.110 

0.100 

0.089 

0.082 

Log. 

69 

09 

32 

36 

22 

88 

33 

57 

59 

37 

91 

79 

Limit 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

Latitude  29"  Declination  Contrary  Name. 


177 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53°      54° 

55° 

56° 

57° 

58° 

59* 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

/     1 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

3128 

38  05 

45  18 

53  10 

61  41 

70  48 
It 

1.18 

/        n 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 
69  00 

1.15 

/       n 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 
67  48 

1.13 

/       n 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 
66  00 

1.10 

/     // 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
4105 
48  13 
55  56 
64  12 

1.07 

/        n 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

1.04 

/      // 

0  16 
105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

1.02 

/      // 

0  15 
103 
2  23 

4  13 
6  36 
9  30 
12  57 
16  54 
21  23 
26  24 
31  56 
38  01 
44  37 
51  44 
59  24 

0.99 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

II 

0.96 

II 

// 

/ 

// 

1 

II 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.071 

88 

0.060 
70 

0.053 
08 

0.041 
39 

0.029 
38 

0.017 
03 

0.008 
60 

9.995 
64 

9.982 
27 

Log. 

liimit 

72 

73 

74 

75 

76 

77 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

•    4° 

3° 

2° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridla.n. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

II 

1 

/ 

1 

1 

// 

/ 

1 

II 

// 

1 
II 

// 

/     // 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 

II 

0.70 

Oil 

0  42 

136 

2  52 

4  28 

6  26 

8  45 

1126 

14  29 

17  52 

2138 

25  43 

30  11 

35  02 

40  12 

II 

0.67 

/      // 

Oil 

0  40 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
II 

0.64 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 

36  36 

II 

0.61 

/      // 

0  10 
0  38 
125 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

/     // 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
2154 
25  41 
29  48 

34  12 

II 

0.57 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.845 
10 

9.826 
07 

9.806 
18 

9.785 
33 

9.770 
85 

9.755 
87 

Log. 

Limit 

88 

88 

89 

90 

91 

92 

Min- 
utes 

Merid- 
ian 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

10° 

Alti- 
tudes 

178 


Latitude  30°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0 

3 

8 
14 
22 
32 
44 
58 
73 
90 

It 
3.4( 

54 
38 
10 
30 
10 
38 
26 
02 
26 
40 

) 

0 
3 
8 
14 
23 
33 
45 
59 
75 

II 
3.5 

56 
45 
25 
59 
24 
42 
52 
54 
49 

I 

0  58 
3  51 
8  41 
15  27 
24  08 
34  46 
47  18 
61  46 
78  12 

II 
3.62 

/     // 

100 
4  00 
8  59 
15  57 
24  56 
35  54 
48  52 
63  50 

II 
3.74 

1 

1 

4 

9 
16 
25 
37 
50 
66 

II 
3.8' 

II 

32 
08 
17 
31 
48 
09 
34 
03 

1 

1 
4 
9 
17 
26 
38 
52 
68 

II 
4.0 

04 
17 
37 
07 
44 
30 
24 
26 

I 

1 

4 

9 
17 
27 
39 
54 
70 

II 
4.1( 

// 

07 
26 
59 
45 
44 
57 
21 
59 

5 

1 

1 
4 
10 
18 
28 
41 
56 
73 

4.3 

// 

D9 
36 
22 
26 
48 
29 
27 
43 

2 

/     // 

1  12 
4  48 
10  48 
19  12 
30  00 
43  12 
58  48 
76  48 

II 
4.50 

1  15 
5  00 
11  15 
20  01 
31  16 
45  02 
61  17 
80  02 

II 
4.69 

/      // 

1  18 
5  13 
11  46 
20  54 
32  40 
47  02 
64  02 
83  38 

II 
4.90 

/     // 

1  22 
5  28 
12  18 
21  54 
34  12 
49  15 
67  02 

II 
5.13 

Min. 
.4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.531 

48 

0.545 
31 

0.558 
71 

0.572 
87 

0.587 
71 

0.603 
14 

0.619 
09 

0.635 
48 

0.653 
21 

0.671 
17 

0.690 
20 

0.710 
12 

Log. 

Limit 

33 

32 

31 

31 

30 

29 

29 

28 

27 

26 

25 

25 

Min- 
utes 

Merid- 
ian 

60° 

61° 

62° 

63° 

64° 

65°. 

66° 

67° 

68° 

69° 

70° 

71° 

Alti- 
tudes 

Declination 

5. 

Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21°  [   22° 

23° 

Hour 
Angles 

1     II 

1     II 

/      // 

/     // 

1     II 

1           H 

/      II 

1     II 

/      // 

Min. 

Min. 

4 

126 

1  31 

1  35 

142 

149 

155 

2  04 

2  14 

2  27 

2  43 

3  02 

3  26 

4 

8 

5  44 

6  03 

6  23 

6  46 

7  13 

7  43 

8  18 

9  00 

9  49 

10  49 

12  05 

13  42 

8 

12 

12  55 

13  36 

14  23 

15  14 

16  14 

17  21 

18  41 

20  14 

22  05 

24  21 

27  11 

30  49 

12 

16 

22  57 

24  12 

25  33 

27  06 

28  50 

30  51 

33  11 

35  58 

39  15 

43  19 

16 

20 

35  52 

37  48 

39  56 

42  20 

45  04 

48  12 

50  52 

56  12 

20 

24 

51  39 

54  26 

57  30 

60  58 

64  54 

24 

28 

70  18 

74  05 

78  17 

82  59 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

5.38 

5.67 

5.99 

6.35 

6.76 

7.23 

7.78 

8.43 

9.20 

10.15 

11.33 

12.84 

■  .h 

Log. 

0.730 

0.753 

0.777 

0.802 

0.829 

0.859 

0.890 

0.925 

0.963 

1.006 

1.054 

1.108 

Log. 

78 

58 

43 

77 

95 

14 

98 

83 

79 

47 

23 

57 

Limit 

24 

23 

22 

21 

20 

19 

18 

17 

15 

14 

13 

12 

Min- 
utes 

Merid- 
ian 

72 

3 

73 

3 

74° 

75° 

76= 

) 

77' 

3 

78' 

> 

79< 

} 

80' 

3 

81' 

82' 

) 

83^ 

Alti- 
tudes 

Latitude  30°  Declination  Same  Name, 
Declinations. 


179 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Miu. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

3 

15 
35 

14.8 

58 
51 
40 

5 

/ 

4 
18 

n 

17.6 

43 
51 

t 
11 

ir 

// 

II 

// 

/      II 
II 

1 

II 

// 

1 

// 

/ 

// 

II 

// 

/     // 

4  15 
17  02 
38  22 

II 
15.98 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.172 
02 

1.247 
48 

1.203 
58 

Log. 

Limit 

10 

8 

7 

6 

4 

2 

0 

2 

4 

6 

8 

9 

Min- 
utes 

Merid- 
ian 

84 

3 

85 

3 

86 

3 

87' 

88' 

89' 

90° 

89' 

88' 

87' 

86' 

85° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47 

3 
// 

Hour 
Angles 

Min. 

1     II 

/     // 

/     // 

/     // 

/      // 

/     // 

1     II 

/     // 

/      // 

/     // 

/     // 

/ 

Min. 

4 

3  31 

2  59 

2  34 

2  15 

2  00 

1  47 

1  37 

128 

121 

1  15 

108 

103 

4 

8 

14  02 

1153 

10  16 

9  01 

8  00 

7  11 

6  29 

5  54 

5  24 

4  57 

4  35 

4  14 

8 

12 

3135 

26  44 

23  06 

20  17 

18  00 

16  09 

14  36 

13  16 

12  09 

1109 

10  18 

9  32 

12 

16 

4106 

36  03 

32  00 

28  43 

25  56 

23  36 

21  35 

19  51 

18  18 

16  56 

16 

20 

56  20 

50  00 

44  52 

40  32 

36  52 

33  44 

3100 

28  36 

26  28 

20 

24 

64  36 

58  22 

53  05 

48  35 

44  39 

41  11 

38  06 

24 

28 

72  16 

66  07 

60  45 

56  04 

51  53 

28 

32 

73  13 

67  46 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

" 

" 

II 

" 

II 

II 

II 

II 

A,h 

13.16 

11.14 

9.63 

8.45 

7.50 

6.73 

6.08 

5.53 

5.06 

4.65 

4.29 

3.97 

A,h 

Log. 

1.119 

1.046 

0.983 

0.926 

0.875 

0.828 

0.783 

0.742 

0.704 

0.667 

0.632 

0.598 

26 

89 

63 

86 

06 

02 

90 

73 

15 

45 

46 

79 

Log. 

Limit 

10 

12 

14 

16 

17 

19 

21 

23 

24 

25 

26 

27 

Min- 
utes 

Merid- 
ian 

84° 

83° 

82° 

81° 

80° 

79» 

78° 

77° 

76° 

75° 

74° 

73° 

Alti- 
tudes 

180 


Latitude  30°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

1      II 

/  // 

/  // 

1      II 

/  // 

/  // 

1     II 

/  // 

/  n 

/  n 

1     II 

/  // 

Min. 

4 

0  59 

0  54 

0  51 

0  47 

0  44 

0  42 

0  39 

0  37 

0  35 

0  33 

0  30 

0  29 

4 

8 

3  55 

3  40 

3  25 

3  11 

2  59 

2  47 

2  38 

2  28 

2  19 

2  11 

2  02 

156 

8 

12 

8  50 

8  14 

7  41 

7  11 

6  42 

6  17 

5  55 

5  32 

5  12 

4  54 

4  37 

4  20 

12 

16 

15  42 

14  38 

13  39 

12  45 

1154 

11  11 

10  29 

9  52 

9  16 

8  42 

8  11 

7  44 

16 

20 

24  32 

22  52 

21  20 

19  56 

18  36 

17  28 

16  24 

15  24 

14  28 

13  36 

12  48 

12  04 

20 

24 

35  20 

32  55 

30  43 

28  42 

26  47 

25  10 

23  37 

22  11 

20  50 

19  35 

18  26 

17  23 

24 

28 

48  05 

44  50 

4149 

39  05 

36  28 

34  14 

32  09 

30  11 

28  21 

36  39 

25  06 

23  39 

28 

32 

62  48 

58  33 

54  37 

5102 

47  37 

44  42 

41  59 

39  25 

37  02 

34  49 

32  46 

30  53 

32 

36 

79  30 

74  05 

69  07 

64  35 

60  16 

56  36 

53  08 

49  54 

46  53 

44  04 

41  28 

39  06 

36 

40 

85  20 

79  44 

74  24 

69  52 

65  36 

6136 

57  52 

54  24 

51  12 

48  16 

40 

44 

79  22 

74  32 

70  02 

65  49 

6157 

58  24 

44 

48 

83  19 

78  20 

73  44 

69  30 

48 

52 

86  32 

81  34 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

3.68 

3.43 

3.20 

2.99 

2.79 

2.62 

2.46 

2.31 

2.17 

2.04 

1.92 

1.81 

A,h 

Log 

0.565 

0.535 

0.505 

0.475 

0.445 

0.418 

0.390 

0.363 

0.336 

0.309 

0.283 

.  0.257 

Log. 

85 

29 

15 

67 

60 

30 

94 

61 

46 

63 

30 

68 

Limit 

29 

30 

32 

32 

33 

34 

36 

38 

39 

41 

43 

45 

Min- 
utes 

Merid- 
ian 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

1      II 

/  // 

Min. 

Min. 

4 

0  27 

0  26 

0  24 

0  22 

0  21 

0  20 

0  19 

0  18 

0  16 

0  15 

0  14 

0  13 

4 

8 

1  49 

142 

136 

131 

125 

120 

1  15 

1  11 

106 

102 

0  57 

0  53 

8 

12 

4  05 

3  50 

3  37 

3  25 

3  11 

3  00 

2  50 

2  39 

2  28 

2  20 

2  10 

159 

12 

16 

7  15 

6  50 

6  27 

6  03 

5  41 

5  20 

5  02 

4  45 

4  24 

4  08 

3  50 

3  33 

16 

20 

11  20 

10  40 

10  04 

9  28 

8  52 

8  20 

7  52 

7  24 

6  52 

6  28 

6  00 

5  32 

20 

24 

16  19 

15  22 

14  30 

13  38 

12  46 

12  00 

11  20 

10  40 

9  53 

9  18 

8  38 

7  58 

24 

28 

22  13 

20  54 

19  44 

18  34 

17  23 

16  20 

15  25 

14  30 

13  28 

12  41 

1146 

10  51 

28 

32 

29  01 

27  18 

25  46 

24  14 

22  42 

2120 

20  08 

18  56 

17  35 

16  34 

15  22 

14  10 

32 

36 

36  43 

34  34 

32  37 

30  40 

28  44 

27  00 

25  30 

23  59 

22  15 

20  57 

19  26 

17  56 

36 

40 

45  20 

42  40 

40  16 

37  52 

35  28 

33  20 

3128 

29  36 

27  28 

25  52 

24  00 

22  08 

40 

44 

54  51 

5138 

48  43 

45  49 

42  55 

40  20 

38  05 

35  49 

33  14 

31  18 

29  02 

26  47 

44 

48 

65  15 

6126 

57  59 

54  32 

5104 

48  00 

45  18 

42  37 

39  33 

37  15 

34  34 

3152 

48 

52 

76  37 

72  06 

68  03 

64  00 

59  56 

56  20 

53  10 

50  01 

46  25 

43  43 

40  34 

37  24 

52 

56 

88  51 

83  38 

78  55 

74  13 

69  31 

65  20 

6141 

58  01 

53  50 

50  42 

47  02 

43  23 

56 

60 

90  36 

85  12 

79  48 

75  00 

70  48 

66  36 

6148 

58  12 

54  00 

49  48 

60 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.70 

1.60 

1.51 

1.42 

1.33 

1.25 

1.18 

1.11 

1.03 

0.97 

0.90 

0.83 

Ajh 

Log. 

0.230 

0.204 

0.178 

0.152 

0.123 

0.096 

0.071 

0.045 

0.012 

9.986 

9.954 

9.919 

Log. 

45 

12 

98 

29 

85 

91 

88 

32 

84 

77 

24 

08 

Limit 

47 

48 

50 

52 

54 

56 

57 

59 

61 

63 

65 

67 

Min- 
utes 

Merid- 
ian 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

Latitude  30°  Declination  G)ntrary  Name* 


181 


Declinations. 


Hoar 
Angles 

0° 

1°  1  2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

0 
3 
8 

14 
22 
32 
44 
58 
73 
90 

II 
3.4 

// 

54 

38 
10 
30 
40 
38 
26 
[)2 
26 
40 

3 

0 
3 
7 
14 
22 
31 
43 
56 
71 
88 

// 
3.3 

53 
31 
55 

05 
00 
11 
07 
19 
17 
30 

3 

0 
3 
7 
13 
21 
30 
41 
54 
69 
85 

II 
3.2 

51 

26 
42 
42 
24 
49 
57 
47 
20 
36 

I 

0 
3 
7 
13 
20 
29 
40 
53 
67 
83 

3.1 

50 
19 
29 
19 
48 
58 
46 
14 
24 
12 

2 

0 
3 
7 

12 
20 
29 
39 
51 
65 
80 

II 
3.0 

// 

48 
14 
16 
56 
12 
05 
36 
43 
27 
48 

3 

1 

0 

3 

7 

12 

19 
28 
38 
50 
63 
78 

2.9 

// 

47 
09 
05 
35 
40 
19 
33 
21 
43 
40 

5 

1 

0 
3 
6 
12 
19 
27 
37 
49 
62 
76 

II 
2.8 

// 

46 
04 
55 
17 
12 
39 
38 
09 
13 
48 

/  II 

0  45 
2  59 
6  43 
11  57 
18  40 
26  53 
36  35 
47  47 
60  29 
74  40 

II 
2.80 

0  44 
2  56 
6  35 
1141 
18  16 
26  18 
35  48 
46  46 
59  11 
73  04 
88  24 

II 
2.74 

/  // 

0  43 

2  51 

6  24 

11  24 

17  48 
25  38 
34  53 
45  34 
57  41 
71  12 
86  10 

II 
2.67 

/   // 

0  42 
2  47 
6  15 
11  09 
17  24 
25  04 
34  06 
44  32 
56  23 
69  36 
84  13 

II 
2.61 

/  II 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  11 
43  21 
54  52 
67  44 
8157 

2.54 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.531 

48 

0.518 
51 

0.506 
51 

0.494 
15 

0.481 
44 

0.469 
82 

0.459 
39 

0.447 
16 

0.437 
75 

0.426 
51 

0.416 
64 

0.404 
83 

Log. 

Limit 

33 

33 

34 

35 

36 

37 

37 

38 

38 

39 

40 

40 

Min- 
utes 

Merid- 
ian 

60°   59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  // 

/  // 

/  // 

/  /' 

/  // 

/  '/ 

1     II 

/  // 

/  // 

/  // 

Min. 

4 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  34 

0  33 

0  33 

0  32 

0  31 

4 

8 

2  40 

2  36 

2  32 

2  28 

2  26 

2  22 

2  19 

2  16 

2  14 

2  11 

2  08 

2  05 

8 

12 

5  59 

5  50 

5  43 

5  34 

5  27 

5  20 

5  14 

5  06 

5  01 

4  54 

4  48 

4  43 

12 

15 

10  37 

10  22 

10  09 

9  54 

9  41 

9  28 

9  18 

9  06 

8  55 

8  42 

8  32 

8  21 

16 

20 

16  36 

16  12 

15  52 

15  28 

15  08 

14  48 

14  32 

14  12 

13  56 

13  36 

13  20 

13  04 

20 

24 

23  54 

23  19 

22  51 

22  17 

21  47 

21  19 

20  56 

20  27 

20  04 

19  35 

19  12 

18  49 

24 

28 

32  33 

31  46 

3106 

30  19 

29  40 

29  01 

28  29 

27  50 

27  19 

26  39 

26  08 

25  37 

28 

32 

42  30 

41  29 

40  37 

39  35 

38  45 

37  53 

37  12 

36  21 

35  40 

34  49 

34  08 

33  27 

32 

36 

53  47 

52  29 

5125 

50  07 

49  02 

47  57 

47  06 

46  01 

45  09 

44  04 

43  12 

42  20 

36 

40 

66  24 

64  48 

63  28 

6152 

60  32 

59  12 

58  08 

56  48 

55  44 

54  24 

53  20 

52  16 

40 

44 

80  20 

78  24 

76  48 

74  52 

73  15 

7138 

70  21 

68  44 

67  26 

65  49 

64  32 

63  14 

44 

48 

95  37 

93  19 

91  23 

89  05 

87  10 

85  15 

83  42 

81  46 

80  15 

78  20 

76  48 

75  16 

48 

52 

107  15 

104  33 

102  18 

100  03 

98  14 

95  59 

94  11 

91  56 

90  08 

88  20 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

II 

Ajh 

2.49 

2.43 

2.38 

2.32 

2.27 

2.22 

2.18 

2.13 

2.09 

2.04 

2.00 

1.96 

A,h 

Log. 

0.396 

0.385 

0.376 

0.365 

0.356 

0.346 

0.338 

0.328 

0.320 

0.309 

0.301 

0.292 

Log. 

20 

61 

58 

49 

03 

35 

46 

38 

15 

63 

03 

26 

,  Limit 

41 

42 

43 

44 

44 

45 

46 

47 

48 

49 

50 

51 

Min- 
utes 

Merid- 
ian 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

Alti- 
tudes 

182 


Latitude  30°  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

0  27 

1  49 
4  05 
7  15 

11  20 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
II 

1.70 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

/      // 

0  31 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

4128 

51  12 

61  57 

73  44 

86  32 

100  21 

115  12 

1.92 

/     // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

31  55 

40  24 

49  52 

60  21 

71  48 

84  16 

97  45 

112  12 

II 

1.87 

/     // 

0  30 

1  58 
4  25 
7  51 

12  16 
17  40 
24  02 
31  24 
39  45 
49  04 
59  22 
70  39 
82  55 
96  10 

110  24 

II 

1.84 

/     II 

0  29 

156 

4  20 

7  44 

12  04 

17  23 

23  39 

30  53 

39  06 

48  16 

58  24 

69  30 

81  34 

94  36 

108  36 

II 

1.81 

/     // 

0  29 

154 

4  15 

7  33 

11  48 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 

1.77 

/     // 

0  28 

1  52 
4  11 
7  25 

1136 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 
90  56 
104  24 

1.74 

/      II 

0  27 

146 

3  59 

7  05 

1104 

15  57 

21  41 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

86  46 

99  36 

II 

1.66 

/      // 

0  26 

1  44 
3  54 
6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 
II 

1.63 

0  26 

1  42 
3  50 
6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

5138 

61  26 

72  06 

83  38 

96  00 
II 

1.60 

/     // 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 
94  12 

1.57 

/      // 

0  25 

1  39 
3  42 
6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.283 
30 

0.271 
84 

0.264 
82 

0.257 
68 

0.247 
97 

0.240 
55 

0.230 
45 

0.220 
11 

0.212 
19 

0.204 
12 

0.195 
90 

0.187 
52 

Log. 

Limit 

51 

52 

53 

53 

54 

55 

56 

57 

58 

59 

60 

60 

Min- 
utes 

Merid- 
ian 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/      // 

/      // 

1     II 

/      // 

/      // 

aiin. 

4 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

0  20 

0  19 

0  19 

4 

8 

1  36 

1  35 

1  33 

131 

129 

127 

1  25 

123 

121 

1  20 

1  18 

1  16 

8 

12 

3  37 

3  34 

3  29 

3  25 

3  20 

3  16 

3  11 

3  07 

3  03 

2  59 

2  56 

2  51 

12 

16 

6  27 

6  18 

6  11 

6  03 

5  56 

5  48 

5  41 

5  33 

5  25 

5  17 

5  12 

5  05 

16 

20 

10  04 

9  52 

9  40 

9  28 

9  16 

9  04 

8  52 

8  40 

8  28 

8  16 

8  08 

7  56 

20 

24 

14  30 

14  12 

13  55 

13  38 

13  21 

13  04 

12  46 

12  29 

12  11 

11  54 

11  43 

11  26 

24 

28 

19  44 

19  21 

18  57 

18  34 

18  10 

17  46 

17  23 

16  59 

16  36 

16  12 

15  57 

15  33 

28 

32 

25  46 

25  16 

24  45 

24  14 

23  43 

23  12 

22  42 

22  11 

21  41 

21  10 

20  49 

20  18 

32 

36 

32  37 

3158 

31  19 

30  40 

30  02 

29  23 

28  44 

28  05 

27  26 

26  47 

26  41 

25  43 

36 

40 

40  16 

39  28 

38  40 

37  52 

37  04 

36  16 

35  28 

34  40 

33  52 

33  04 

32  32 

31  44 

40 

44 

48  43 

47  45 

46  47 

45  49 

44  51 

44  53 

42  55 

4157 

40  59 

40  00 

39  22 

38  24 

44 

48 

57  59 

56  50 

55  41 

54  32 

53  22 

52  13 

51  04 

49  55 

48  46 

47  37 

46  51 

45  41 

48 

52 

68  03 

66  42 

65  21 

64  00 

62  38 

61  17 

59  56 

58  35 

57  14 

55  53 

54  59 

53  37 

52 

56 

78  55 

77  21 

75  47 

74  13 

72  39 

7105 

69  31 

67  57 

66  23 

64  48 

63  46 

62  12 

56 

60 

90  36 
II 

88  48 
II 

87  00 
II 

85  12 
II 

83  24 
II 

8136 

79  48 

78  00 

II 

76  12 

74  24 

II 

73  12 

II 

71  24 

II 

60 

A,h 

1.51 

1.48 

1.45 

1.42 

1.39 

1.36 

1.33 

1.30 

1.27 

1.24 

1.22 

1.19 

A,h 

Log. 

0.178 

0.170 

0.161 

0.152 

0.143 

0.133 

0.123 

0.113 

0.103 

0.093 

0.086 

0.075 

Log. 

98 

26 

37 

29 

01 

54 

85 

94 

80 

42 

36 

55 

Limit 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

Min- 
utes 

Merid- 
ian 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

Alti- 
tudes 

Latitude  30°  Decimation  Contrary  Name* 


183 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55°      56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/      // 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 
69  36 

1.16 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 

68  24 

// 

1.14 

/      // 

0  18 

1  11 

2  59 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 

/      // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 

1.08 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

II 

1.06 

/      // 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

/      // 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 
17  04 
21  36 
26  40 
32  16 
38  24 
45  04 
52  16 
60  00 

n 

1.00 

/     II 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
II 

0.97 

/      // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

II 

0.95 

/ 

// 

1 
1 

// 

/     II 

. . . 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.064 
46 

0.056 
90 

0.045 
32 

0.033 
42 

0.025 
31 

0.012 
84 

0.00 

9.986 
77 

9.977 
72 

. 

Log. 

Limit 

73 

73 

74 

75 

76 

77 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

Alti- 
tudes 

Declination 

s.  —  Inferior  Meridian. 

Hour 

Angles 

60° 

61° 

62° 

63° 

64°  1   65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

// 

1 

II 

1 
1 

/      II 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

0.75 

/     // 

Oil 
0  46 
144 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 
43  12 

0.72 

/      // 

Oil 

0  44 

1  39 

2  57 
4  36 
6  38 
9  01 

11  46 
14  55 
18  24 
22  16 
26  29 
31  05 
36  04 
4124 

0.69 

/      // 

Oil 

0  42 

136 

2  52 

4  28 

6  26 

8  45 

11  26 

14  29 

17  52 

21  38 

25  43 

30  11 

35  02 

40  12 

II 

0.67 

Oil 

0  40 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 
13  50 
17  04 
20  39 
24  34 
28  50 
33  27 
38  24 

0.64 

/      // 

0  10 

0  39 

1  27 

2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 

36  36 

II 

0.61 

/      // 

0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

/      // 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
2154 
25  41 
29  48 
34  12 

0.57 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.875 
06 

9.857 
33 

9.838 
85 

9.826 
07 

9.806 
18 

9.785 
33 

9.770 
85 

9.755 

87 

Log. 

Limit 

86 

87 

87 

88 

88 

89 

90 

91 

Min- 
utes 

Merid- 
ian 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Alti- 
tudes 

184 


Latitude  31°  Decimation  Same  Name* 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0 
3 

7 
13 
21 
31 
42 
55 
70 
87 

If 
3.2 

52 
30 
51 

57 
48 
23 
44 
49 
38 
12 

1 

0 
3 

8 
14 
22 
32 
44 
57 
72 
89 

3.3 

54 
36 
05 
23 
28 
21 
D2 
31 
18 
52 

1 

0 
3 
8 
14 
23 
33 
45 
59 
74 
92 

// 
3.4 

// 

55 
43 
20 
48 
08 
18 
21 
14 
57 
32 

1 

/ 

1 
2 
3 
4 
6 
7 

3 

0 
3 

8 
5 
3 
4 
6 
1 
7 

// 
.5 

57 
49 
36 
16 
52 
22 
47 
06 
20 

1        n 

0  59 
3  57 
8  53 
15  47 
24  40 
35  31 
48  21 
63  09 
79  55 

3.70 

1 
4 
9 
16 
25 
36 
49 
65 

3.8 

// 

01 
05 
10 
18 
28 
41 
55 
11 

2 

1 
4 
9 
16 
26 
38 
51 
67 

II 
3.9 

// 

03 
13 
31 
53 
24 
01 
45 
35 

3 

1 
4 
9 
17 
27 
39 
53 
70 

II 
4.1 

n 

06 
23 
51 
33 
24 
28 
42 
08 

1 

/     // 

108 
4  34 
10  15 
18  13 
28  28 
40  59 
55  48 
72  53 

II 
4.27 

/     // 

1  11 
4  45 
10  40 
18  56 
29  36 
42  37 
58  01 
75  47 

II 
4.44 

I  II 

1  14 
4  56 

II  06 
19  46 
30  52 
44  27 
60  30 
79  01 

II 
4.63 

/      // 

1  17 
5  09 
11  35 
20  37 
32  12 
46  22 
63  07 
82  26 

II 
4.83 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.514 
55 

0.527 
63 

0.540 
33 

0.553 

,   88 

0.568 
20 

0.582 
06 

0.597 
70 

0.613 

84 

0.630 
43 

0.647 
38 

0.665 
58 

0.683 
95 

Log. 

Limit 

34 

33 

•  32 

32 

31 

30 

30 

29 

28 

27 

26 

26 

Min- 
utes 

Merid- 
ian 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

Min. 

Min. 

4 

121 

125 

129 

134 

1  40 

147 

154 

2  03 

2  12 

2  25 

2  39 

2  59 

4 

8 

5  24 

5  40 

5  56 

6  17 

6  40 

7  05 

7  35 

8  09 

8  51 

9  39 

10  38 

11  52 

8 

12 

12  09 

12  44 

13  21 

14  10 

15  00 

15  57 

17  05 

18  21 

19  54 

21  43 

23  58 

26  42 

12 

16 

2135 

22  40 

23  43 

25  10 

26  40 

28  23 

30  23 

32  39 

35  22 

38  37 

42  34 

16 

20 

33  44 

35  24 

37  04 

39  20 

4140 

44  20 

47  28 

5100 

55  16 

20 

24 

48  35 

50  59 

53  23 

56  38 

60  00 

63  51 

24 

28 

66  07 

69  23 

72  39 

77  06 

8140 

28 

32 

32 

36 

36 

40 

40 

44 

•  • 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

A,h 

5.06 

5.31 

5.56 

5.90 

6.25 

6.65 

7.12 

7.65 

8.29 

9.05 

9.98 

11.13 

A,h 

Log. 

0.704 

0.725 

0.945 

0.770 

0.795 

0.822 

0.852 

0.883 

0.918 

0.956 

0.999 

1.046 

Log. 

15 

09 

07 

85 

88 

82 

48 

66 

55 

65 

13 

50 

Limit 

25 

■  24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

Min- 
utes 

Merid- 
ian 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

Alti- 
tudes 

Latitude  3 J"  Declination  Same  Name. 


185 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

3 

13 
30 
53 

n 

12.6 

22 
27 
17 
51 

2 

3 
15 
35 
62 

n 

14.5 

n 

54 
34 
31 
15 

J 

4 
18 
41 

II 
17.3 

n 

J8 
31 
10 

5 

II 

// 

II 

1 

II 

/ 

// 

/ 

II 

II 

r 
II 

// 

/ 

// 

/ 

// 

/ 

n 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.101 
06 

1.164 
06 

1.239 
55 

■  ■ 

Log. 

Limit 

13 

12 

10 

8 

6 

4 

2 

0 

2 

4 

6 

7 

Min- 
utes 

Merid- 
ian 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/       // 

/      // 

/       n 

/      // 

/      II 

/     // 

/     // 

/      // 

/     // 

/      // 

Min. 

Min. 

4 

4  10 

3  26 

2  54 

2  30 

2  12 

157 

1  45 

134 

126 

118 

112 

107 

4 

8 

16  40 

13  43 

1136 

11  02 

8  48 

7  48 

7  00 

6  18 

5  44 

5  14 

4  49 

4  26 

8 

12 

37  39 

30  52 

26  06 

22  34 

19  47 

17  32 

15  45 

14  13 

12  55 

1149 

10  51 

9  59 

12 

16 

46  25 

40  06 

35  09 

31  12 

27  59 

25  15 

22  57 

20  59 

19  17 

17  45 

16 

20 

54  56 

48  44 

43  44 

39  28 

35  52 

32  48 

30  08 

27  44 

20 

24 

62  59 

56  50 

51  39 

47  14 

43  24 

39  57 

24 

28 

70  18 

64  18 

59  04 

54  21 

28 

28 

70  59 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

" 

" 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

15.62 

12.86 

10.88 

9.40 

8.24 

7.31 

6.56 

5.92 

5.38 

4.92 

4.52 

4.16 

A,h 

Log. 

1.193 

1.109 

1.036 

0.973 

0.915 

0.863 

0.816 

0.772 

0.730 

0.691 

0.655 

0.619 

Log. 

68 

24 

63 

13 

93 

92 

90 

32 

78 

97 

14 

09 

Limit 

9 

11 

13 

15  • 

16 

17 

19 

21 

23 

24 

25 

26 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

186 


Latitude  3i°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58°      59° 

Hour 
Angles 

Min. 

/      // 

/     // 

/      // 

/      // 

/     /' 

/            rl 

/     // 

1     II 

/      // 

/     /' 

/     //    /      // 

Min. 

4 

102 

0  57 

0  53 

0  50 

0  46 

0  43 

0  40 

0  38 

0  35 

0  33 

0  31      0  30 

4 

8 

4  06 

3  49 

3  32 

3  18 

3  05 

2  53 

2  42 

2  32 

2  23 

2  14 

2  05      1  58 

8 

12 

9  14 

8  34 

7  58 

7  26 

6  56 

6  29 

6  04 

5  41 

5  21 

5  01 

4  43      4  26 

12 

16 

16  26 

15  14 

14  10 

13  14 

12  20 

1130 

10  48 

10  07 

9  31 

8  55 

8  21      7  54 

16 

20 

25  40 

23  48 

22  08 

20  40 

19  16 

18  00 

16  52 

15  48 

14  52 

13  56 

13  04    12  20 

20 

24 

36  58 

34  16 

31  53 

29  46 

27  45 

25  55 

24  17 

22  45 

21  24 

20  04 

18  49,   17  46 

24 

28 

50  18 

46  39 

43  23 

40  30 

37  46 

35  17 

33  04 

30  58 

29  09 

27  19 

25  37    24  10 

28 

32 

65  42 

60  56 

56  39 

52  54 

49  19 

46  05 

43  11 

40  27 

38  04 

35  40 

33  27    31  34 

32 

36 

77  07 

7143 

66  58 

62  26 

58  19 

54  39 

51  12 

48  10 

45  09 

42  20    39  58 

36 

40 

72  00 

67  28 

63  12 

59  28 

55  44 

52  16    49  20 

40 

44 

76  39 

7157 

67  26 

63  14 

59  42 

44 

48 

80  15 

75  16 

71  02 

48 

52 

83  22 

52 

56 

56 

60 

60 

n 

II 

" 

II 

II 

II 

II 

II 

" 

II 

// 

II 

Ajh 

3.85 

3.57 

3.32 

3.10 

2.89 

2.70 

2.53 

2.37 

2.23 

2.09 

1.96 

1.85 

A,h 

0.585 

0.552 

0.521 

0.491 

0.460 

0.431 

0.403 

0.374 

0.348 

0.320 

0.292 

0.267 

Log. 

Log. 

46 

67 

14 

36 

90 

36 

12 

75 

30 

15 

26 

17 

Limit 

28 

30 

31 

31 

32 

33 

35 

37 

38 

40 

42 

44 

Min- 
utes 

Merid- 
ian 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

y-jo    j  Hour 
'        I  Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  28 

152 

4  11 

7  25 

1136 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

II 
1.74 

/      // 

0  26 

1  44 
3  54 
6  58 

10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 

II 
1.63 

1      II 

0  24 

138 

3  40 

6  32 

10  12 

14  41 

20  00 

26  07 

33  03 

40  48 

49  22 

58  45 

68  57 

79  58 

91  48 
II 

1.53 

/     II 

0  22 

1  33 
3  28 
6  08 
9  36 

13  49 
18  49 
24  35 
31  06 
38  24 
46  27 
55  18 
64  54 
75  15 

86  24 

II 

1.44 

0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

81  00 
II 

1.35 

/      // 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

2141 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
II 

1.27- 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 
15  33 
20  18 
25  43 
31  44 
38  24 
45  41 
53  37 
62  12 
7124 

1.19 

/     // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

1      II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/      II 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

31  37 

37  38 

44  10 

51  13 

58  48 

0.98 

/      // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
41  01 
47  33 
54  36 

0.91 

/       // 

0  13 

0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 

50  24 

// 

0.84 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.240 
55 

0.212 
19 

0.184 
69 

0.158 
36 

0.130 
33 

0.103 
80 

0.075 
55 

0.049 
22 

0.021 
19 

9.991 
23 

9.959 
04 

9.924 

28 

Log. 

Limit 

46 

47 

49 

51 

53 

55 

56 

58 

60 

62 

64 

66 

Min- 
utes 

Merid- 
ian 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

Alti- 
tudes 

Latitude  31°  Decimation  Contrary  Name. 


187 


Declinations. 

Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0 
3 
7 

13 

21 

31 

42 

55 

70 

87 

II 
3.2 

II 

52 
30 
51 
57 
18 
23 
14 
19 
38 
12 

1 

0 
3 
7 

13 
21 
30 
41 
54 
68 
84 

II 
3.1 

// 

51 
23 
38 
34 
12 
32 
33 
16 
12 
18 

3 

1      II 

0  49 
3  18 
7  25 
13  11 
20  36 
29  40 
40  23 
52  44 
66  45 
82  24 

II 
3.09 

1       n 

0  48 
3  13 

7  13 
12  51 
20  04 
28  54 
39  20 
51  22 
65  01 
80  16 

II 
3.01 

0 
3 

7 
12 
19 
28 
38 
50 
63 
78 

II 
2.9 

// 

46 

07 
02 
30 
32 
07 
18 
01 
17 
08 

J 

0 
3 
6 
12 
19 
27 
37 
48 
61 
76 

II 
2.8 

// 

46 
02 
50 
10 
00 
22 
14 
38 
34 
00 

5 

0 
2 
6 
11 
18 
26 
36 
47 
60 
74 

II 
2.7 

// 

44 
58 
41 
51 
32 
41 
20 
27 
03 
08 

3 

/     // 

0  43 
2  54 
6  30 
1134 
18  04 
26  01 
35  25 
46  15 
58  32 
72  16 
87  26 

II 
2.71 

/     // 

0  43 
2  49 
6  21 
11  19 
17  40 
25  27 
34  37 
45  13 
57  15 
70  40 
85  31 

2.65 

0  41 
2  46 
6  13 
1103 
17  16 
24  52 
33  31 
44  12 
55  57 
69  04 
83  34 

II 
2.59 

1      II 

0  40 
2  42 
6  04 

10  48 
16  52 
24  17 
33  04 
43  11 
54  39 
67  28 
81  38 

II 
2.53 

0  39 
2  39 
5  56 
10  32 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 
94  51 

II 

2.47 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

iiOg. 

0.514 
55 

0.502 
43 

0.489 
96 

0.478 
57 

0.466 
87 

0.454 
84 

0.444 
04 

0.432 
97 

0.423 
25 

0.413 
30 

0.403 
12 

0.392 
70 

Log. 

Limit 

34 

34 

35 

36 

37 

38 

38 

39 

39 

40 

41 

41 

Min- 
utes 

Merid- 
ian 

59°  t    58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

/       II 

1      II 

1     II 

/     // 

/     // 

/     // 

/     // 

/      // 

/     // 

/      // 

/      /' 

/      // 

Min. 

4 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  34 

0  33 

0  33 

0  31 

0  31 

0  30 

4 

8 

2  35 

2  31 

2  28 

2  25 

2  22 

2  19 

2  15 

2  13 

2  11 

2  07 

2  04 

2  02 

8 

12 

5  47 

5  40 

5  32 

5  26 

5  18 

5  12 

5  05 

5  00 

4  54 

4  47 

4  41 

4  35 

J2 

16 

10  17 

10  04 

9  52 

9  38 

9  26 

9  16 

9  03 

8  52 

8  42 

8  29 

8  19 

8  09 

16 

20 

16  04 

15  44 

15  24 

15  04 

14  44 

14  28 

14  08 

13  52 

13  36 

13  16 

13  00 

12  44 

20 

24 

23  08 

22  40 

22  11 

21  42 

21  13 

20  50 

20  22 

19  58 

19  35 

19  06 

18  43 

18  20 

24 

28 

31  30 

30  50 

30  11 

29  32 

28  53 

28  21 

27  42 

27  11 

26  39 

26  01 

25  29 

24  58 

28 

32 

4108 

40  16 

39  25 

38  34 

37  43 

37  02 

36  10 

35  30 

34  49 

33  58 

33  17 

32  36 

32 

36 

52  03 

50  59 

49  54 

48  49 

47  44 

46  53 

45  48 

44  56 

44  04 

4259I  42  07 

41  15 

36 

40 

64  16 

62  56 

61  36 

60  16 

58  56 

57  52 

56  32 

55  28 

54  24 

53  04    52  00 

50  56 

40 

44 

77  45 

76  09 

74  32 

72  55 

71  18 

70  02 

68  25 

67  07 

65  49 

64  12    62  55 

6137 

44 

48 

92  33 

90  37 

88  42 

86  47 

84  52 

83  19 

8124 

79  52 

78  20 

76  25    74  53 

73  21 

48 

52 

106  21 

104  06 

101  51 

99  36 

97  47 

95  32 

93  44 

9156 

89  41 

87  53 

86  05 

52 

56 

103  29 

101  55 

99  49 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

/' 

II 

A,h 

2.41 

2.36 

2.31 

2.26 

2.21 

2.17 

2.12 

2.08 

2.04 

1.99 

1.95 

1.91 

Ajh 

Log. 

0.382 

0.372 

0.363 

0.354 

0.344 

0.336 

0.326 

0.318 

0.309 

0.298 

0.290 

0.281 

Log. 

02 

91 

61 

11 

39 

46 

34 

06 

63 

85        03 

03 

Limit 

42 

43 

44 

45 

45 

46 

47 

48 

49 

50 

51 

52 

Min- 
utes 

Merid- 
ian 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

Alti- 
tudes 

188 


Latitude  31°  Declination  G)ntfafy  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       n 

0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

98  15 

112  48 

1.88 

/      II 

0  29 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
// 

1.83 

/      // 

0  29 

1  55 
4  19 
7  41 

12  00 
17  17 
23  31 
30  43 
38  53 
48  00 
58  05 
69  07 
8107 
94  05 

108  00 

II 

1.80 

/       n 

0  28 

154 

4  16 

7  33 

1148 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 

1.77 

/     // 

0  27 

151 

4  09 

7  23 

11  32 

16  36 

22  37 

29  32 

37  22 

46  08 

55  49 

66  24 

77  58 

90  25 

103  48 

II 

1.73 

/      II 

0  27 

1  49 
4  05 
7  15 

11  20 
16  19 
22  13 
29  01 
36  43 
45  20 
54  51 
65  15 
76  37 
88  51 

102  00 

II 

1.70 

/      // 

0  27 

146 

3  59 

7  05 

1104 

15  57 

21  41 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

86  46 

99  36 
II 

1.66 

/      // 

0  26 

144 

3  54 

6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 
II 

1.63 

/      // 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

5138 

61  26 

72  06 

83  38 

96  00 

II 

1.60 

/     // 

0  25 

1  41 
3  46 
6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41  52 

50  40 

60  17 

70  45 

82  04 

94  12 
II 

1.57 

/      // 

0  25 

1  39 
3  42 
6  34 

10  16 
14  47 
20  07 
26  17 
33  16 
41  04 
49  41 
59  08 
69  24 
80  29 

92  24 

II 

1.54 

/       n 

0  24 

136 

3  37 

6  27 

10  04 

14  30 

19  44 

25  46 

32  37 

40  16 

48  43 

57  59 

68  03 

78  55 

90  36 
II 

1.51 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.274 
16 

0.262 
45 

0.255 
27 

0.247 
97 

0.238 
05 

0.230 
45 

0.220 
11 

0.212 
19 

0.204 
12 

0.195 
90 

0.187 
52 

0.178 
98 

Log. 

Limit 

52 

53 

53 

54 

55 

56 

57 

57 

58 

59 

60 

61 

Min- 
utes 

Merid- 
ian 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/     // 

0  23 

135 

3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

3158 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

1     II 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
II 

1.45 

0  22 

131 

3  25 

6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
II 

1.42 

/      // 

0  22 

1  30 
3  22 
5  58 
9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

0  22 

1  27 
3  16 
5  48 
9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

8136 
II 

1.36 

/      // 

0  22 
125 
3  11 
5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 
II 

1.33 

/      // 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 

1.31 

/      // 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

1     II 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
II 

1.26 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

/      // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

1.20 

/      // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.170 
26 

0.161 
37 

0.152 
29 

0.146 
13 

0.133 
54 

0.123 
85 

0.117 
27 

0.107 
21 

0.100 
27 

0.089 
91 

0.079 
18 

0.068 
19 

Log. 

Limit 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

Min- 
utes 

Merid- 
ian 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

Alti- 
tudes 

Latitude  3i°  Declination  Contrary  Name. 


189 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/   /' 

/  /' 

/   // 

/  /' 

r       n 

/  // 

/  // 

1     II 

/  II 

/  // 

/  // 

/  // 

Min. 

4 

0  19 

0  18 

0  18 

0  17 

0  17 

0  16 

0  15 

4 

8 

1  13 

1  11 

1  10 

1  08 

107 

105 

1  03 

8 

12 

2  45 

2  41 

2  38 

2  34 

2  30 

2  27 

2  23 

12 

16 

4  55 

4  47 

4  42 

4  34 

4  26 

4  21 

4  13 

16 

20 

7  40 

7  28 

7  20 

7  08 

6  56 

6  48 

6  36 

20 

24 

1103 

10  46 

10  34 

10  16 

9  59 

9  48 

9  30 

24 

28 

15  01 

14  38 

14  22 

13  59 

13  35 

13  20 

12  57 

28 

32 

19  37 

19  06 

18  46 

18  16 

17  45 

17  24 

16  54 

32 

36 

24  51 

24  12 

23  46 

23  07 

22  28 

22  02 

2123 

36 

40 

30  40 

29  52 

29  20 

28  32 

27  44 

27  12 

26  24 

40 

44 

37  07 

36  09 

35  30 

34  32 

33  33 

32  55 

3156 

44 

48 

44  09 

43  00 

42  14 

41  05 

39  56 

39  10 

38  01 

48 

52 

51  49 

50  28 

49  34 

48  13 

46  52 

45  58 

44  37 

52 

56 

60  07 

58  33 

57  30 

55  56 

54  21 

53  19 

5144 

56 

60 

69  00 

67  12 

66  00 

1/ 

64  12 

62  24 

61  12 

ir 

59  24 

// 

// 

// 

60 

A,h 

1.15 

1.12 

1.10 

1.07 

1.04 

1.02 

0.99 

Ajh 

Log. 

0.060 

0.049 

0.041 

0.029 

0.017 

0.008 

9.995 

Log. 

70 

22 

39 

38 

03 

60 

64 

Limit 

74 

74 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

/   // 
II 

II 

II 

II 

1     II 
0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 

15  59 

19  44 

23  52 

28  23 

33  21 

38  40 

44  24 
II 

0.74 

1     II 
Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 

43  12 

II 

0.72 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

1146 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

41  24 

II 

0.69 

/  // 

Oil 

0  42 

135 

2  49 

4  24 

6  21 

8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 

0.66 

/  II 

0  10 

0  40 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
II 

0.63 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 

36  36 

II 

0.61 

',  " 
0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

/  // 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
2154 
25  41 
29  48 

34  12 

II 

0.57 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.869 
23 

9.857 
33 

9.838 

85 

9.819 
54 

9.799 
34 

9.785 
33 

9.770 

85 

9.755 
87 

Log. 

Limit 

86 

87 

87 

87 

88 

89 

90 

91 

Min- 
utes 

Merid-I  -lo 

ian  1  '• 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

Alti- 
tudes 

190 


Latitude  32°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

0 
3 
7 
13 
20 
30 
41 
53 
67 
83 

3.1 

// 

51 
21 
32 
24 
56 
D9 
Dl 
35 
50 
14 

i 

0 

3 
7 

13 
21 
31 
42 
55 
69 
86 

3.2 

// 

51 

27 
45 
i7 
32 
DO 
13 
D8 
46 
08 

3 

/ 

0 
3 

7 

14 
22 
31 
43 
56 
71 
88 

II 
3.3 

// 

53 
33 
59 
13 
12 
58 
31 
50 
56 
i8 

3 

0 

3 
8 
14 
22 
32 
44 
58 
74 
91 

II 
3.4 

// 

54 

iO 
14 
38 
52 
55 
50 
33 
35 
28 

3 

0 
3 
8 
15 
23 
33 
46 
60 
76 

■ 
3.5 

// 

57 
47 
30 
06 
36 
59 
15 
25 
28 

i 

/      // 

0  59 
3  53 
8  45 
15  35 
24  20 
35  03 
47  41 
62  17 
78  51 

3.65 

/           H 

1  00 
4  02 
9  05 
16  07 
25  12 
36  17 
49  24 
64  31 

3.78 

/     // 

102 
4  10 
9  23 
16  41 
26  04 
37  32 
51  06 
66  44 

II 
3.91 

/     // 

1  05 
4  19 
9  43 
17  17 
27  00 
38  53 
52  55 
69  07 

4.05 

/      // 

1  07 
4  30 
10  06 
17  58 
28  04 
40  25 
55  01 
7151 

4.21 

/     // 

1  10 
4  40 
10  31 
18  41 
29  12 
42  03 
57  14 
74  45 

II 
4.38 

/     II 

1  13 
4  52 
10  57 
19  27 
30  24 
43  47 
59  55 
77  49 

■/;■ 

4.56 

Min. 

\ 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Log. 

0.496 
93 

0.509 
20 

0.522 
44 

0.535 
29 

0.549 
00 

0.562 
29 

0.577 
49 

0.592 
18 

0.607 
46 

0.624 

28 

0.641 
47 

0.658    , 
96   ^°^- 

JJmit 

35 

34 

33 

32 

32 

31 

31  . 

30 

29 

28 

28 

27 

Min- 
utes 

Merid- 
ian 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

eqo       Alti- 
°y        tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

/      // 

1      II 

1     II 

/      // 

/      // 

1     II 

/      // 

/      // 

1      II 

/      II 

/      // 

Min. 

4 

1  16 

1  19 

123 

128 

1  33 

1  39 

1  45 

152 

2  00 

2  11 

2  22 

2  37 

4 

8 

5  05 

5  18 

5  35 

5  52 

6  12 

6  33 

6  59 

7  28 

8  02 

8  41 

9  29 

10  27       8 

12 

11  26 

11  58 

12  33 

13  12 

13  56 

14  45 

15  43 

16  48 

18  04 

19  33 

21  20 

23  31      12 

16 

20  18 

21  14 

22  19 

23  28 

24  48 

26  15 

27  57 

29  52 

32  08 

34  47 

37  56 

41  49      16 

20 

31  44 

33  12 

34  52 

36  40 

38  44 

41  00 

43  40 

46  40 

50  12 

54  20 

20 

24 

45  42 

47  48 

50  12 

52  48 

55  47 

59  03 

62  53 

24 

28 

62  10 

65  03 

68  21 

7152 

75  55 

80  21 

28 

32 

81  14 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

A,h 

4.76 

4.98 

5.23 

5.50 

5.81 

6.15 

6.55 

7.00 

7.53 

8.15 

8.89 

9.80 

A,h 

Log. 

0.677 

0.697 

0.718 

0.740 

0.764 

0.788 

0.816 

0.845 

0.876 

0.911 

0.948 

0.991 

Log. 

61 

23 

50 

36 

18 

88 

24 

10 

79 

16 

90 

23 

Limit 

26 

25 

24 

24 

23 

22 

21 

20 

19 

18 

16 

14 

Min- 
utes 

Merid- 
ian 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

QTo        Alti- 
°^     1  tudes 

Latitude  32°  Declination  Same  Name. 
Declinations. 


191 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2 
11 
26 
46 

10.9 

// 

55 
10 
14 
38 

3 

3 
13 

29 
48 

12.3 

18 
12 
13 
33 

B 

1 

3. 
15 
34. 

It 
14.3 

50 

18 
22 

2 

4 
18 

17.0 

32 
39 

2 

/ 

1 

// 

II 

// 

/ 

/ 

1 

It 

/ 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.038 
62 

1.092 
72 

1.155 
94 

1.230 
96 

Log. 

Limit 

13 

12 

10 

8 

6 

5 

4 

2 

0          2 

4 

r:      1  Min- 

Merid- 
ian 

82 

a 

83 

0 

84 

3 

85 

0 

86 

3 

87 

3 

88 

D 

89 

} 

9( 

D° 

8< 

)° 

88° 

87 

3 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

1      II 

/     // 

/     // 

/     // 

/      // 

/     // 

/     // 

/      // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

4  04 

3  21 

2  50 

2  27 

2  08 

154 

1  42 

132 

123 

116 

1  10 

4 

8 

16  17 

13  23 

11  19 

9  46 

8  34 

7  36 

6  48 

6  09 

5  35 

5  06 

4  42 

8 

12 

30  07 

25  29 

21  59 

19  14 

17  06 

15  19 

13  50 

12  33 

11  29 

10  32 

12 

16 

45  19 

39  05 

34  16 

30  26 

27  13 

24  34 

22  19 

20  23 

18  44 

16 

20 

53  32 

47  32 

42  32 

38  24 

34  52 

31  52 

29  16 

20 

24 

61  15 

55  18 

50  12 

45  53 

42  09 

24 

28 

68  21 

62  26 

57  22 

28 

32 

74  55 

32 

36 

36 

40 

40 

44 

44 

48 

,  . . 

48 

52 

52 

56 

56 

60 

60 

1 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

15.26 

12.55 

10.62 

9.16 

8.03 

7.13 

6.38 

5.76 

5.23 

4.78 

4.39 

Aih 

Log. 

1.183 

1.098 

1.026 

0.961 

0.904 

0.853 

0.804 

0.760 

0.718 

0.679 

0.642 

55 

64 

12 

90 

72 

09 

82 

42 

50 

43 

46 

Log. 

Limit 

6 

8 

10 

12 

14 

15 

17 

19 

21 

23 

25 

26 

Min- 
utes 

Merid- 
ian 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79«» 

78° 

77° 

76° 

75° 

Alti- 
tudes 

192 


Latitude  32°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

1     II 

/       n 

/       n 

/     II 

/     II 

/     II 

Min. 

Min. 

4 

1  05 

100 

0  55 

0  51 

0  48 

0  45 

0  42 

0  39 

0  36 

0  35 

0  32 

0  30 

4 

8 

4  19 

4  00 

3  42 

3  26 

3  12 

2  59 

2  47 

2  37 

2  27 

2  17 

2  09 

2  01 

8 

12 

9  42 

8  59 

8  19 

7  44 

7  12 

6  43 

6  15 

5  52 

5  30 

5  09 

4  49 

4  32 

12 

16 

17  14 

15  57 

14  45 

13  43 

12  48 

1157 

1109 

10  24 

9  46 

9  11 

8  35 

8  04 

16 

20 

26  56 

24  56 

23  03 

2128 

20  00 

18  40 

17  24 

16  16 

15  16 

14  20 

13  24 

12  36 

20 

24 

38  47 

35  54 

33  13 

30  55 

28  48 

26  53 

25  04 

23  25 

2159 

20  39 

19  18 

18  09 

24 

28 

52  47 

48  52 

45  13 

42  05 

39  12 

36  35 

34  06 

3153 

29  56 

28  05 

26  16 

24  42 

28 

32 

68  57 

63  50 

59  03 

54  57 

51  12 

47  47 

44  32 

41  39 

39  05 

36  41 

34  18 

32  15 

32 

36 

74  44 

69  33 

64  48 

60  29 

56  23 

52  42 

49  28 

46  27 

43  25 

40  50 

36 

40 

74  40 

69  36 

65  04 

6104 

57  20 

53  36 

50  24 

40 

44 

78  43 

73  53 

69  23 

64  51 

60  59 

44 

48 

82  33 

77  11 

72  34 

48 

52 

85  10 

52 

56 

56 

60 

60 

It 

11 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

4.04 

3.74 

3.46 

3.22 

3.00 

2.80 

2.61 

2.44 

2.29 

2.15 

2.01 

1.89 

A,h 

Log. 

0.606 

0.572 

0.539 

0.507 

0.477 

0.447 

0.416 

0.387 

0.359 

0.332 

0.303 

0.276 

Log. 

38 

87 

08 

86 

12 

16 

64 

39 

84 

44 

20 

46 

Limit 

27 

28 

30 

31 

32 

33 

35 

36 

38 

40 

42 

44 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

1     II 

/      // 

/     // 

/     // 

/      // 

/      // 

/     // 

/     // 

/           // 

/      // 

/      '/ 

Min. 

4 

0  28 

0  27 

0  25 

0  23 

0  22 

0  20 

0  19 

0  18 

0  17 

0  15 

0  14 

0  14 

4 

8 

154 

147 

140 

1  34 

128 

123 

1  17 

1  12 

108 

103 

0  58 

0  54 

8 

12 

4  16 

4  00 

3  45 

3  32 

3  19 

3  06 

2  54 

2  42 

2  33 

2  23 

2  13 

2  02 

12 

16 

7  33 

7  08 

6  39 

6  16 

5  53 

5  30 

5  10 

4  50 

4  31 

4  13 

3  55 

3  38 

16 

20 

11  48 

1108 

10  24 

9  48 

9  12 

8  36 

8  04 

7  32 

7  04 

6  36 

6  08 

5  40 

20 

24 

16  59 

16  02 

14  59 

14  06 

13  15 

12  23 

1137 

10  51 

10  11 

9  30 

8  50 

8  10 

24 

28 

23  08 

2149 

20  23 

19  13 

18  02 

16  52 

15  49 

14  46 

13  51 

12  57 

12  02 

1106 

28 

32 

30  13 

28  30 

26  37 

25  06 

23  33 

22  01 

20  39 

19  17 

18  05 

16  54 

15  42 

14  30 

32 

36 

38  14   36  05 

33  42 

3145 

29  49 

27  52 

26  08 

24  25 

22  54 

21  23 

19  52 

18  22 

36 

40 

47  12    44  32 

4136 

39  12 

36  48 

34  24 

32  16 

30  08 

28  16 

26  24 

24  32 

22  40 

40 

44 

57  07;  53  54 

50  20 

47  26 

44  32 

41  37 

39  02 

36  28 

34  12 

3156 

39  41 

27  26 

44 

48 

67  56    64  07 

59  54 

56  27 

52  59 

49  32 

46  28 

43  23 

40  42 

38  01 

35  20 

32  28 

48 

52 

79  46 

75  15 

70  18 

66  15 

62  11 

58  08 

54  32 

50  55 

47  46 

44  37 

41  28 

38  18 

52 

56 

87  18 

8132 

76  50 

72  08 

67  25 

63  14 

59  04 

55  24 

51  44 

48  05 

44  26 

56 

60 

// 

II 

93  36 

II 

88  12 
II 

82  48 
II 

77  24 

72  36 

67  48 
II 

63  36 
II 

59  24 
II 

55  12 
II 

5100 
II 

60 

A,h 

1.77 

1.67 

1.56 

1.47 

1.38 

1.29 

1.21 

1.13 

1.06 

0.99 

0.92 

0.85 

A,h 

0.247 

0.222 

0.193 

0.167 

0.139 

0.110 

0.082 

0.053 

0.025 

9.995 

9.963 

9.929 

Log. 

97 

72 

12 

32 

88 

59 

79 

08 

31 

64 

79 

42 

Limit 

46 

48 

50 

52 

53 

54 

56 

58 

60 

62 

64 

66 

Min- 
utes 

Merid- 
ian 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

Alti- 
tudes 

Latitude  32°  Declination  Contrary  Name. 

Declinations. 


193 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

IP 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

1 

0 
3 
7 
13 
20 
30 
41 
53 
67 
83 

II 
3.1 

51 

21 
32 
24 
56 
39 
31 
35 
50 
14 

1 

0 
3 

7 
13 
20 
29 
39 
52 
66 
81 

II 
3.0 

// 

49 
16 
21 
33 
24 
23 
59 
13 
36 
36 

3 

1 

0 
3 

7 
12 
19 
28 
38 
50 
64 
79 

II 
2.9 

47 
10 
10 
42 
52 
36 
57 
52 
22 
28 

3 

1 

0 
3 
6 
12 
19 
27 
37 
49 
62 
77 

II 
2.9 

// 

46 
35 
58 
22 
20 
50 
54 
30 
38 
20 

3 

/      // 

0  45 
3  01 
6  47 
12  05 
18  52 
27  10 
36  59 
48  18 
61  08 
75  28 

II 
2.83 

0 

2 

6 

11 

18 
26 
36 
47 
59 
73 

II 
2.7 

44 
57 
38 
46 
24 
30 
34 
36 
37 
36 

5 

0  43 
2  52 
6  27 
11  29 
17  56 
25  50 
35  09 
45  54 
58  07 
71  44 
86  48 

2.69 

0  42 
2  48 
6  18 
11  14 
17  32 
25  15 
34  22 
44  53 
56  49 
70  08 
84  52 

2.63 

/     // 

0  41 
2  45 
6  10 
10  58 
17  08 
24  40 
33  35 
43  52 
55  31 
68  32 
82  56 

II 
2.57 

/     // 

0  40 
2  41 
6  01 
10  43 
16  44 
24  06 
32  48 
42  50 
54  13 
66  56 
80  59 
96  23 

II 
2.51 

1       n 

0  39 
2  37 
5  53 
10  27 
16  20 
23  31 
32  01 
41  49 
52  55 
65  20 
79  03 
94  05 

II 
2.45 

0  38 
2  34 
5  46 
10  14 
16  00 
23  02 
31  22 
40  58 
5150 
64  00 
77  26 
92  10 

II 
2.40 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.496 
93 

0.485 
72 

0.474 
22 

0.462 
40 

0.451 
79 

0.440 
91 

0.429 
75 

0.419 
96 

0.409 
93 

0.399 
67 

0.389 
17 

0.380 
21 

Log. 

Limit 

35 

36 

37 

38 

38 

39 

40 

40 

41 

41 

42 

42 

Min- 
utes 

Merid- 
ian 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  38 

2  30 

5  37 

9  59 

15  36 

22  28 

30  34 

39  56 

50  33 

62  24 

75  30 

89  51 

105  27 

2.34 

1     II 

0  36 

2  27 

5  30 

9  46 

15  16 

21  59 

29  56 

39  05 

49  28 

6104 

73  53 

87  56 

103  12 

II 
2.29 

0  36 

2  24 

5  24 

9  36 

15  00 

2136 

29  24 

38  24 

48  36 

60  00 

72  36 

86  24 

101  24 

II 
2.25 

/      // 

0  35 
2  21 
5  17 

9  23 
14  40 
2107 
28  45 
37  33 
47  31 
58  40 
70  59 
84  29 
99  09 

II 
2.20 

/     // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

/      // 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

II 
2.11 

/      // 

0  33 

2  13 

4  58 

8  50 

13  48 

19  52 

27  03 

35  20 

44  43 

55  12 

66  48 

79  29 

93  17 

2.07 

/     // 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

91  29 

II 
2.03 

/     // 

0  31 

2  07 
4  47 
8  29 
13  16 
19  06 
26  01 
33  58 
42  59 
53  04 
64  12 
76  25 
89  41 

II 
1.99 

/     II 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

10155 

_ 

II 

1.95 

/      // 

0  30 

2  02 
4  35 
8  09 
12  44 
18  20 
24  58 
32  36 
41  15 
50  56 
61  37 
73  21 
86  05 
99  49 

II 
1.91 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

3155 

40  24 

49  52 

60  21 

7148 

84  16 

97  45 

1.87 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.369 
22 

0.359 
84 

0.352 

18 

0.342 
42 

0.332 
44 

0.324 

28 

0.315 
97 

0.307 
50 

0.298 

85 

0.290 
03 

0.281 
03 

0.271 

84 

Log. 

Limit 

43 

44 

45 

46 

46 

47 

48 

49 

49 

50 

51 

52 

Min- 
utes 

Merid- 
ian 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

Alti- 
tudes 

194 


Latitude  32°  Declination  Contrary  Name. 
Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34°      35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  29 

1  57 
4  23 
7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
It 

1.83 

/      // 

0  28 

1  55 
4  18 
7  38 

11  56 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 
II 

1.79 

0  28 

153 

4  14 

7  30 

1144 

16  54 

23  00 

30  02 

38  01 

46  56 

56  47 

67  33 

79  19 

9159 

105  36 

II 

1.76 

/     // 

0  27 

151 

4  09 

7  23 

11  32 

16  36 

22  37 

29  22 

37  22 

46  08 

55  49 

66  24 

77  58 

90  25 

103  48 

1.73 

/     // 

0  27 

1  49 
4  05 
7  15 

11  20 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
II 

1.70 

0  27 

1  47 
4  00 
7  08 

11  08 
16  02 
21  49 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 
87  18 

100  12 

II 

1.67 

/     // 

0  26 

1  44 
3  54 
6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 
II 

1.63 

/     // 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 

II 

1.60 

/     // 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41.52 

50  40 

60  17 

70  45 

82  04 

94  12 

II 

1.57 

/     // 

0  25 

1  39 
3  42 
6  34 

10  16 
14  47 
20  07 
26  17 
33  16 
41  04 
49  41 
59  08 
69  24 
80  29 

92  24 

II 

1.54 

/     // 

0  24 

136 

3  37 

6  27 

10  04 

14  30 

19  44 

25  46 

32  37 

40  16 

48  43 

57  59 

68  03 

78  55 

90  36 

II 

1.51 

/     II 

0  23 

135 

3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.262 
45 

0.252 
85 

0.245 
.    51 

0.238 
05 

0.230 
45 

0.222 
72 

0.212 
19 

0.204 
12 

0.195 
90 

0.187 
52 

0.178 
98 

0.170 
26 

Log. 

Limit 

53 

54 

54 

55 

56 

57 

58 

58 

59 

60 

61 

62 

Min- 
utes 

Merid- 
ian 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

4^170      Hour 
*'       Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  47 

87  00 

II 

1.45 

/      // 

0  22 

131 

3  25 

6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 

1.42 

0  22 
130 
3  22 

5  58 
9  20 
13  26 
18  18 
23  54 
30  14 
37  20 
45  10 
53  46 
63  06 
73  10 

84  00 

If 

1.40 

/     // 

0  22 

128 

3  17 

5  51 

9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

71  37 

82  12 

II 

1.37 

/      // 

0  22 

126 

3  13 

5  43 

8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

51  27 

60  23 

70  02 

80  24 
II 

1.34 

/     // 

0  21 

1  23 
3  08 
5  36 
8  44 

12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

1.31 

/     // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 

1.29 

1     II 

0  20 

1  21 
3  02 

5  22 
8  24 
12  06 
16  28 
2130 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 
75  36 

1.26 

0  20 

1  20 

2  59 
5  17 
8  16 

11  54 
16  12 
21  10 
26  47 
33  04 
40  00 
47  37 
55  53 
64  48 
74  24 

n 

1.24 

/     // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 
72  36 

1.21 

/     // 

0  19 

1  15 

2  50 
5  02 

7  52 
11  20 
15  25 
20  08 
25  30 
3128 
38  05 
45  18 
53  10 
6141 
70  48 

1.18 

/       // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  52 
52  16 
60  38 
69  36 

1.16 

Min. 

4 

8 
12 
16 
80 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.161 
37 

0.152 
29 

0.146 
13 

0.136 
72 

0.127 
10 

0.117 
27 

0.110 
59 

0.100 
37 

0.093 
42 

0.082 
79 

0.071 

88 

0.064 
46 

Log. 

Limit 

62 

63 

65 

66 

67 

68 

69 

70 

71 

71 

72 

73 

Min- 
utes 

Merid- 
ian 

22° 

21° 

20°  j    19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

Alti- 
tudes 

Latitude  32°  Declination  Contrary  Name. 


195 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/       /' 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

1     II 

/     // 

/      // 

/      // 

/      // 

Min. 

4 

0  18 

0  18 

0  17 

0  17 

0  16 

0  16 

4 

8 

1  12 

1  11 

1  10 

108 

106 

104 

8 

12 

2  42 

2  39 

2  37 

2  33 

2  28 

2  25 

12 

16 

4  50 

4  45 

4  39 

4  31 

4  24 

4  19 

16 

20 

7  32 

7  24 

7  16 

7  04 

6  52 

6  44 

20 

24 

10  51 

10  40 

10  28 

10  11 

9  53 

9  42 

24 

28 

14  46 

14  30 

14  15 

13  51 

13  28 

13  12 

28 

32 

19  17 

18  56 

18  36 

18  05 

17  35 

17  14 

32 

36 

24  25 

23  59 

23  33 

22  54 

22  15 

21  49 

36 

40 

30  08 

29  36 

29  04 

28  16 

27  28 

26  56 

40 

44 

36  28 

35  49 

35  10 

34  12 

33  14 

32  35 

44 

48 

43  23 

42  37 

41  51 

40  42 

39  33 

38  47 

48 

52 

50  55 

50  01 

49  07 

47  46 

46  25 

45  31 

52 

56 

59  04 

58  01 

56  58 

55  24 

53  50 

52  47 

56 

60 

67  48 

66  36 

It 

65  24 

63  36 
II 

6148 
II 

60  36 

// 

1 

// 

II 

// 

„ 

60 

Ajh 

1.13 

1.11 

1.09 

1.06 

1.03 

1.01 

A,h 

Log. 

0.053 
08 

0.045 
32 

0.037 
43 

0.025 
31 

0.012 

84 

0.004 
32 

Log. 

Limit 

73 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

Alti- 
tudes 

Declinations. — -Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

Min. 

4 

0  12 

0  11 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

4 

8 

0  49 

0  47 

0  45 

0  43 

0  42 

0  40 

0  38 

0  37 

0  36 

8 

12 

150 

145 

142 

137 

135 

130 

126 

124 

1  21 

12 

16 

3  14 

3  07 

3  02 

2  54 

2  49 

2  42 

2  34 

2  28 

2  23 

16 

20 

5  04 

4  52 

4  44 

4  32 

4  24 

4  12 

4  00 

3  52 

3  44 

20 

24 

7  18 

7  00 

6  49 

6  32 

6  21 

6  03 

5  46 

5  32 

5  23 

24 

28 

9  56 

9  33 

9  17 

8  53 

8  37 

8  14 

7  50 

7  35 

7  19 

28 

32 

12  58 

12  28 

12  07 

11  36 

11  15 

10  45 

10  14 

9  54 

9  33 

32 

36 

16  25 

15  46 

15  20 

14  42 

14  16 

13  37 

12  58 

12  32 

12  06 

36 

40 

20  16 

19  28 

18  56 

18  08 

17  36 

16  48 

16  00 

15  28 

14  56 

40 

44 

24  31 

23  33 

22  54 

2157 

21  18 

20  20 

19  22 

18  43 

18  04 

44 

48 

29  09 

28  00 

27  14 

26  08 

25  20 

24  11 

23  02 

22  16 

21  30 

48 

52 

34  15 

32  54 

32  00 

30  38 

29  44 

28  23 

27  02 

26  09 

25  14 

52 

56 

39  43 

38  09 

37  06 

35  33 

34  30 

32  56 

3122 

30  19 

29  16 

56 

60 

45  36 

43  48 

42  36 

40  48 

39  36 

37  48 

36  00 

34  48 

33  36 

60 

// 

// 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

0.76 

0.73 

0.71 

0.68 

0.66 

0.63 

0.60 

0.58 

0.56 

A,h 

Log. 

9.880 

9.863 

9.851 

9.832 

9.819 

9.799 

9.778 

9.763 

9.748 

Log. 

81 

32 

26 

51 

54 

34 

15 

43 

19 

Limit 

85 

86 

86 

87 

87 

88 

88 

89 

90 

Min- 
utes 

Merid- 
ian 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

Alti- 
tudes 

196 


Latitude  33°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

4 

8 

12 
16 
20 
24 
"  28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0' 

3 

7 

12. 
20  ( 
29  ( 
39 
51 
65 
80 

II 
3.0 

// 

18 
13 
15 
53 
38 
30 
28 
?2 
14 
32 

2 

1 

0 
3 
7 
13 
20 
29 
40 
53 
67 
82 

II 
3.1 

u 

50 
19 
27 
17 
14 
52 
38 
34 
11 
56 

1 

/ 
0 

? 

13 
21 
30 
41 
54 
69 
85 

II 
3.2 

// 

51 
25 
11 
39 
20 
13 
49 
37 
37 
20 

3 

0 
3 

7 
14 
21 
31 
43 
56 
71 
87 

II 
3.2 

II 

52 
31 
54 
32 
56 
35 
30 
39 
34 
14 

3 

0 
3 

8 
14 
22 
32 
44 
57 
73 
90 

II 
3.3 

// 

54 
37 
38 
28 
36 
33 
18 
51 
14 
24 

3 

0 

3 

8 
14 
23 
33 
45 
59 
75 

II 
3.4 

// 

55 
14 
23 
53 
16 
30 
37 
34 
23 

3 

0 
3 

8 
15 
24 
34 

47 
61 
77 

3.6 

n 

58 
51 
39 
25 
34 
40 
10 
36 
59 

1 

/      // 

0  59 
4  00 
8  57 
15  55 
24  52 
35  48 
48  45 
63  40 

II 
3.73 

/     // 

102 
4  07 
9  16 
16  28 
25  44 
37  04 
50  26 
65  52 

II 
3.86 

/     // 

104 
4  16 
9  36 
17  04 
26  40 
38  24 
52  16 
68  16 

II 
4.00 

/     // 

107 
4  25 
9  57 
17  43 
27  40 
39  51 
54  13 
70  49 

II 
4.15 

/     // 

109 
4  36 
10  22 
18  26 
28  48 
41  29 
56  27 
73  43 

II 
4.32 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Log. 

0.480 
01 

0.492 
76 

0.505 
15 

0.517 
20 

0.530 
20 

0.542 
83 

0.557 
51 

0.571 
71 

0.586 
59 

0.602 
06 

0.618 
05 

0.635 

48 

Log. 

Limit 

36 

35 

34 

33 

32 

32 

32 

31 

30 

29 

29 

28 

Min- 
utes 

Merid- 
ian 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

Yl° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/      // 

1     II 

/      // 

/      // 

1     II 

1      II 

/      II 

/     // 

1      II 

/      // 

1      II 

1    Min. 

4 

1  11 

1  15 

1  18 

123 

126 

131 

137 

143 

150 

158 

2  08 

2  19 

4 

8 

4  48 

5  00 

5  14 

5  29 

5  47 

6  06 

6  27 

6  53 

7  20 

7  53 

8  32 

9  19 

8 

12 

10  47 

11  15 

11  47 

12  21 

12  59 

13  42 

14  31 

15  28 

16  31 

17  44 

19  12 

20  57 

12 

16 

19  09 

20  01 

20  57 

2159 

23  05 

24  22 

25  49 

27  28 

29  21 

3132 

34  08 

37  15 

16 

20 

29  56 

31  16 

32  44 

34  20 

36  04 

38  04 

40  20 

42  56 

45  52 

49  16 

53  20 

58  12 

20 

24 

43  05 

45  02 

47  08 

49  27 

5156 

54  49 

58  05 

61  49 

66  03 

24 

28 

58  41 

61  17 

64  10 

67  17 

70  42 

74  37 

79  03 

84  09 

28 

32 

76  38 

80  02 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

4.49 

4.69 

4.91 

5.15 

5.41 

5.71 

6.05 

6.44 

6.88 

7.39 

8.00 

8.73 

A,h 

Log. 

0.652 

0.671 

0.691 

0.711 

0.733 

0.756 

0.781 

0.808 

0.837 

0.868 

0.903 

0.941 

Log. 

25 

17 

08 

81 

20 

64 

76 

89 

59 

64 

09 

01 

Limit 

27 

26 

25 

25 

24 

23 

22 

20 

19 

18 

17 

16 

Min- 
utes 

Merid- 
ian 

69 

3 

70 

D 

71 

J 

72< 

J 

73' 

•> 

74= 

) 

75' 

> 

76° 

77' 

> 

78' 

79= 

80= 

Alti- 
tudes 

Latitude  33°  Declination  Same  Name. 

Declinations. 


19^ 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30°      31° 

32° 

33° 

34°      35° 

Hour 

Angles 

Mia. 

/       // 

/     // 

/     // 

/      // 

/     // 

/     // 

/ 

//    /     // 

1     II 

/     // 

/ 

//    /     // 

Min. 

4 

2  34 

2  55 

3  15 

3  45 

4  27 

4 

8 

10  15 

1126 

12  57 

14  59 

17  47 

8 

12 

23  05 

25  44 

29  08 

33  42 

12 

16 

4103 

45  44 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

' 

/ 

//         // 

Ajh 

9.62 

10.72 

12.14 

14.04 

16.68 

A,h 

Log. 

0.983 
18 

1.030 
19 

1.084 
22 

1.147 
37 

1.222 
20 

Log, 

Limit 

14 

13 

11 

9 

8 

7 

5 

3 

2 

0 

2         4 

Min- 
utes 

Merid- 
ian 

8P 

82° 

83° 

84° 

85° 

86° 

87 

=      88° 

89° 

90° 

89°      88° 

Alti- 
tudes 

Declinations, 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/     // 

/     // 

1     II 

/     // 

Min. 

Min. 

4 

3  58 

3  16 

2  46 

2  22 

2  05 

151 

139 

130 

121 

1  14 

4 

8 

15  53 

13  04 

1102 

9  31 

8  20 

7  24 

6  38 

5  58 

5  25 

4  57 

8 

12 

35  44 

29  23 

24  50 

21  26 

18  46 

16  40 

14  54 

13  26 

12  12 

1108 

12 

16 

46  53 

44  10 

38  06 

33  22 

29  36 

26  30 

23  54 

2140 

19  48 

16 

20 

59  32 

52  08 

46  16 

4124 

37  20 

33  52 

30  56 

20 

24 

66  37 

59  37 

53  46 

48  46 

44  33 

24 

28 

60  37 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

Aih 

14.89 

12.24 

10.35 

8.93 

7.82 

6.94 

6.21 

5.60 

5.08 

4.64 

Aih 

Log. 

1.172 

1.087 

1.014 

0.950 

0.893 

0.841 

0.793 

0.748 

0.705 

0.666 

Log. 

89 

78 

94 

85 

21 

36 

09 

19 

86 

52 

Limit 

6 

8 

10 

12 

13 

15 

17 

19 

20 

21 

23 

25 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

Alti- 
tudes 

198 


Latitude  33°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

t     II 

/     // 

/     // 

/     // 

Min. 

4 

108 

102 

0  58 

0  54 

0  50 

0  47 

0  43 

0  40 

0  38 

0  35 

0  33 

0  30 

4 

8 

4  33 

4  10 

3  51 

3  34 

3  19 

3  05 

2  53 

2  41 

2  31 

2  22 

2  12 

2  03 

8 

12 

10  14 

9  25 

8  41 

8  02 

7  27 

6  58 

6  29 

6  03 

5  40 

5  18 

4  57 

4  38 

12 

16 

18  10 

16  43 

15  27 

14  18 

13  17 

12  22 

1131 

10  45 

10  04 

9  26 

8  47 

8  14 

16 

20 

28  24 

26  08 

24  08 

22  20 

20  44 

19  20 

18  00 

16  48 

15  44 

14  44 

13  44 

12  52 

20 

24 

40  54 

37  38 

34  46 

32  10 

29  52 

27  50 

25  55 

24  12 

22  40 

21  13 

19  47 

18  31 

24 

28 

55  40 

51  14 

47  18 

43  46 

40  38 

37  54 

35  17 

32  56 

30  50 

28  53 

26  55 

25  14 

28 

32 

72  42 

66  54 

61  46 

57  10 

53  04 

49  30 

46  05 

43  00 

40  16 

37  43 

35  09 

32  57 

32 

36 

78  12 

72  22 

67  11 

62  38 

58  19 

54  26 

50  59 

47  44 

44  30 

41  41 

36 

40 

77  20 

72  00 

67  12 

62  56 

58  56 

54  56 

51  28 

40 

44 

81  19 

76  09 

71  18 

66  28 

62  16 

44 

48 

84  52 

79  06 

74  07 

48 

52 

86  59 

52 

56 

56 

60 

60 

n 

" 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

A,h 

4.26 

3.92 

3.62 

3.35 

3.11 

2.90 

2.70 

2.52 

2.36 

2.21 

2.06 

1.93 

A,h 

Log. 

0.629 

0.593 

0.558 

0.525 

0.492 

0.462 

0.431 

0.401 

0.372 

0.344 

0.313 

0.285 

Log. 

41 

29 

71 

04 

76 

40 

36 

40 

91 

39 

87 

56 

Limit 

26 

27 

29 

31 

32 

33 

34 

36 

38 

40 

42 

43 

Min- 
utes 

Merid- 
ian 

75= 

74= 

) 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/       // 

/     /' 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  29 

0  27 

0  25 

0  24 

0  22 

0  21 

0  19 

0  19 

0  17 

0  16 

0  14 

0  14 

4 

8 

156 

1  49 

1  42 

136 

130 

1  23 

1  19 

1  13 

109 

104 

0  59 

0  54 

8 

12 

4  20 

4  05 

3  49 

3  36 

3  22 

3  08 

2  57 

2  45 

2  36 

2  25 

2  14 

2  02 

12 

16 

7  44 

7  15 

6  47 

6  24 

5  58 

5  36 

5  15 

4  55 

4  36 

4  19 

3  58 

3  38 

16 

20 

12  04 

11  20 

10  36 

10  00 

9  20 

8  94 

8  12 

7  40 

7  12 

6  44 

6  12 

5  40 

20 

24 

17  23 

16  19 

15  16 

14  24 

13  26 

12  35 

11  48 

1103 

10  22 

9  42 

8  55 

8  10 

24 

28 

23  39 

22  13 

20  47 

19  36 

18  18 

17  07 

16  05 

15  01 

14  07 

13  12 

12  10 

1106 

28 

32 

30  53 

29  01 

27  08 

25  36 

23  54 

22  21 

21  00 

19  37 

18  26 

17  14 

15  53 

14  30 

32 

36 

39  06 

36  43 

34  21 

32  24 

30  14 

28  18 

26  34 

24  51 

23  20 

21  49 

20  05 

18  22 

36 

40 

48  16 

45  20 

42  24 

40  00 

37  20 

34  56 

32  48 

30  40 

28  48 

26  56 

24  48 

22  40 

40 

44 

58  24 

54  51 

51  18 

48  24 

45  10 

42  16 

39  41 

37  07 

34  51 

32  35 

30  00 

27  26 

44 

48 

69  30 

65  15 

6103 

57  36 

53  46 

50  18 

47  14 

44  09 

41  28 

38  47 

35  43 

32  38 

48 

52 

81  34 

76  37 

71  39 

67  36 

63  06 

59  02 

55  26 

51  49 

48  40 

45  31 

41  55 

38  18 

52 

56 

88  51 

83  06 

78  24 

73  10 

68  28 

64  17 

60  07 

56  27 

52  47 

48  36 

44  26 

56 

60 

II 

II 

90  00 

84  00 

78  36 

73  48 

69  00 

64  48 
II 

60  36 

II 

55  48 

5100 

II 

60 

Ajh 

1.81 

1.70 

1.59 

1.50 

1.40 

1.31 

1.23 

1.15 

1.08 

1.01 

0.93 

0.85 

A,h 

Log. 

0.257 

0.230 

0.201 

0.176 

0.146 

0.117 

0.089 

0.060 

0.033 

0.004 

9.968 

9.929 

Log. 

68 

45 

40 

09 

13 

27 

91 

70 

42 

32 

48 

42 

Limit 

45 

46 

48 

50 

51 

53 

55 

57 

59 

61 

63 

65 

Min- 
utes 

Merid- 
ian 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

52° 

Alti- 
tudes 

Latitude  33°  Declination  Contrary  Name. 


199 


Declixatioxs. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Mill. 

/   // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  II 

/  // 

/  // 

/  // 

/   // 

Min. 

4 

0  48 

0  47 

0  46 

0  45 

0  43 

0  43 

0  42 

0  41 

0  39 

0  38 

0  38 

0  37 

4 

8 

3  13 

3  08 

3  04 

2  59 

2  55 

2  50 

2  46 

2  43 

2  40 

2  36 

2  32 

2  29 

8 

12 

7  15 

7  04 

6  53 

6  43 

6  33 

6  23 

6  14 

6  06 

5  59 

5  50 

5  43 

5  35 

12 

16 

12  53 

12  32 

12  15 

1157 

11  39 

11  21 

11  06 

10  50 

10  37 

10  22 

10  09 

9  57 

16 

20 

20  08 

19  36 

19  08 

18  40 

18  12 

17  44 

17  20 

16  56 

16  36 

16  12 

15  52 

15  32 

20 

24 

29  00 

28  13 

27  33 

26  53 

26  12 

25  33 

24  58 

24  23 

23  54 

23  19 

22  51 

22  22 

24 

28 

39  28 

38  25 

37  30 

36  35 

35  41 

34  45 

33  58 

33  11 

32  33 

3146 

3106 

30  27 

28 

32 

51  32 

50  11 

48  59 

47  47 

46  36 

45  23 

44  22 

43  21 

42  30 

41  29 

40  37 

39  46 

32 

36 

65  14 

63  30 

62  00 

60  29 

58  58 

57  28 

56  10 

54  52 

53  47 

52  29 

51  25 

50  20 

36 

40 

80  32 

78  24 

76  32 

74  40 

72  48 

70  56 

69  20 

67  44 

66  24 

64  48 

63  28 

62  08 

40 

44 

88  05 

85  50 

83  54 

8157 

80  20 

78  24 

76  48 

75  11 

44 

48 

95  37 

93  19 

91  23 

89  28 

48 

52 

107  15 

105  00 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

Ajh 

3.02 

2.94 

2.87 

2.80 

2.73 

2.66 

2.60 

2.54 

2.49 

2.43 

2.38 

2.33 

Ajh 

Log. 

0.480 

0.468 

0.457 

0.447 

0.436 

0.424 

0.414 

0.404 

0.396 

0.385 

0.376 

0.367 

Log. 

01 

35 

88 

16 

16 

88 

97 

83 

20 

61 

58 

36 

Limit 

36 

36 

37 

38 

39 

40 

40 

41 

41 

42 

42 

43 

Min- 
utes 

Merid-! 

ian  i 

57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

Alti- 
tudes 

Declinatioxs. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

/   // 

/  // 

/  // 

/  // 

/  // 

/  // 

1     II 

/  // 

/  // 

1     II 

/  // 

/  /' 

Min. 

4 

0  36 

0  35 

0  35 

0  35 

0  34 

0  33 

0  32 

0  31 

0  31 

0  30 

0  30 

0  29 

4 

8 

2  26 

2  23 

2  19 

2  17 

2  14 

2  12 

2  09 

2  06 

2  04 

2  01 

159 

157 

8 

12 

5  29 

5  21 

5  14 

5  08 

5  02 

4  57 

4  51 

4^ 

4  40 

4  34 

4  28 

4  23 

12 

16 

9  43 

9  31 

9  18 

9  08 

8  58 

8  47 

8  37 

8  26 

8  16 

8  06 

7  56 

7  49 

16 

20 

15  12 

14  52 

14  32 

14  16 

14  00 

13  44 

13  28 

13  12 

12  56 

12  40 

12  24 

12  12 

20 

24 

21  53 

21  24 

20  56 

20  33 

20  10 

19  47 

19  24 

19  00 

18  37 

18  14 

17  52 

17  34 

24 

28 

29  48 

29  09 

28  29 

27  57 

27  26 

26  55 

26  24 

25  53 

25  21 

24  50 

24  18 

23  55 

28 

32 

38  55 

38  04 

37  12 

36  31 

35  50 

35  09 

34  28 

33  48 

33  07 

32  26 

3144 

31  13 

32 

36 

49  15 

48  10 

47  06 

46  14 

45  22 

44  30 

43  38 

42  46 

41  54 

4102 

40  11 

39  32 

36 

40 

60  48 

59  28 

58  08 

57  04 

56  00 

54  56 

53  52 

52  48 

5144 

50  40 

49  36 

48  48 

40 

44 

73  34 

71  57 

70  21 

69  03 

67  46 

66  28 

65  11 

63  53 

62  35 

61  18 

60  01 

59  03 

44 

48 

87  33 

85  38 

83  42 

82  10 

80  38 

79  06 

67  34 

76  02 

74  30 

72  58 

71  25 

70  16 

48 

52 

102  45 

100  30 

98  14 

96  26 

94  38 

92  50 

9102 

89  14 

87  26 

85  38 

83  49 

82  28 

52 

56 

105  35 

103  29 

10123 

99  18 

97  13 

95  39 

56 

60 

114  00 

111  36 

109  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.28 

2.23 

2.18 

2.14 

2.10 

2.06 

2.02 

1.98 

1.94 

1.90 

1.86 

1.83 

Ajh 

Log. 

0.357 

0.348 

0.338 

0.330 

0.322 

0.313 

0.305 

0.296 

0.287 

0.278 

0.269 

0.262 

Log. 

93 

30 

46 

41 

22 

87 

35 

67 

80 

75 

51 

45 

Limit 

44 

45 

46 

47 

47 

48 

48 

49 

50 

51 

52 

53 

Min- 
utes 

Merid- 
ian 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

Alti- 
tudes 

200 


Latitude  33°  Declination  Contrary  Name. 


Dkcltxations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

/      // 

/     // 

/      // 

1     " 

/      // 

/     // 

/      // 

/     // 

/      // 

/     " 

/     // 

/      // 

Min. 

4 

0  28 

0  28 

0  27 

0  27 

0  27 

0  26 

0  26 

0  25 

0  25 

0  24 

0  23 

0  23 

4 

8 

155 

152 

1  50 

1  48 

1  46 

1  44 

1  42 

1  41 

139 

1  36 

1  35 

134 

8 

12 

4  18 

4  12 

4  08 

4  03 

3  59 

3  54 

3  50 

3  46 

3  42 

3  37 

3  34 

3  31 

12 

16 

7  38 

7  28 

7  20 

7  13 

7  05 

6  58 

6  50 

6  42 

6  34 

6  27 

6  18 

6  13 

16 

20 

1156 

11  40 

11  28 

11  16 

11  04 

10  52 

10  40 

10  28 

10  16 

10  04 

9  52 

9  44 

20 

24 

17  11 

16  48 

16  31 

16  14 

15  57 

15  39 

15  22 

15  04 

14  47 

14  30 

14  12 

14  01 

24 

28 

23  24 

22  52 

22  29 

22  05 

2141 

21  18 

20  54 

20  31 

20  07 

19  44 

19  21 

19  05 

28 

32 

30  33 

29  52 

29  21 

28  50 

28  19 

27  49 

27  18 

26  48 

26  17 

25  46 

25  16 

24  55 

32 

36 

38  40 

37  48 

37  09 

36  31 

35  52 

35  13 

34  34 

33  55 

33  16 

32  37 

3158 

31  32 

36 

40 

47  44 

46  40 

45  52 

45  04 

44  16 

43  28 

42  40 

41  52 

41  04 

40  16 

39  28 

38  56 

40 

44 

57  45 

56  28 

55  30 

54  32 

53  34 

52  36 

51  38 

50  40 

49  41 

48  43 

47  45 

47  06 

44 

48 

68  42 

67  10 

66  01 

64  53 

63  44 

62  35 

61  26 

60  17 

59  08 

57  59 

56  50 

56  04 

48 

52 

80  40 

78  52 

77  31 

76  09 

74  48 

73  27 

72  06 

70  45 

69  24 

68  03 

66  42 

65  48 

52 

56 

89  54 

88  20 

86  46 

85  12 

83  38 

82  04 

80  29 

78  55 

77  21 

76  18 

56 

60 

96  00 

94  12 

92  24 

90  36 

88  48 

87  36 

60 

" 

// 

It 

II 

II 

" 

" 

" 

" 

II 

II 

II 

Ajh 

1.79 

1.75 

1.72 

1.69 

1.66 

1.63 

1.60 

1.57 

1.54 

1.51 

1.48 

1.46 

A,h 

Log. 

0.252 

0.243 

0.235 

0.227 

0.220 

0.212 

0.204 

0.195 

0.187 

0.178 

0.170 

0.164 

Log. 

85 

04 

53 

89 

11 

19 

12 

90 

52 

98 

26 

35 

Limit 

54 

54 

55 

56 

57 

58 

59 

59 

60 

61 

62 

63 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      // 

1     II 

/      // 

/      // 

/      // 

/      // 

/      // 

/     // 

/     // 

1     II 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  20 

0  19 

0  19 

0  19 

0  18 

4 

8 

132 

130 

1  28 

1  26 

1  24 

1  23 

1  21 

1  20 

1  18 

1  16 

1  15 

1  13 

8 

12 

3  24 

3  22 

3  17 

3  14 

3  10 

3  06 

3  03 

2  59 

2  56 

2  51 

2  48 

2  44 

12 

16 

6  06 

5  58 

5  51 

5  46 

5  38 

5  30 

5  25 

5  17 

5  12 

5  05 

5  00 

4  52 

16 

20 

9  32 

9  20 

9  08 

9  00 

8  48 

8  36 

8  28 

8  16 

8  08 

7  56 

7  48 

7  36 

20 

24 

13  43 

13  26 

13  09 

12  58 

12  41 

12  23 

12  11 

11  54 

1143 

U  26 

11  14 

10  57 

24 

28 

18  42 

18  18 

17  54 

17  38 

17  15 

16  52 

16  36 

16  12 

15  57 

15  33 

15  17 

14  53 

28 

32 

24  25 

23  54 

23  23 

23  02 

22  31 

22  01 

21  41 

21  10 

20  49 

20  18 

19  58 

19  27 

32 

36 

30  53 

30  14 

29  36 

29  10 

28  31 

27  52 

27  26 

26  47 

26  21 

25  43 

25  17 

24  38 

36 

40 

38  08 

37  20 

36  32 

36  00 

35  12 

34  24 

33  52 

33  04 

32  32 

31  44 

31  12 

30  24 

40 

44 

46  08 

45  10 

44  13 

43  34 

42  36 

4137 

40  59 

40  00 

39  22 

38  24 

37  46 

36  47 

44 

48 

54  55 

53  46 

52  36 

51  50 

50  41 

49  32 

48  46 

47  37 

46  51 

45  41 

44  55 

43  46 

48 

52 

64  27 

63  06 

61  44 

60  50 

59  29 

58  08 

57  14 

55  53 

54  59 

53  37 

52  43 

51  22 

52 

56 

74  44 

73  10 

7137 

70  34 

69  00 

67  25 

66  23 

64  48 

63  46 

62  12 

61  10 

59  35 

56 

60 

85  48 

84  00 

82  12 

8100 

79  12 

77  24 

76  12 

74  24 

73  12 

7124 

70  12 

68  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

1.43 

1.40 

1.37 

1.35 

1.32 

1.29 

1.27 

1.24 

1.22 

1.19 

1.17 

1.14 

A,h 

Log. 

0.155 

0.146 

0.136 

0.130 

0.120 

0.110 

0.103 

0.093 

0.086 

0.075 

0.068 

0.056 

Log. 

34 

13 

72 

33 

57 

59 

80 

42 

36 

55 

19 

90 

Limit 

64 

65 

66 

67 

68 

69 

70 

71 

72 

72 

73 

74 

Min- 
utes 

Merid- 
ian 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

Alti- 
tudes 

Latitude  33°  Declination  Contrary  Name. 


201 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Anglea 

Miu. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

n 

1.12 

/  // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 
65  24 

n 

1.09 

/  // 

0  17 
108 
2  34 
4  34 

7  08 
10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
41  05 
48  13 
55  56 
64  12 

n 

1.07 

/  // 

0  17 
107 
2  31 

4  29 
7  00 
10  05 
13  43 
17  55 
22  41 
28  00 
33  53 
40  19 
47  19 
54  53 
63  00 

n 

1.05 
0.021 
19 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

" 
1.02 

1 

n 

/ 

/  // 

1 

■ 

/ 
• 

// 

/ 

/ 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.049 
22 

0.037 
43 

0.029 
38 

0.008 
60 

Log. 

Limit 

75 

75 

76 

77 

77 

Min- 
utes 

Merid- 
ian 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/   // 

/  // 

/   // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

Min. 

4 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

4 

8 

0  50 

0  48 

0  46 

0  45 

0  43 

0  42 

0  39 

0  38 

0  37 

0  36 

8 

12 

151 

148 

144 

141 

137 

135 

129 

126 

124 

121 

12 

16 

3  17 

3  12 

3  04 

2  59 

2  54 

2  49 

2  39 

2  34 

2  28 

2  23 

16 

20 

5  08 

5  00 

4  48 

4  40 

4  32 

4  24 

4  08 

4  00 

3  52 

3  44 

20 

24 

7  23 

7  12 

6  55 

6  43 

6  32 

6  21 

5  58 

5  46 

5  32 

5  23 

24 

28 

10  04 

9  48 

9  25 

9  09 

8  53 

8  37 

8  06 

7  50 

7  35 

7  19 

28 

32 

13  09 

12  48 

12  17 

1157 

1136 

11  15 

10  34 

10  14 

9  54 

9  33 

32 

36 

16  38 

16  12 

15  33 

15  07 

14  42 

14  16 

13  24 

12  58 

12  32 

12  0& 

36 

40 

20  32 

20  00 

19  12 

18  40 

18  08 

17  36 

16  32 

16  00 

15  28 

14  56 

40 

44 

24  51 

24  12 

23  14 

22  35 

2157 

21  18 

20  01 

19  22 

18  43 

18  04 

44 

48 

29  32 

28  46 

27  37 

26  51 

26  06 

25  20 

23  48 

23  02 

22  16 

2130 

48 

52 

34  42 

33  48 

32  27 

31  33 

30  38 

29  44 

27  56 

27  02 

26  09 

25  14 

52 

56 

40  15 

39  12 

37  38 

36  35 

35  33 

34  30 

32  25 

3122 

30  19 

29  16 

56 

60 

46  12 

45  00 

43  12 

42  00 

40  48 

39  36 

37  12 

36  00 

34  48 

33  36 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

0.77 

0.75 

0.72 

0.70 

0.68 

0.66 

0.63 

0.60 

0.58 

0.56 

A,h 

Log. 

9.886 

9.875 

9.857 

9.845 

9.832 

9.819 

9.799 

9.778 

9.763 

9.748 

Log. 

49 

06 

33 

10 

51 

54 

34 

15 

43 

19 

Limit 

84 

85 

86 

86 

87 

87 

88 

88 

89 

89 

Min- 
utes 

Merid- 
ian 

3= 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

Alti- 
tudes 

202 


Latitude  34°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

•  9° 

10° 

11° 

Hour 
Angles 

Min. 

1      II 

/      // 

/     // 

/      II 

/      " 

/     /' 

/      // 

/      // 

/     // 

1     II 

/     // 

/      /' 

Min. 

4 

0  46 

0  47 

0  49 

0  51 

0  52 

0  54 

0  55 

0  57 

0  59 

101 

103 

105 

4 

8 

3  06 

3  11 

3  17 

3  22 

3  28 

3  34 

3  41 

3  48 

3  55 

4  03 

4  12 

4  22 

8 

12 

6  59 

711 

7  22 

7  35 

7  48 

8  01 

8  17 

8  33 

8  50 

9  07 

9  28 

9  49 

12 

16 

12  25 

12  45 

13  06 

13  29 

13  52 

14  15 

14  43 

15  11 

15  42 

16  13 

16  48 

17  27 

16 

20 

19  24 

19  56 

20  28 

2104 

21  40 

22  16 

23  00 

23  44 

24  32 

25  20 

26  16 

27  16 

20 

24 

27  56 

28  42 

29  28 

30  21 

31  12 

32  04 

33  07 

34  11 

35  20 

36  29 

37  49 

39  16 

24 

28 

38  02 

39  05 

40  07 

41  17 

42  28 

43  38 

45  05 

46  31 

48  05 

49  39 

5129 

53  27 

28 

32 

49  40 

5102 

52  24 

53  55 

55  28 

57  00 

58  53 

60  45 

62  48 

64  51 

67  15 

69  48 

32 

36 

62  51 

64  35 

66  19 

68  16 

70  12 

72  09 

74  31 

76  54 

79  30 

36 

40 

77  36 

79  44 

8152 

84  16 

86  40 

89  04 

92  00 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

. . 

60 

II 

11 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.91 

2.99 

3.07 

3.16 

3.25 

3.34 

3.45 

3.56 

3.68 

3.80 

3.94 

4.09 

A,h 

Log. 

0.463 

0.475 

0.487 

0.499 

0.511 

0.523 

0.537 

0.551 

0.565 

0.57S 

0.595 

0.611 

Log. 

89 

67 

14 

69 

88 

75 

82 

45 

85 

78 

50 

72 

Limit 

37 

36 

35 

34 

33 

33 

33 

32 

31 

30 

30 

29 

Min- 
utes 

Merid- 
ian 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/     /' 

/      // 

/      // 

Min. 

Min, 

4 

108 

1  10 

1  14 

1  17 

121 

125 

1  30 

135 

141 

149 

156 

2  06 

4 

8 

4  32 

4  44 

4  55 

5  09 

5  24 

5  40 

5  59 

6  20 

6  44 

7  13 

7  45 

8  22 

8 

12 

10  12 

10  38 

1105 

11  35 

12  09 

12  46 

13  27 

14  17 

15  10 

16  14 

17  26 

18  50 

12 

16 

18  08 

18  54 

19  43 

20  37 

21  35 

22  42 

23  57 

25  23 

26  58 

28  50 

30  58 

33  30 

16 

20 

28  20 

29  22 

30  48 

32  12 

33  44 

35  28 

37  24 

39  40 

42  08 

45  04 

48  24 

52  20 

20 

24 

40  48 

42  31 

44  22 

46  22 

48  35 

51  05 

53  52 

57  07 

60  41 

64  54 

24 

28 

55  32 

57  54 

60  22 

63  07 

66  07 

69  31 

73  18 

77  45 

82  35 

28 

32 

72  32 

75  37 

78  50 

82  26 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

, 

56 

60 

60 

II 

II 

II 

n 

II 

II 

" 

II 

II 

II 

// 

II 

A,h 

4.25 

4.43 

4.62 

4.83 

5.06 

5.32 

5.61 

5.95 

6.32 

6.76 

7.26 

7.85 

A,h 

Log. 

0.628 

0.646 

0.664 

0.683 

0.704 

0.725 

0.748 

0.774 

0.800 

0.829 

0.860 

0.894 

Log. 

39 

40 

64 

95 

15 

91 

96 

52 

72 

95 

94 

87 

Limit 

28 

27 

26 

26 

25 

24 

23 

22 

21 

20 

19 

17 

Min- 
utes 

Merid- 
ian 

68 

3 

69 

3 

70 

3 

71 

3 

72 

3 

73 

3 

74< 

3 

75 

3 

76° 

77< 

> 

78' 

> 

79' 

) 

Alti- 
tudes 

Latitude  34°  Declination  Same  Name. 
Declinations. 


203 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

2 

9 

20 

36 

57 

It 
8.5 

// 

17 
08 
33 
31 
D4 

5 

1 

2 
10 
22 
40 
62 

II 
9.4 

// 

30 
04 
38 
14 
52 

3 

/ 

1 
2 
4 

1 

2 

1 
5 
4 

// 
0. 

48 
13 
13 
51 

51 

1 

3 
12 

28 

II 
11. 

10 
41 
34 

JO 

/      // 

3  40 
14  41 
33  00 

II 
13.75 

/ 

4 
17 
39 

II 
16. 

22 
26 
10 

34 

1 

// 

// 

/ 

// 

1 

// 

II 

/ 

// 

/ 

// 

// 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.932 

47 

0.974 
51 

1.021 
60 

1.075 
55 

1.138 
30 

1.213 
25 

Log. 

Limit 

15 

14 

13 

12 

10 

8 

7 

6 

4 

2 

0 

2 

Min- 
utes 

Merid- 
ian 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/      // 

Min. 

Min. 

4 

3  52 

3  11 

2  41 

2  19 

2  02 

148 

136 

127 

1  18 

4 

8 

15  28 

12  43 

10  45 

9  16 

8  07 

7  12 

6  26 

5  49 

5  15 

8 

12 

34  49 

28  38 

24  12 

20  51 

18  15 

16  11 

14  28 

13  04 

1150 

12 

16 

43  00 

37  05 

32  29 

28  45 

25  44 

23  12 

21  02 

16 

20 

57  56 

50  44 

44  56 

40  12 

36  16 

32  52 

20 

24 

64  42 

57  54 

52  13 

47  19 

24 

28 

64  26 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

1 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

14.51 

11.93 

10.08 

8.69 

7.61 

6.74 

6.03 

5.44 

4.93 

A,h 

Log. 

1.161 

1.076 

1.003 

0.939 

0.881 

0.828 

0.780 

0.735 

0.692 

Log. 

67 

64 

46 

02 

38 

66 

32 

60 

85 

Litnit 

4 

6 

8 

10 

11 

13 

15 

17 

19 

20 

22 

24 

Min- 
utes 

Merid- 
ian 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80* 

79° 

78° 

77° 

Alti- 
tudes 

204 


Latitude  34°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

aiin. 

/      // 

/        n 

/     // 

/     // 

/     // 

/     // 

/     // 

1     II 

/     // 

/     /' 

/     // 

/     // 

Min. 

4 

112 

106 

101 

0  56 

0  52 

0  48 

0  44 

0  42 

0  38 

0  36 

0  34 

0  31 

4 

8 

4  48 

4  23 

4  03 

3  44 

3  28 

3  13 

2  59 

2  46 

2  36 

2  26 

2  15 

2  06 

8 

12 

10  48 

9  53 

9  07 

8  24 

7  47 

7  13 

6  42 

6  14 

5  50 

5  27 

5  05 

4  46 

12 

16 

19  12 

17  35 

16  13 

14  56 

13  49 

12  51 

1154 

1106 

10  22 

9  41 

9  03 

8  26 

16 

20 

30  00 

27  28 

25  20 

23  20 

21  36 

20  04 

18  36 

17  20 

16  12 

15  08 

14  08 

13  12 

20 

24 

43  12 

39  34 

36  29 

33  36 

31  06 

28  54 

26  47 

24  58 

23  19 

2147 

20  22 

19  00 

24 

28 

58  48 

53  50 

49  39 

45  44 

42  20 

39  20 

36  28 

33  58 

3146 

29  40 

27  42 

25  53 

28 

32 

76  48 

70  18 

64  51 

59  44 

55  18 

5122 

47  37 

44  22 

41  29 

38  45 

36  10 

33  48 

32 

36 

75  36 

69  59 

65  01 

60  16 

56  10 

52  29 

49  02 

45  48 

42  46 

36 

40 

80  16 

74  24 

69  20 

64  48 

60  32 

56  32 

52  48 

40 

44 

83  54 

78  24 

73  15 

68  25 

63  53 

44 

48 

87  10 

81  24 

76  02 

48 

52 

89  14 

52 

56 

56 

60 

60 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

4.50 

4.12 

3.80 

3.50 

3.24 

3.01 

2.79 

2.60 

2.43 

2.27 

2.12 

1.98 

A,h 

Log. 

0.653 

0.614 

0.579 

0.544 

0.510 

0.478 

0.445 

0.414 

0.385 

0.356 

0.326 

0.296 

Log. 

21 

90 

78 

07 

55 

57 

60 

97 

61 

03 

34 

67 

Limit 

26 

27 

28 

30 

31 

32 

33 

35 

36 

38 

40 

42 

Min- 
utes 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  30 

159 

4  28 

7  56 

12  24 

17  52 

24  18 

3144 

40  11 

49  36 

60  01 

7125 

83  49 

1.86 

/     // 

0  28 

152 

4  11 

7  24 

1136 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

II 
1.74 

1     II 

0  26 

144 

3  54 

6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

II 
1.63 

/     // 

0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 
II 

1.52 

/     // 

0  22 

132 

3  24 

6  06 

9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
11 

1.43 

1     II 

0  21 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 
II 

1.33 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
II 

1.25 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/      // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

II 

1.09 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

II 

1.02 

/     // 

0  15 

100 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
II 

0.95 

/     // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
66 
60 

A,h 

Log. 

0.269 
51 

0.240 
55 

0.212 
19 

0.181 

84 

0.155 
34 

0.123 
85 

0.096 
91 

0.068 
19 

0.037 
43 

0.008 
60 

9.977 
72 

9.944 
48 

Log. 

Limit 

44 

45 

47 

49 

51 

52 

54 

56 

58 

60 

62 

64 

Min- 
utes 

Merid- 
ian 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

54° 

53° 

Alti- 
tudes 

Latitude  34°  Declination  Contrary  Name. 


205 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       // 

/           H 

/     // 

/       n 

/     // 

/     // 

/     '/ 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  46 

0  46 

0  44 

0  43 

0  43 

0  41 

0  40 

0  39 

0  38 

0  3.8 

0  37 

0  36 

4 

8 

3  06 

3  02 

2  58 

2  53 

2  49 

2  45 

2  41 

2  38 

2  35 

2  31 

2  28 

2  25 

8 

12 

6  59 

6  49 

6  39 

6  29 

6  20 

6  12 

6  03 

5  55 

5  47 

5  40 

5  32 

5  26 

12 

16 

12  25 

12  07 

11  49 

1131 

11  16 

1100 

10  45 

10  29 

10  17 

10  04 

9  52 

9  38 

16 

20 

19  24 

18  56 

18  28 

18  00 

17  36 

17  12 

16  48 

16  24 

16  04 

15  44 

15  24 

15  04 

20 

24 

27  56 

27  16 

26  35 

25  55 

25  21 

24  46 

24  12 

23  37 

23  08 

22  40 

22  11 

21  42 

24 

28 

38  02 

37  06 

36  12 

35  17 

34  29 

33  43 

32  56 

32  09 

3130 

30  50 

30  11 

29  32 

28 

32 

49  40 

48  28 

47  17 

46  05 

45  03 

44  02 

43  00 

4159 

41  08 

40  16 

39  25 

38  34 

32 

36 

62  51 

6121 

59  50 

58  19 

57  02 

55  44 

54  26 

53  08 

52  03 

50  59 

49  54 

48  49 

36 

40 

77  36 

75  44 

73  52 

72  00 

70  24 

68  48 

67  12 

65  36 

64  16 

62  56 

6136 

60  16 

40 

44 

87  07 

85  11 

83  15 

81  19 

79  22 

77  45 

76  09 

74  32 

72  55 

44 

48 

94  28 

92  33 

90  37 

88  42 

86  47 

48 

52 

106  21 

104  06 

10151 

52 

56 

56 

60 

60 

// 

n 

If 

" 

" 

" 

" 

" 

" 

" 

" 

II 

Ajh 

2.91 

2.84 

2.77 

2.70 

2.64 

2.58 

2.52 

2.46 

2.41 

2.36 

2.31 

2.26 

Ajh 

Log. 

0.463 

0.453 

0.442 

0.431 

0.421 

0.411 

0.401 

0.390 

0.382 

0.372 

0.363 

0.354 

Log. 

89 

32 

48 

36 

60 

62 

40 

94 

02 

91 

61 

11 

Limit 

37 

37 

38 

39 

39 

40 

40 

41 

42 

43 

43 

44 

Min- 
utes 

Merid- 
ian 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/      /' 

Min. 

Min. 

4 

0  35 

0  35 

0  34 

0  33 

0  33 

0  32 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

4 

8 

2  22 

2  19 

2  16 

2  13 

2  11 

2  08 

2  05 

2  03 

2  01 

159 

1  56 

1  54 

8 

12 

5  18 

5  12 

5  06 

5  00 

4  54 

4  48 

4  43 

4  38 

4  32 

4  28 

4  22 

4  17 

12 

16 

9  26 

9  16 

9  06 

8  52 

8  42 

8  32 

8  21 

8  14 

8  04 

7  56 

7  46 

7  35 

16 

20 

14  44 

14  28 

14  12 

13  52 

13  36 

13  20 

13  04 

12  52 

12  36 

12  24 

12  08 

11  52 

20 

24 

21  13 

20  50 

20  27 

19  58 

19  35 

19  12 

18  49 

18  31 

18  09 

17  52 

17  29 

17  05 

24 

28 

28  53 

28  21 

27  50 

27  11 

26  39 

26  08 

25  37 

25  14 

24  42 

24  18 

23  47 

23  16 

28 

32 

37  43 

37  02 

36  21 

35  30 

34  49 

34  08 

33  27 

32  57 

32  15 

3144 

31  03 

30  23 

32 

36 

47  44 

46  53 

46  01 

44  56 

44  04 

43  12 

42  20 

4141 

40  50 

40  11 

39  19 

38  27 

36 

40 

58  56 

57  52 

56  48 

55  28 

54  24 

53  20 

52  16 

5128 

50  24 

49  36 

48  32 

47  28 

40 

44 

71  18 

70  02 

68  44 

67  07 

65  49 

64  32 

63  14 

62  16 

60  59 

60  01 

58  44 

57  26 

44 

48 

84  52 

83  19 

81  46 

79  52 

78  20 

76  48 

75  16 

74  07 

72  34 

7125 

69  53 

68  19 

48 

52 

99  36 

97  47 

95  59 

93  44 

9156 

90  08 

88  20 

86  59 

85  10 

83  49 

82  01 

80  13 

52 

56 

104  32 

102  26 

100  52 

98  47 

97  13 

95  08 

93  02 

56 

60 

113  24 

11136 

109  12 

106  48 

60 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.21 

2.17 

2.13 

2.08 

2.04 

2.00 

1.96 

1.93 

1.89 

1.86 

1.82 

1.78 

Ajh 

Log. 

0.344 

0.336 

0.328 

0.318 

0.309 

0.301 

0.292 

0.285 

0.276 

0.269 

0.260 

0.250 

Log. 

39 

46 

38 

06 

63 

03 

26 

56 

46 

51 

07 

42 

Limit 

45 

46 

47 

47 

47 

48 

49 

50 

51 

51 

52 

53 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

206 


Latitude  34°  Declination  G)ntfary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  28 

1  52 
4  12 
7  28 

1140 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 
9128 
105  00 

1.75 

/     // 

0  27 

1  50 
4  06 
7  18 

11  24 
16  25 
22  21 
29  11 
36  56 
45  36 
55  10 
65  38 
77  04 
89  22 
102  36 

1.71 

0  27 

1  47 
4  02 
7  10 

11  12 
16  08 
21  57 
28  40 
36  18 
44  48 
54  13 
64  30 
75  42 
87  49 

100  48 

11 

1.68 

/     // 

0  27 

145 

3  57 

7  03 

11  00 

15  51 

2133 

28  09 

35  39 

44  00 

53  15 

63  21 

74  21 

86  15 

99  00 

II 

1.65 

/     // 

0  26 

1  44 
3  54 
6  58 

10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 
97  48 

1.63 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
5138 
61  26 
72  06 
83  38 

96  00 

1/ 

1.60 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
4152 
50  40 
60  17 
70  45 
82  04 

94  12 

II 

1.57 

/     // 

0  25 

1  39 
3  42 
6  34 

10  16 
14  47 
20  07 
26  17 
33  16 
4104 
49  41 
59  08 
69  24 
80  29 

92  24 

II 

1.54 

/     // 

0  24 

136 

3  37 

6  27 

10  04 

14  30 

19  44 

25  46 

32  37 

40  16 

48  43 

57  59 

68  03 

78  55 

90  36 

II 

1.51 

/      // 

0  23 

1  35 
3  34 
6  18 
9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

/      // 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 

II 

1.46 

0  22 

1  32 
3  24 
6  06 
9  32 

13  43 
18  42 
24  25 
30  53 
38  08 
46  08 
54  55 
64  27 
74  44 
85  48 

1.43 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.243 
04 

0.233 
00 

0.225 
31 

0.217 
48 

0.212 
19 

0.204 
12 

0.195 
90 

0.187 
52 

0.178 
98 

0.170 
26 

0.164 
35 

0.155 
34 

Log. 

Limit 

54 

55 

55 

56 

57 

58 

59 

59 

60 

61 

62 

63 

Min- 
utes 

Merid- 
ian 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 

II 

1.40 

/     // 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 

1.38 

/      // 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 
17  38 
23  02 
29  10 
36  00 
43  34 
5150 
60  50 
70  34 

8100 

II 

1.35 

/     // 

0  21 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

51  04 

59  56 

69  31 

79  48 
II 

1.33 

/      // 

0  21 

123 

3  07 

5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 
II 

1.30 

/      // 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

2141 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 

II 

1.27 

/      // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
2120 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 

75  00 

II 

1.25 

/     // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

II 

1.22 

/      // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

1.20 

/     // 

0  19 

1  15 

2  50 
5  02 

7  52 
11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 

70  48 

II 

1.18 

/     // 

0  19 

1  13 

2  45 
4  55 
7  40 

11  03 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

5149 

60  07 

69  00 
II 

1.15 

/      // 

0  16 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 
67  48 

1.13 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.146 
13 

0.139 
.  88 

0.130 
33 

0.123 
85 

0.113 
94 

0.103 
80 

0.096 
91 

0.086 
36 

0.079 
18 

0.071 
88 

0.060 
70 

0.053 
08 

Log. 

Limit 

64 

65 

66 

67 

69 

70 

71 

72 

73 

73 

74 

75 

Min- 
utes 

Merid- 
ian 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

Alti- 
tudes 

Latitude  34°  Decimation  Contrary  Name. 


207 


Declixations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/        n 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

1     II 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 
14  07 
18  26 
23  20 
28  48 
34  51 
41  28 
48  40 
56  27 

64  48 

II 

1.08 

0  17 

1  08 

2  33 
4  31 
7  04 

10  11 
13  51 
18  05 
22  54 
28  16 
34  12 
40  42 
47  46 
55  24 

63  36 

II 

1.06 

0  16 

1  06 

2  28 
4  24 
6  52 
9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 
II 

1.03 

/ 

// 

II 

II 

II 

1 

II 

// 

II 

// 

II 

// 

// 

II 

// 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

0.041 
39 

0.033 
42 

0.025 
31 

0.012 
84 

Log. 

Ldmit 

75 

75 

76 

76 

Min- 
utes 

Merid- 
ian 

8° 

7° 

6° 

5° 

4° 

3 

o 

2 

0 

1= 

0 

o 

1° 

2° 

3° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

Min. 

4 

0  13 

0  12 

0  12 

0  12 

0  11 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

4 

8 

0  52 

0  51 

0  49 

0  47 

0  46 

0  44 

0  42 

0  41 

0  39 

0  38 

0  37 

0  35 

8 

12 

1  56 

154 

150 

147 

144 

139 

136 

133 

129 

126 

122 

118 

12 

16 

3  28 

3  22 

3  14 

3  09 

3  04 

2  57 

2  52 

2  47 

2  39 

2  34 

2  26 

2  18 

16 

20 

5  24 

5  16 

5  04 

4  56 

4  48 

4  36 

4  28 

4  20 

4  08 

4  00 

3  48 

3  36 

20 

24 

7  47 

7  35 

7  18 

7  06 

6  55 

6  38 

6  26 

6  15 

5  58 

5  46 

5  28 

5  11 

24 

28 

10  35 

10  20 

9  56 

9  40 

9  25 

9  01 

8  45 

8  29 

8  06 

7  50 

7  27 

7  03 

28 

32 

13  49 

13  29 

12  58 

12  38 

12  17 

11  46 

11  26 

1105 

10  34 

10  14 

9  44 

9  13 

32 

36 

17  30 

17  04 

16  25 

15  59 

15  33 

14  55 

14  29 

14  03 

13  24 

12  58 

12  18 

1140 

36 

40 

2136 

2104 

20  16 

19  44 

19  12 

18  24 

17  52 

17  20 

16  32 

16  00 

15  12 

14  24 

40 

44 

26  08 

25  29 

24  31 

23  52 

23  14 

22  16 

2138 

20  59 

20  01 

19  22 

18  24 

17  25 

44 

48 

3106 

30  18 

29  09 

28  23 

27  37 

26  29 

25  43 

24  57 

23  48 

23  02 

2154 

20  44 

48 

52 

36  30 

35  36 

34  15 

33  21 

32  27 

3105 

30  11 

29  17 

27  56 

27  02 

25  41 

24  20 

52 

56 

42  20 

41  17 

39  43 

38  40 

37  38 

36  04 

35  02 

33  59 

32  25 

31  22 

29  48 

28  13 

56 

60 

48  36 

47  24 

45  36 

44  24 

43  12 

4124 

40  12 

39  0& 

37  12 

36  00 

31  12 

32  24 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

0.81 

0.79 

0.76 

0.74 

0.72 

0.69 

0.67 

0.65 

0.62 

0.60 

0.57 

0.54 

Ajh 

Log. 

9.908 

9.897 

9.880 

9.869 

9.857 

9.838 

9.826 

9.812 

9.792 

9.778 

9.755 

9.732 

Log. 

49 

63 

81 

23 

33 

85 

07 

91 

39 

15 

87 

39 

Limit 

84 

84 

84 

85 

85 

86 

86 

87 

87 

88 

89 

90 

Min- 
utes 

Merid- 
ian 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

Alti- 
tudes 

208 


Latitude  35°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/       v 

/     // 

/     // 

/        n 

/     // 

/       n 

/      // 

/      // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  45 

0  46 

0  47 

0  48 

0  50 

0  51 

0  53 

0  54 

0  56 

0  58 

100 

102 

4 

8 

2  59 

3  04 

3  09 

3  14 

3  19 

3  25 

3  31 

3  38 

3  45 

3  51 

4  00 

4  08 

8 

12 

6  43 

6  55 

7  05 

7  16 

7  29 

7  41 

7  55 

8  10 

8  25 

8  41 

9  00 

9  19 

12 

16 

1157 

12  17 

12  35 

12  56 

13  19 

13  39 

14  05 

14  30 

14  59 

15  27 

16  00 

16  33 

16 

20 

18  40 

19  12 

19  40 

20  12 

20  48 

21  20 

22  00 

22  40 

23  24 

24  08 

25  00 

25  52 

20 

24 

26  53 

27  39 

28  19 

29  05 

29  58 

30  43 

31  41 

32  38 

33  42 

34  46 

36  00 

37  15 

24 

28 

36  35 

37  38 

38  33 

39  36 

40  46 

41  49 

43  07 

44  26 

45  52 

47  18 

49  00 

50  42 

28 

32 

47  47 

49  09 

50  21 

5143 

53  14 

54  37 

56  19 

58  02 

59  54 

6146 

64  00 

66  13 

32 

36 

60  29 

62  13 

63  43 

65  27 

67  24 

69  07 

71  17 

73  26 

75  49 

78  12 

36 

40 

74  40 

76  48 

78  40 

80  48 

83  12 

85  20 

88  00 

90  40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

2.80 

2.88 

2.95 

3.03 

3.12 

3.20 

3.30 

3.40 

3.51 

3.62 

3.75 

3.88 

A,h 

Log. 

0.447 

0.459 

0.469 

0.481 

0.494 

0.505 

0.518 

0.531 

0.545 

0.558 

0.574 

0.588 

Log. 

16 

39 

82 

44 

15 

15 

51 

48 

31 

71 

03 

83 

Limit 

38 

37 

36 

35 

34 

34 

33 

33 

32 

32 

31 

30 

Min- 
utes 

Merid- 
ian 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65' 

) 

66° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

t       II 

/       n 

1     It 

/       u 

/     // 

/     // 

t     II 

/      // 

1     II 

/     II 

1     II 

t     II 

Min. 

4 

104 

107 

1  10 

1  13 

1  16 

1  19 

123 

128 

134 

139 

146 

154 

4 

8 

4  18 

4  27 

4  38 

4  51 

5  04 

5  18 

5  35 

5  53 

6  14 

6  38 

7  04 

7  35 

8 

12 

9  40 

10  02 

10  26 

10  54 

11  24 

1158 

12  33 

13  15 

14  01 

14  54 

15  54 

17  05 

12 

16 

17  12 

17  50 

18  34 

19  22 

20  16 

21  14 

22  19 

23  33 

24  55 

26  30 

28  18 

30  23 

16 

20 

26  52 

27  52 

29  00 

30  16 

3140 

33  12 

34  52 

36  48 

38  56 

41  24 

44  12 

47  28 

20 

24 

38  41 

40  08 

4146 

43  35 

45  36 

47  48 

50  12 

53  00 

56  04 

59  37 

63  39 

24 

28 

52  40 

54  37 

56  50 

59  19 

62  02 

65  03 

68  21 

72  08 

76  18 

8109 

28 

32 

68  47 

7120 

74  14 

77  29 

8104 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

// 

" 

" 

" 

" 

" 

II 

II 

II 

Aih 

4.03 

4.18 

4.35 

4.54 

4.75 

4.98 

5.23 

5.52 

5.84 

6.21 

6.63 

7.12 

A,h 

Log. 

0.605 

0.621 

0.638 

0.657 

0.676 

0.697 

0.718 

0.741 

0.766 

0.793 

0.821 

0.852 

Log. 

31 

18 

49 

06 

69 

23 

50 

94 

41 

09 

51 

48 

Limit 

29 

28 

27 

27 

26 

25 

24 

23 

22 

21 

20 

19 

Min- 
utes 

Merid- 
ian 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

Alti- 
tudes 

Latitude  35°  Declination  Same  Name. 

Declinations. 


209 


24° 


2  03 

8  13 

18  29 

32  51 

51  20 


7.70 


0.886 
49 


25= 


2  14 

8  57 

20  08 

35  48 

55  56 


.39 


0.923 
76 


26° 


2  28 

9  52 

22  11 

39  25 


9.24 


0.965 
67 


27° 


28° 


2  45     3  07 
10  59    12  25 


24  43 
43  57 


10.30 


1.012 
84 


27  57 
49  43 


11.65 


1.066 
33 


29° 


3  35 
14  21 
32  17 


13.45 


1.128 
72 


30° 


4  16 
17  02 
38  22 


15.98 


1.203 
51 


31° 


32° 


33° 


34° 


35° 


I  Hour 
{Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 


Log. 


17 


16 


15 


14 


13 


11 


Min- 
utes 


79° 


80° 


81° 


82° 


83= 


84° 


85° 


86° 


87° 


88° 


89° 


90° 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42°      4 

JO 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/      // 

/       n 

/        n 

/     // 

/     // 

/      //    / 

// 

/      // 

/     // 

/     // 

/     // 

Min. 

4 

3  47 

3  06 

2  37      2 

15 

158 

145 

134 

124 

4 

8 

15  05 

12  23 

10  28     9 

01 

7  54 

6  59 

6  15 

5  38 

8 

12 

33  56 

27  51 

23  32    20 

17 

17  46 

15  43 

14  04 

12  41 

12 

16 

. 

41  52    36 

03 

31  34 

27  57 

25  00 

22  31 

16 

20 

...      56 

20 

49  20 

43  40 

39  04 

35  12 

20 

24 

56  16 

50  41 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

. 

52 

56 

56 

60 

60 

n 

/ 

1 

II 

II 

II 

//          // 

II 

II 

II 

II 

A,h 

14.14 

11.61 

9.81      8. 

i5 

7.40 

6.55 

5.86 

5.28 

Ajh 

Log. 

1.150 

1.064 

0.991    0. 

)26 

0.869 

0.816 

0.767 

0.722 

Log. 

45 

83 

67 

86 

23 

24 

90 

63 

Limit 

2 

4 

6 

8 

9 

11 

13        1 

5 

17 

18 

20 

22 

Min- 
utes 

Merid- 
ian 

89° 

88° 

87° 

86° 

85° 

84° 

83°     8: 

1° 

81° 

80° 

79° 

78° 

Alti- 
tudes 

210 


Latitude  35"  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Miu. 

1     11 

/     // 

/     // 

/     II 

1     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/       n 

/     // 

Min. 

4 

1  16 

1  10 

103 

0  59 

0  54 

0  50 

0  46 

0  43 

0  40 

0  38 

0  35 

0  33 

4 

8 

5  06 

4  39 

4  15 

3  55 

3  37 

3  20 

3  05 

2  53 

2  41 

2  30 

2  19 

2  11 

8 

12 

11  29 

10  28 

9  35 

8  48 

8  08 

7  30 

6  58 

6  29 

6  01 

5  37 

5  14 

4  54 

12 

16 

20  23 

18  36 

17  01 

15  40 

14  28 

13  22 

12  22 

1131 

10  43 

9  59 

9  18 

8  42 

16 

20 

31  52 

29  04 

26  36 

24  48 

22  36 

20  52 

19  20 

18  00 

16  44 

15  36 

14  32 

13  36 

20 

24 

45  53 

41  52 

38  18 

35  14 

32  33 

30  03 

27  50 

25  55 

24  06 

22  28 

20  56 

19  35 

24 

28 

62  26 

56  58 

52  09 

47  57 

44  18 

40  54 

37  54 

35  17 

32  48 

30  34 

28  29 

26  39 

28 

32 

68  06 

62  38 

57  51 

53  25 

49  30 

46  05 

42  50 

39  56 

37  12 

34  49 

32 

36 

73  14 

67  37 

62  38 

58  19 

54  13 

50  33 

47  06 

44  04 

36 

40 

72  00 

66  56 

62  24 

58  08 

54  24 

40 

44 

75  30 

70  21 

65  49 

44 

48 

78  20 

48 

52 

52 

56 

56 

60 

60 

" 

H 

" 

II 

II 

II 

II 

II 

II 

II 

II 

" 

A,h 

4.78 

4.36 

3.99 

3.67 

3.39 

3.13 

2.90 

2.70 

2.51 

2.34 

2.18 

2.04 

A,h 

Log. 

0.679 

0.639 

0.600 

0.564 

0.530 

0.495 

0.462 

0.431 

0.399 

0.369 

0.338 

0.309 

Log. 

43 

49 

97 

67 

20 

54 

40 

36 

67 

22 

46 

63 

Limit 

24 

25 

26 

28 

29 

30 

31 

32 

34 

36 

38 

40 

Min- 
utes 

Merid- 
ian 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66°      67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

1     II 

/     // 

Jlin. 

4 

0  30 

0  28 

0  27 

0  25 

0  23 

0  22 

0  20 

0  19 

0  18 

0  16 

0  15 

0  14 

4 

8 

2  01 

154 

146 

140 

133 

126 

121 

1  15 

1  11 

106 

101 

0  57 

8 

12 

4  34 

4  17 

3  59 

3  45 

3  29 

3  14 

3  03 

2  50 

2  39 

2  28 

2  19 

2  08 

12 

16 

8  06 

7  35 

7  05 

6  39 

6  11 

5  46 

5  25 

5  02 

4  45 

4  24 

4  05 

3  48 

16 

20 

12  40 

11  52 

1104 

10  24 

9  40 

9  00 

8  28 

7  52 

7  24 

6  52 

6  24 

5  56 

20 

24 

18  14 

17  05 

15  57 

14  59 

13  55 

12  58 

12  11 

1120 

10  40 

9  53 

9  13 

8  33 

24 

28 

24  50 

23  16 

2141 

20  23 

18  57 

17  38 

16  36 

15  25 

14  30 

13  28 

12  33    11  38 

28 

32 

32  26 

30  23 

28  19 

26  37 

24  45 

23  02 

2141 

20  08 

18  56 

17  35 

16  23    15  11 

32 

36 

4102 

38  27 

35  52 

33  42 

31  19 

29  10 

27  26   25  30 

23  59 

22  15 

20  44I   19  14 

36 

40 

50  40 

47  28 

44  16 

41  36 

38  40 

36  00 

33  52 

31  28 

29  36 

27  28 

25  36    23  44 

40 

44 

61  18 

57  26 

53  34 

50  20 

46  47 

43  34 

40  59 

38  05 

35  49 

33  14 

30  581  28  43 

44 

48 

72  58 

68  19 

63  44 

59  54 

55  41 

5150 

48  46 

45  18    42  37 

39  33    36  52    34  10 

48 

52 

85  38 

80  13 

74  48 

70  18 

65  21 

60  50 

57  14   53  lO;  50  01 

46  25    43  16    40  06 

52 

56 

81  32 

75  37 

70  34 

66  23 

61  41 

58  01 

53  50    50  10    46  31 

56 

60 

II 

II 

II 

87  00 
II 

81  00 

76  12 

70  48 

66  36 

61  48    57  36 

53  24 

60 

A,h 

1.90 

1.78 

1.66 

1.56 

1.45 

1.35 

1.27 

1.18 

1.11 

1.03 

0.96 

0.89 

A,h 

Log. 

0.278 

0.250 

0.220 

0.193 

0.161 

0.130 

0.103 

0.071 

0.045 

0.012 

9.982|  9.949 

Log. 

75 

42 

11 

12 

37 

33 

80 

88 

32 

84 

27 

39 

Limit 

43 

44 

46 

48 

50 

51 

53 

55 

57 

59 

61 

63 

Min- 
utes 

Merid- 
ian 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55°  !    54° 

Alti- 
tudes 

Latitude  35°  Decimation  Contrary  Name. 


211 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8°    .    9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

0 

2 

6 

11 

18 
26 
36 
47 
60 
74 

It 
2.8( 

II 

45 
59 
43 
57 
40 
53 
35 
47 
29 
iO 

) 

/      // 

0  44 
2  56 
6  35 
1141 
18  16 
26  18 
35  48 
46  46 
59  11 
73  04 
88  24 

II 
2.74 

/      // 

0  43 

2  51 

6  24 

1124 

17  48 
25  38 
34  53 
45  34 
57  41 
71  12 
86  10 

II 
2.67 

1       n 

0  42 
2  47 
6  15 
1109 
17  24 
25  04 
34  06 
44  32 
56  23 
69  36 
84  13 

II 
2.61 

/     // 

0  41 
2  43 
6  07 
10  53 
17  00 
24  29 
33  19 
43  31 
55  05 
68  00 
82  17 

II 
2.55 

0  39 
2  40 
5  59 
10  37 
16  36 
23  54 
32  33 
42  30 
53  47 
66  24 
80  20 
95  37 

II 
2.49 

0  39 
2Z1 
5  52 
10  24 
16  16 
23  25 
3153 
41  39 
52  42 
65  04 
78  43 
93  42 

II 
2.44 

/      II 

0  38 

2  33 

5  44 

10  12 

15  56 

22  57 

31  14 

40  47 

5138 

63  44 

77  07 

9146 

107  42 

II 
2.39 

/      // 

0  38 

2  30 

5  37 

9  59 

15  36 

22  28 

30  34 

39  56 

50  33 

62  24 

75  30 

89  51 

105  27 

II 
2.34 

0  36 

2  27 

5  30 

9  46 

15  16 

2159 

29  56 

39  05 

49  28 

61  04 

73  53 

87  56 

103  12 

II 
2.29 

/     // 

0  36 

2  24 

5  23 

9  33 

14  56 

21  30 

29  16 

38  14 

48  23 

59  44 

72  16 

86  01 

100  57 

II 
2.24 

/      // 

0  35 

2  20 

5  15 

9  21 

14  36 

2102 

28  37 

37  22 

47  19 

58  24 

70  40 

84  05 

98  41 

II 
2.19 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

■Log. 

0.447 
16 

0.437 

75 

0.426 
51 

0.416 
64 

0.406 
54 

0.396 
20 

0.387 
39 

0.378 
40 

0.369 
22 

0.359 
84 

0.350 
25 

0.340 

44 

Log. 

Limit 

38 

38 

39 

40 

41 

41 

41 

42 

42 

43 

44 

45 

Min- 
utes 

Merid-     rro 
ian        33 

54° 

53° 

52° 

51° 

50°  1   49° 

48° 

47° 

46° 

45° 

44° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

1     II 

/      '/ 

/     // 

1     II 

1     II 

/      // 

/      // 

/      // 

/     // 

/     // 

1     II 

Min. 

4 

0  35 

0  34 

0  33 

0  32 

0  31 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

0  28 

4 

8 

2  17 

2  15 

2  13 

2  10 

2  07 

2  04 

2  02 

2  00 

158 

156 

1  54 

152 

8 

12 

5  09 

5  03 

4  58 

4  52 

4  47 

4  41 

4  37 

4  31 

4  26 

4  20 

4  17 

4  12 

12 

16 

9  11 

9  01 

8  50 

8  40 

8  29 

8  19 

8  11 

8  01 

7  54 

7  44 

7  35 

7  28 

16 

20 

14  20 

14  04 

13  48 

13  32 

13  16 

13  00 

12  48 

12  32 

12  20 

12  04 

1152 

1140 

20 

24 

20  39 

20  16 

19  52 

19  29 

19  06 

18  43 

18  26 

18  03 

17  46 

17  23 

17  05 

16  48 

24 

28 

28  05 

27  34 

27  03 

26  32 

26  01 

25  29 

25  06 

24  34 

24  10 

23  39 

23  16 

22  52 

28 

32 

36  41 

36  00 

35  20 

34  39 

33  58 

33  17 

32  46 

32  05 

3134 

30  53 

30  23 

29  52 

32 

36 

46  27 

45  35 

44  43 

43  51 

42  59 

42  07 

41  28 

40  37 

39  58 

39  06 

38  27 

37  48 

36 

40 

57  20 

56  16 

55  12 

54  08 

53  04 

52  00 

51  12 

50  08 

49  20 

48  16 

47  28 

46  40 

40 

44 

69  23 

68  05 

66  48 

65  30 

64  12 

62  55 

61  57 

60  49 

59  42 

58  24 

57  26    56  28 

44 

48 

82  33 

81  01 

79  29 

77  57 

76  25 

74  53 

73  44 

72  11 

7102 

69  30 

68  19    67  10 

48 

52 

96  53 

95  05 

93  17 

9129 

89  41 

87  53 

86  32 

84  43 

83  22    81  34 

80  13    78  52 

52 

56 

104  01 

10155 

100  21 

98  15    96  42|  94  36 

93  02    91  28 

56 

60 

112  48 

11100 

108  36 

106  48 

105  00 

60 

II 

II 

II 

" 

" 

" 

// 

II 

II 

II 

" 

II 

A,h 

2.15 

2.11 

2.07 

2.03 

1.99 

1.95 

1.92 

1.88 

1.85 

1.81 

1.78 

1.75 

A,h 

Log. 

0.332 

0.324 

0.315 

0.307 

0.298 

0.290 

0.283 

0.274 

0.267 

0.257 

0.250   0.243 

Log. 

44 

28 

97 

50 

85 

03 

30         16 

17 

68 

42        04 

Limit 

46 

46 

47 

48 

48 

49 

50 

51 

52 

52 

53       54 

Min- 
utes 

Merid- 
ian 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

Alti- 
tudes 

212 


Latitude  35°  Declination  Contrary  Name 


. 

Declinations. 

Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/     // 

/     II 

/     // 

1     II 

'       n 

/       n 

/      // 

/     // 

/       n 

/     II 

/     // 

'      // 

Min. 

4 

0  27 

0  27 

0  27 

0  26 

0  25 

0  25 

0  25     0  24 

0  23 

0  23 

0  22 

0  22 

4 

8 

150 

147 

145 

143 

142 

141 

139 

1  36 

135 

133 

1  32 

1  30 

8 

12 

4  06 

4  00 

3  57 

3  53 

3  49 

3  46 

3  42 

3  37 

3  34 

3  29 

3  24 

3  22 

12 

16 

7  18 

7  08 

7  03 

6  55 

6  47 

6  42 

6  34 

6  27 

6  18 

6  11 

6  06 

5  58 

16 

20 

1124 

1108 

1100 

10  48 

10  36 

10  28 

10  16 

10  04 

9  52 

9  40 

9  32 

9  20 

20 

24 

16  25 

16  02 

15  51 

15  34 

15  16 

15  04 

14  47 

14  30 

14  12 

13  55 

13  43 

13  26 

24 

28 

22  21 

21  49 

21  33 

21  10 

20  47 

20  31 

20  07 

19  44 

19  21 

18  57 

18  42 

18  18 

28 

32 

29  11 

28  30 

28  09 

27  38 

27  08 

26  48 

26  17 

25  46 

25  16 

24  45 

24  25 

23  54 

32 

36 

36  56 

36  05 

35  39 

35  00 

34  21 

33  55 

33  16 

32  37 

3158 

31  19 

30  53 

30  14 

36 

40 

45  36 

44  32 

44  00 

43  12 

42  24 

4152 

41  04 

40  16 

39  28 

38  40 

38  08 

37  20 

40 

44 

55  10 

53  54 

53  15 

52  17 

51  18 

50  40 

49  41 

48  43 

47  45 

46  47 

46  08 

45  10 

44 

48 

65  38 

64  07 

63  21 

62  12 

6103 

60  17 

59  08 

57  59 

56  50 

55  41 

54  55 

53  46 

48 

52 

77  04 

75  15 

74  21 

73  00 

7139 

70  35 

69  24 

68  03 

66  42 

65  21 

64  27 

63  06 

52 

56 

89  22 

87  18 

86  15 

84  41 

83  06 

82  04 

80  29 

78  55 

77  21 

75  47 

74  44 

73  10 

56 

60 

102  36 

100  12 

99  00 

97  12 

95  24 

94  12 

92  24 

90  36 

88  48 

87  00 

85  48 

84  00 

60 

II 

II 

II 

" 

II 

II 

// 

II 

II 

II 

II 

II 

Ajh 

1.71 

1.67 

1.65 

1.62 

1.59 

1.57 

1.54 

1.51 

1.48 

1.45 

1.43 

1.40 

A,h 

Log. 

0.233 

0.222 

0.217 

0.209 

0.201 

0.195 

0.187 

0.178 

0.170 

0.161 

0.155 

0.146 

Log. 

00 

72 

48 

52 

40 

90 

52 

98 

26 

37 

34 

13 

Limit 

55 

56 

56 

57 

58 

59 

60 

60 

61 

62 

63 

64 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

Alti- 
tudes, 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
A  nglea 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,li 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
II 

1.38 

/     // 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

8100 
II 

1.35 

0  21 

1  25 
3  11 
5  41 
8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 
II 

1.33 

/     // 

0  21 

123 

3  07 

5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 

II 

1.30 

/     // 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

2141 

27  26 

33  52 

40  59 

48  45 

57  14 

66  23 

76  12 
II 

1.27 

/     // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
2120 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 

75  00 

II 

1.25 

/      // 

0  19 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

1.20 

/     // 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
6141 
70  48 

1.18 

/     // 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

II 

1.16 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 
68  24 

1.14 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.139 

88 

0.130 
33 

0.123 
85 

0.113 
94 

0.103 
80 

0.096 
91 

0.089 
91 

0.079 
18 

0.071 

88 

0.064 
46 

0.056 
90 

0.045 
32 

Log. 

Limit 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

75 

Min- 
utes 

Merid- 
ian 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

Alti- 
tudes 

Latitude  35''  Declination   Contrary  Name* 


213 


Declinations. 


Hour 
A.ngleB 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/      // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 
65  24 

1.09 

/     // 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
41  05 
48  13 
55  56 
64  12 

1.07 

/      // 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

1.04 

/ 
1 

// 

II 

// 

II 

// 

/ 

// 

// 

II 

II 

/ 

// 

// 

II 

n 

II 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.037 
43 

0.029 
38 

0.017 
03 

Log. 

Limit 

75 

76 

76 

Min- 
utes 

Merid- 
ian 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

Alti- 
tudes 

Declinations,  —  Inferior  Meridian 

% 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/      /' 

/      // 

/      // 

/      // 

1     II 

/        ir 

/      // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  13 

0  12 

0  12 

0  12 

Oil 

Oil 

0  11 

Oil 

0  10 

0  09 

0  09 

0  09 

4 

8 

0  51 

0  50 

0  48 

0  47 

0  45 

0  44 

0  42 

0  40 

0  39 

0  38 

0  37 

0  35 

8 

12 

155 

1  52 

1  48 

147 

142 

1  39 

1  36 

1  32 

127 

125 

1  22 

1  19 

12 

16 

3  25 

3  19 

3  12 

3  09 

3  02 

2  57 

2  52 

2  44 

2  37 

2  31 

2  26 

2  21 

16 

20 

5  20 

5  12 

5  00 

4  56 

4  44 

4  36 

4  28 

4  16 

4  04 

3  56 

3  48 

3  40 

20 

24 

7  41 

7  29 

7  12 

7  06 

6  49 

6  38 

6  26 

6  09 

5  52 

5  40 

5  28 

5  17 

24 

28 

10  27 

10  12 

9  48 

9  40 

9  17 

9  01 

8  45 

8  21 

7  58 

7  43 

7  27 

7  11 

28 

32 

13  39 

13  19 

12  48 

12  38 

12  07 

11  46 

1126 

10  55 

10  24 

10  04 

9  44 

9  23 

32 

36 

17  17 

16  51 

16  12 

15  59 

15  20 

14  55 

14  29 

13  50 

13  11 

12  45 

12  18 

11  53 

36 

40 

2120 

20  48 

20  00 

19  44 

18  56 

18  24 

17  52 

17  04 

16  16 

15  44 

15  12 

14  40 

40 

44 

25  49 

25  10 

24  12 

23  52 

22  54 

22  16 

2138 

20  39 

19  41 

19  02 

18  24 

17  45 

44 

48 

30  43 

29  55 

28  46 

28  23 

27  14 

26  29 

25  43 

24  34 

23  25 

22  39 

21  54 

21  07 

48 

52 

36  03 

35  09 

33  48 

33  21 

32  00 

3105 

30  11 

28  50 

27  29 

26  35 

25  41 

24  47 

52 

56 

41  49 

40  46 

39  12 

38  40 

37  06 

36  04 

35  02 

33  27 

3153 

30  50 

29  48 

28  45 

56 

60 

48  00 

II 

46  48 

45  00 

44  24 

42  36 

II 

41  24 

II 

40  12 

11 

38  24 

II 

36  36 

II 

35  24 

II 

34  12 

II 

33  00 

II 

60 

A,h 

0.80 

0.78 

0.75 

0.73 

0.71 

0.69 

0.67 

0.64 

0.61 

0.59 

0.57 

0.55 

A,h 

Log. 

9.903 

9.892 

9.875 

9.863 

9.851 

9.838 

9.826 

9.806 

9.785 

9.770 

9.755 

9.740 

Log. 

09 

09 

06 

32 

26 

85 

07 

18 

33 

85 

87 

36 

Limit 

83 

83 

84 

84 

85 

86 

87 

87 

88 

88 

88 

90 

Min- 
utes 

Merid- 
ian 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

Alti- 
tudes 

214 


Latitude  36°  Decimation  Same  Name* 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       // 

/            V 

/     // 

/     // 

/     // 

/     // 

/       n 

/     // 

/     II 

/     // 

/     // 

/     // 

Min. 

4 

0  43 

0  44 

0  46 

0  46 

0  47 

0  49 

0  51 

0  52 

0  54 

0  55 

0  57 

0  59 

4 

8 

2  53 

2  58 

3  02 

3  06 

3  11 

3  17 

3  22 

3  28 

3  34 

3  42 

3  49 

3  56 

8 

12 

6  29 

6  39 

6  49 

6  59 

7  11 

7  22 

7  35 

7  48 

8  02 

8  19 

8  34 

8  51 

12 

16 

11  31 

11  49 

12  07 

12  25 

12  45 

13  06 

13  29 

13  52 

14  18 

14  45 

15  14 

15  45 

16 

20 

18  00 

18  28 

18  56 

19  24 

19  56 

20  28 

2104 

2140 

22  20 

23  04 

23  48 

24  36 

20 

24 

25  55 

26  35 

27  16 

27  56 

28  42 

29  28 

30  21 

31  12 

32  10 

33  13 

34  16 

35  26 

24 

28 

35  17 

36  12 

37  06 

38  02 

39  05 

40  07 

41  17 

42  28 

43  46 

45  13 

46  39 

48  13 

28 

32 

46  05 

47  17 

48  28 

49  40 

5102 

52  24 

53  55 

55  28 

57  10 

59  03 

60  56 

62  58 

32 

36 

58  19 

59  50 

6121 

62  51 

64  35 

66  19 

68  16 

70  12 

72  22 

74  44 

77  07 

79  43 

36 

40 

72  00 

73  52 

75  44 

77  36 

79  44 

8152 

84  16 

86  40 

89  20 

92  16 

40 

44 

87  07 

44 

48 

48 

52 

52 

56 

56 

60 

n 

It 

II 

II 

II 

II 

// ' 

II 

// 

II 

II 

// ' 

60 

A,h 

2.70 

2.77 

2.84 

2.91 

2.99 

3.07 

3.16 

3.25 

3.35 

3.46 

3.57 

3.69 

Aih 

Log. 

0.431 

0.442 

0.453 

0.463 

0.475 

0.487 

0.499 

0.511 

0.525 

0.539 

0.552 

0.567 

Log. 

36 

48 

32 

89 

67 

14 

69 

88 

04 

08 

67 

03 

Limit 

38 

38 

37 

36 

35 

35 

35 

34 

33 

33 

32 

31 

Min- 
utes 

Merid- 
ian 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

1     II 

/       n 

/     II 

1     II 

/      // 

/      // 

/     II 

/      // 

/     // 

1     II 

/      // 

Min. 

Min. 

4 

101 

103 

106 

108 

1  11 

1  15 

1  18 

123 

1  26 

1  31 

137 

144 

4 

8 

4  05 

4  13 

4  23 

4  34 

4  46 

4  59 

5  13 

5  29 

5  47 

6  07 

6  30 

6  56 

8 

12 

9  10 

9  31 

9  51 

10  17 

10  43 

11  12 

1144 

12  20 

13  01 

13  45 

14  37 

15  36 

12 

16 

16  18 

16  53 

17  33 

18  15 

19  01 

19  56 

20  52 

21  56 

23  07 

24  27 

25  59 

27  44 

16 

20 

25  28 

26  24 

27  24 

28  32 

29  44 

3108 

32  36 

34  16 

36  08 

38  12 

40  36 

43  20 

20 

24 

36  41 

38  01 

39  28 

41  05 

42  48 

44  50 

46  57 

49  21 

52  02 

55  00 

58  28 

62  24 

24 

28 

49  55 

51  45 

53  42 

55  56 

57  17 

61  01 

63  54 

67  09 

70  50 

74  53 

79  35 

28 

32 

65  11 

67  35 

70  08 

73  03 

76  07 

79  42 

83  27 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.82 

3.96 

4.11 

4.28 

4.46 

4.67 

4.89 

5.14 

5.42 

5.73 

6.09 

6.50 

A,h 

Log. 

0.582 

0.597 

0.613 

0.631 

0.649 

0.669 

0.689 

0.710 

0.734 

0.758 

0.784 

0.812 

Log. 

06 

70 

84 

44 

33 

32 

31 

96 

00 

15 

62 
21 

91 
20 

Limit 

30 

29  ■ 

28 

28 

27 

26 

25 

24 

23 

22 

Min- 
utes 

Merid- 
ian 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

Alti- 
tudes 

Latitude  36°  Declination  Same  Name. 
Declinations. 


215 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/        n 

1       n 

/     // 

/     // 

1     II 

/     // 

/     // 

/     // 

1     II 

/     // 

/     // 

/     // 

Min. 

4 

151 

2  01 

2  11 

2  25 

2  41 

3  02 

3  31 

4  10 

4 

8 

7  26 

8  03 

8  46 

9  39 

10  45 

12  10 

14  02 

16  39 

8 

12 

16  46 

18  06 

19  44 

21  43 

24  12 

27  22 

3135 

37  39 

12 

16 

29  46 

32  10 

35  04 

38  37 

43  00 

16 

20 

46  32 

50  16 

54  48 

20 

24 

24 

28 

28 

32 

■  ■ 

32 

36 

. 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

6.98 

7.54 

8.22 

9.05 

10.08 

11.40 

13.16 

15.62 

A,h 

Log. 

0.843 

0.877 

0.914 

0.956 

1.003 

1.056 

1.119 

1.193 

Log. 

86 

37 

87 

65 

46 

90 

26 

68 

Limit 

19 

17 

16 

15 

14 

12 

11 

9 

8 

6 

4 

2 

Min- 
utes 

Merid- 
ian 

78° 

79^ 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

Alti- 
tudas 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39' 

'      40' 

>      41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

1     If 

/      // 

Min. 

Min. 

4 

3  40 

3  00 

2  32 

2  11 

1  55 

142 

131 

4 

8 

14  40 

12  03 

10  10 

8  46 

7  39 

6  47 

6  03 

8 

12 

33  00 

27  06 

22  52 

19  42 

17  14 

15  16 

13  38 

12 

16 

40  40 

35  02 

30  38 

27  08 

24  14 

16 

20 

54  44 

47  52 

42  24 

37  52 

20 

24 

6104 

54  32 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

^. 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

// 

// 

// 

II 

" 

II 

II 

II 

II 

II 

II 

Ajh 

13.75 

11.29 

9.53 

8.21 

7.18 

6.36 

5.68 

Aih 

Log. 

1.138 

1.052 

0.979 

0.914 

0.856 

0.803 

0.754 

30 

69 

09 

34 

12 

46 

35 

Limit 

0 

2 

4 

6 

8 

10 

12 

14 

16 

17 

19 

21 

Min- 
utes 

Merid- 
ian 

90° 

89° 

88° 

87= 

'      W 

'      85° 

84° 

83° 

82° 

81° 

80° 

79° 

Alti- 
tudes 

216 


Latitude  36°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  It 

1     It 

1     It 

1     II 

/  // 

t       n 

/  // 

1     II 

/  // 

/  // 

Min. 

4 

1  22 

1  14 

107 

102 

0  57 

0  52 

0  48 

0  44 

0  42 

0  38  0  36 

0  33 

4 

8 

5  27 

4  56 

4  30 

4  07 

3  47 

3  30 

3  13 

2  59 

2  46 

'2  35  2  24 

2  14 

8 

12 

12  15 

11  06 

10  08 

9  16 

8  31 

7  53 

7  15 

6  42 

6  14 

5  47  5  24 

5  01 

12 

16 

21  49 

19  46 

18  00 

16  28 

15  09 

13  59 

12  53 

11  54 

1106 

10  17  9  36 

8  55 

16 

20 

34  04 

30  52 

28  08 

25  44 

23  40 

21  52 

20  08 

18  36 

17  20 

16  04  15  00 

13  56 

20 

24 

49  04 

44  27 

40  31 

37  04 

34  05 

31  29 

29  00 

26  47 

24  58 

23  08  21  36 

20  04 

24 

28 

66  46 

60  30 

55  09 

50  26 

46  23 

42  52 

39  28 

36  28 

33  58 

31  30  29  24 

27  19 

28 

32 

60  35 

55  59 

51  32 

47  37 

44  22 

41  08  38  24 

35  40 

32 

36 

70  51 

65  14 

60  16 

56  10 

52  03  48  36 

45  09 

36 

40 

80  32 

74  24 

69  20 

64  16 

60  00 

55  44 

40 

44 

83  54 

77  45 

72  36 

67  26 

44 

48 

80  15 

48 

52 

52 

56 

56 

60 

60 

" 

•  // 

It 

11 

" 

ir 

II 

" 

II 

II 

II 

II 

A,h 

5.11 

4.63 

4.22 

3.86 

3.55 

3.28 

3.02 

2.79 

2.60 

2.41 

2.25 

2.09 

A,h 

Log. 

0.708 

0.665 

0.625 

0.586 

0.550 

0.515 

0.480 

0.445 

0.414 

0.382 

0.352 

0.320 

Log. 

42 

58 

31 

59 

23 

87 

01 

60 

97 

02 

18 

15 

Limit 

22 

24 

25 

27 

29 

31 

32 

33 

34 

36 

38 

40 

Min- 
utes 

Merid- 
ian 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67°. 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1      II 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

II 
1.95 

0  29 

1  56 
4  22 
7  47 

12  08 
17  29 
23  47 
3103 
39  19 
48  32 
58  44 
69  53 
82  01 

II 
1.82 

1     II 

0  27 

149 
4  05 
7  15 
1120 
16  19 
22  13 
29  01 
36  43 
45  20 
54  51 
65  15 
76  37 

II 
1.70 

/  // 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

6103 

7139 

83  06 

II 
1.59 

1     II 

0  23 

135 

3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

3158 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

/  // 

0  22 

1  28 
3  19 
5  53 
9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
II 

1.38 

/  // 

0  20 

1  23 
3  06 
5  30 
8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 
II 

1.29 

/  // 

0  19 

1  17 

2  53 
5  07 
8  00 

1131 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

II 

1.20 

/  // 

0  18 

1  11 

2  41 

4  47 
7  28 
10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

II 

1.12 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/  // 

0  15 
102 
2  20 

4  08 
6  28 
9  18 
12  41 
16  34 
20  57 
25  52 
31  18 
37  15 
43  43 
50  42 

58  12 

II 

0.97 

/  // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

II 

0.89 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48  . 
52 
56 
60 

A,li 

Log. 

0.290 
03 

0.260 
07 

0.230 
45 

0.201 
40 

0.170 
26 

0.139 

88 

0.110 
59 

0.079 
18 

0.049 
22 

0.021 
19 

9.986 
77 

9.949 
39 

Log. 

Limit 

42 

43 

45 

47 

49 

50 

52 

54 

56 

58 

60 

62 

Min- 
utes 

Merid- 
ian 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

55° 

Alti- 
tudes 

Latitude  36°  Decimation  Contrary  Name. 


217 


Declixations. 


Hour 
Angles 

1    0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

1      11 

/     // 

/     // 

/     // 

1     II 

/     // 

/     // 

/      "  1  '      "  i  '      " 

/     II 

/      // 

Min. 

4 

0  43 

0  43 

0  41 

0  40 

0  39 

0  38 

0  38 

0  37     0  36     0  35 

0  35 

0  34 

4 

8 

2  53 

2  49 

2  45 

2  41 

2  39 

2  35 

2  31 

2  28     2  25|     2  22 

2  19 

2  16 

8 

12 

6  29 

6  20 

6  12 

6  03 

5  56 

5  47 

5  40 

5  32     5  26|     5  20 

5  12 

5  06 

12 

16 

1131 

11  16 

1100 

10  45 

10  32 

10  17 

10  04 

9  52     9  38     9  28 

9  16 

9  06 

16 

20 

18  00 

17  36 

17  12 

16  48 

16  28 

16  04 

15  44 

15  24    15  04    14  48 

14  28 

14  12 

20 

24 

25  55 

25  21 

24  46 

24  12 

23  42 

23  08 

22  40 

22  11    21  42    21  19 

20  50 

20  27 

24 

28 

35  17 

34  29 

33  43 

32  56 

32  17 

31  30 

30  50 

30  11    29  32    29  01 

28  21 

27  50 

28 

32 

46  05 

45  03 

44  02 

43  00 

42  10 

4108 

40  16 

39  251  38  34    37  53 

37  02 

36  21 

32 

36 

58  19 

57  02 

55  44 

54  26 

53  21 

52  03 

50  59 

49  54j  48  49    47  57 

46  53 

46  01 

36 

40 

72  00 

70  24 

68  48 

67  12 

65  52 

64  16 

62  56 

61  36;  60  16'  59  12 

57  22 

56  48 

40 

44 

87  07 

85  11 

83  15 

81  19 

79  42 

77  45 

76  09 

74  32j  72  55    71  38 

70  02 

68  44 

44 

48 

94  51 

92  33 

90  37 

88  42    86  47 

85  15 

83  19 

8146 

48 

52 

106  21 

104  06  101  51 

100  03 

97  47 

95  59 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

" 

" 

II 

II 

II 

A,h 

2.70 

2.64 

2.58 

2.52 

2A7 

2.41 

2.36 

2.31 

2.26 

2.22 

2.17 

2.13 

A,h 

Log. 

0.431 

0.421 

0.411 

0.401 

0.392 

0.382 

0.372 

0.363 

0.354 

0.346 

0.336 

0.328 

36 

60 

62 

40 

70 

02 

91 

61 

11 

35 

46 

38 

Log. 

Limit 

38 

38 

39 

40 

41 

42 

42 

43 

43 

44 

45 

45 

Min- 
utes 

Merid- 
ian 

54° 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Anglea 

Min. 

Min. 

4 

0  33 

0  33 

0  32 

0  31 

0  31 

0  30 

0  30 

0  29 

0  29 

0  28 

0  28 

0  27 

4 

8 

2  14 

2  11 

2  09 

2  05 

2  04 

2  01 

2  00 

157 

155 

154 

1  52 

150 

8 

12 

5  01 

4  55 

4  49 

4  44 

4  40 

4  34 

4  29 

4  23 

4  19 

4  16 

4  11 

4  06 

12 

16 

8  55 

8  45 

8  35 

8  24 

8  16 

8  06 

7  59 

7  49 

7  41 

7  33 

7  25 

7  18 

16 

20 

13  56 

13  40 

13  24 

13  08 

12  56 

12  40 

12  28 

12  12 

12  00 

1148 

1136 

11  24 

20 

24 

20  04 

19  41 

19  18 

18  54 

18  37 

18  14 

17  57 

17  34 

17  17 

16  59 

16  42 

16  25 

24 

28 

27  19 

26  47 

26  16 

25  45 

25  21 

24  50 

24  26 

23  55 

23  31 

23  08 

22  44 

22  21 

28 

32 

35  40 

34  59 

34  18 

33  38 

33  07 

32  26 

3155 

31  13 

30  43 

30  13 

29  42 

29  11 

32 

36 

45  09 

44  17 

43  25 

42  33 

4154 

4102 

40  24 

39  32 

38  53 

38  14 

37  35 

36  56 

36 

40 

55  44 

54  40 

53  36 

52  32 

5144 

50  40 

49  52 

48  48 

48  00 

47  12 

46  24 

45  36 

40 

44 

67  26 

66  09 

64  51 

63  34 

62  35 

61  18 

60  21 

59  03 

58  05 

57  07 

56  08 

55  10 

44 

48 

80  15 

78  43 

77  11 

75  39 

74  30 

72  58 

7148 

70  16 

69  07 

67  56 

66  47 

65  38 

48 

52 

94  11 

92  23 

90  35 

88  47 

87  26 

85  38 

84  16 

82  28   8107 

79  46 

78  25 

77  04 

52 

56 

105  03 

102  57 

10123 

99  18 

97  45 

95  39 

94  05 

92  31 

90  56 

89  22 

56 

60 

114  00 

112  12 

109  48 

108  36 

106  12 

104  24 

102  36 

60 

II 

" 

" 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.09 

2.05 

2.01 

1.97 

1.94 

1.90 

1.87 

1.83 

1.80 

1.77 

1.74 

1.71 

A,h 

Log. 

0.320 

0.311 

0.303 

0.294 

0.287 

0.278 

0.271 

0.262 

0.255 

0.247 

0.240 

0.233 

Log. 

15 

75 

20 

47 

80 

75 

84 

45 

27 

97 

55 

00 

Limit 

46 

47 

48 

49 

49 

50 

51 

52 

53 

53 

54 

55 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

218 


Latitude  36°  Declination  Contrary  Name. 


Dkclixation.s. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

0  27 

147 

4  02 

7  10 

11  12 

16  08 

2157 

28  40 

36  18 

44  48 

54  13 

64  30 

75  42 

87  49 

100  48 

1.68 

/  It 

0  27 

145 

3  56 

7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 

1.64 

/  // 

0  26 

1  42 
3  51 
6  53 

10  44 

15  28 

21  02 

27  28 

34  47 

42  56 

51  57 

61  49 

72  33 

84  09 

96  36 
II 

1.61 

0  25 

141 

3  48 

6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/  // 

0  25 

1  40 
3  45 
6  39 

10  24 
14  59 
20  23 
26  37 
33  42 
41  36 
50  20 
59  54 
70  18 
8132 
93  36 

1.56 

/  n 

0  24 

1  38 
3  40 
6  32 

10  11 

14  41 

20  00 

26  07 

33  03 

40  48 

49  22 

58  45 

68  57 

79  58 

9148 
II 

1.53 

/    H 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 
90  36 

1.51 

/  II 

0  23 

1  35 
3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

/   n 

0  23 

133 

3  29 

6  11 

9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
II 

1.45 
0.161 
37 

/  // 

0  22 

1  32 
3  24 
6  06 
9  32 

13  43 
18  42 
24  25 
30  53 
38  08 
46  08 
54  55 
64  27 
74  44 
85  48 

1.43 

/  // 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

/  n 

0  22 

1  28 
3  19 
5  53 
9  12 

13  15 
18  02 
23  33 
29  49 
36  48 
44  32 
52  59 
62  11 
72  08 
82  48 

1.38 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.225 
31 

0.214 
84 

0.206 
83 

0.198 
66 

0.193 
12 

0.184 
69 

0.178 
98 

0.170 
26 

0.155 
34 

0.146 
13 

0.139 

88 

Log. 

Limit 

56 

57 

57 

58 

59 

60 

61 

61 

62 

63 

64 

65 

Min- 
utes 

Merid- 
ian 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

Alti- 
tudes 

Declixations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

5150 

60  50 

70  34 

8100 

II 

1.35 

0  21 
125 
3  11 
5  41 

8  52 
12  46 
17  23 
22  42 
28  44 
35  28 
42  55 
51  04 
59  56 
69  31 
79  48 

1.33 

/  // 

0  21 

123 

3  07 

5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 

II 

1.30 

/  // 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

/  // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
21  20 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 

75  00 

II 

1.25 

/  // 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 
16  05 
2100 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 

73  48 

II 

1.23 

/  // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

II 

1.21 

/  // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

31  44 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

/  // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

II 

1.17 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 
68  24 

1.14 

/  // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

II 

1.12 

/  // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.130 
33 

0.123 

85 

0.113 
94 

0.107 
21 

0.096 
91 

0.089 
91 

0.082 
79 

0.075 
55 

0.068 
19 

0.056 
90 

0.049 
22 

0.041 
39 

Log. 

Limit 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

75 

76 

Min- 
utes 

Merid- 
ian 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

Alti- 
tudes 

Latitude  36°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


219 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1     II 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
II 

1.07 

/     // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

1      II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
II 

1.03 

/ 

// 

/ 

// 

// 

/ 

// 

II 

// 

1 

// 

/ 

// 

/ 

// 

II 

1       n 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 
II 

0.82 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.029 
38 

0.021 
19 

0.012 
84 

9.913 
81 

Log. 

Limit 

76 

77 

78 

82 

Min- 
utes 

Merid- 
ian 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  12 

0  51 

1  54 
3  22 
5  16 
7  35 

10  20 
13  29 
17  04 
2104 
25  29 
30  18 
35  36 
41  17 

47  24 

II 

0.59 

/     // 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

II 

0.77 

/     // 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

II 

0.75 

/      // 

0  11 

0  47 

1  45 

3  07 

4  52 
7  00 
9  33 

12  28 
15  46 
19  28 
23  33 
28  00 
32  54 
38  09 

43  48 

II 

0.73 

Oil 
0  45 
142 

3  02 

4  44 
6  49 
9  17 

12  07 

15  20 

18  56 

22  54 

27  14 

32  00 

37  06 

42  36 
II 

0.71 

/     // 

Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

1136 

14  42 

18  08 

21  57 

26  06 

30  38 

35  33 

40  48 

II 

0.68 

/      // 

Oil 

0  42 

135 

2  49 

4  24 

6  21 

8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 
II 

0.66 

/      // 

0  10 

0  40 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
II 

0.63 

1     II 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
31  53 

36  36 

II 

0.61 

/     // 

0  09 
0  38 
125 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

1     II 

0  09 

0  36 

1  21 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
2120 
25  14 
29  16 

33  36 

II 

0.56 

/     // 

0  09 

0  34 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

11  27 
14  08 
17  06 
20  21 
23  53 
27  42 

31  48 

II 

0.53 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.897 
63 

9.886 
49 

9.875 
06 

9.863 
32 

9.851 
26 

9.832 
51 

9.819 
54 

9.799 
34 

9.785 
33 

9.770 
85 

9.748 
19 

9.724 
28 

Log. 

Limit 

83 

83 

84 

84 

85 

85 

86 

86 

87 

87 

88 

89 

Min- 
utes 

Merid  - 
ian 

6° 

7° 

8° 

9° 

10° 

IP 

12° 

13° 

14° 

15° 

16° 

17° 

Alti- 
tudes 

220 


Latitude  37°  Declination  Same  Name* 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8°    i     9° 

10° 

11° 

Hour 
Angles 

/       n 

/       n 

/     ti 

/           ff    \    1          ff 

Min. 

Min. 

4 

0  42 

0  43 

0  43 

0  45 

0  46 

0  47 

0  48 

0  50 

0  51 

0  53 

0  54 

0  56 

4 

8 

2  47 

2  51 

2  55 

2  59 

3  04 

3  09 

3  14 

3  19 

3  25 

3  31 

3  38 

3  45 

8 

12 

6  15 

6  24 

6  33 

6  43 

6  53 

7  05 

7  16 

7  27 

7  41 

7  55 

8  10 

8  25 

12 

16 

1109 

11  24 

1139 

1157 

12  15 

12  35 

12  56 

13  17 

13  39 

14  05 

14  30 

14  59 

16 

20 

17  24 

17  48 

18  12 

18  40 

19  08 

19  40 

20  12 

20  44 

21  20    22  00 

22  40 

23  24 

20 

24 

25  04 

25  38 

26  12 

26  53 

27  33 

28  19 

29  05 

29  52 

30  43    31  41 

32  38 

33  42 

24 

28 

34  06 

34  53 

35  41 

36  35 

37  30 

38  33 

39  36 

40  38 

41  49    43  07 

44  26 

45  52 

28 

32 

44  32 

45  34 

46  36 

47  47 

48  59 

50  21 

5143 

53  04 

54  37 

56  19 

58  02 

59  54 

32 

36 

56  23 

57  41 

58  58 

60  29 

62  00 

63  43 

65  27 

67  11 

69  07 

71  17 

73  26 

75  49 

36 

40 

69  36 

71  12 

72  48 

74  40 

76  32 

78  40 

80  48 

82  56 

85  20 

88  00 

90  40 

40 

44 

84  13 

86  10 

88  05 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

" 

" 

II 

II 

II 

II 

II 

// 

II 

II 

II 

Ajh 

2.61 

2.67 

2.73 

2.80 

2.87 

2.95 

3.03 

3.11 

3.20 

3.30 

3.40 

3.51 

A,h 

Log. 

0.416 

0.426 

0.436 

0.447 

0.457 

0.469 

0.481 

0.492 

0.505 

0.518 

0.531 

0.545 

Log. 

64 

51 

16 

16 

88 

82 

44 

76 

15 

51 

48 

31 

Limit 

39 

39 

38 

37 

36 

36 

35 

35 

34 

34 

33 

32 

Min- 
utes 

Merid- 
ian 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/       // 

/      // 

/     // 

Min. 

Min. 

4 

0  58 

100 

102 

105 

107 

1  10 

1  13 

1  17 

121 

125 

130 

1  35 

4 

8 

3  52 

4  01 

4  09 

4  19 

4  30 

4  40 

4  53 

5  07 

5  23 

5  40 

5  59 

6  22 

8 

12 

8  42 

9  02 

9  20 

9  42 

10  06 

10  31 

1100 

1131 

12  06 

12  44 

13  29 

14  20 

12 

16 

15  30 

16  02 

16  36 

17  14 

17  58 

18  41 

19  32 

20  29 

2130 

22  40 

23  59 

25  28 

16 

20 

24  12 

25  04 

25  56 

26  56 

28  04 

29  12 

30  32 

32  00 

33  36 

35  24 

37  28 

39  48 

20 

24 

34  51 

36  06 

37  21 

38  47 

40  25 

42  03 

43  58 

46  05 

48  23 

50  59 

53  58 

57  18 

24 

28 

47  26 

49  08 

50  50 

52  47 

55  01 

57  14 

59  51 

62  43 

65  51 

69  23 

73  26 

78  01 

28 

32 

6157 

64  10 

66  23 

68  57 

7151 

74  45 

78  10 

8155 

32 

36 

78  25 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

n 

II 

n 

II 

A,h 

3.63 

3.76 

3.89 

4.04 

4.21 

4.38 

4.58 

4.80 

5.04 

5.31 

5.62 

5.97 

A,h 

Log. 

0.559 

0.575 

0.589 

0.606 

0.624 

0.641 

0.660 

0.681 

0.702 

0.726 

0.7*9 

0.775 

Log. 

91 

19 

95 

38 

28 

47 

87 

24 

43 

09 

74 

97 

Limit 

31 

30 

29 

29 

28 

27 

26 

24 

23 

23 

22 

21 

Min- 
utes 

Merid- 
ian 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

Alti- 
tudes 

Latitude  37°  Declination  Same  Name. 


221 


D;:cLiNATioxs. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

/      // 

/      /' 

Min. 

Min. 

4 

142 

150 

158 

2  09 

2  22 

2  38 

2  59 

3  26 

4  04 

4 

8 

6  48 

7  18 

7  53 

8  35 

9  26 

10  30 

11  53 

13  43 

16  17 

8 

12 

15  17 

16  25 

17  44 

19  19 

21  14 

23  38 

26  44 

30  52 

36  38 

12 

16 

27  11 

29  11 

31  32 

34  21 

37  46 

42  02 

16 

20 

42  28 

45  36 

49  16 

53  40 

20 

24 

61t)9 

65  40 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

" 

II 

II 

II 

II 

II 

II 

" 

// 

// 

A,h 

6.37 

6.8 

1 

7.39 

8.05 

8.85 

9.85 

11.14 

12.86 

15.26 

Aih 

Log. 

0.804 

0.8 

35 

0.868 

0.905 

0.946 

0.993 

1.046 

1.109 

1.183 

Log. 

14 

06 

64 

80 

94 

44 

89 

24 

55 

Limit 

20 

19 

18 

17 

16 

14 

12 

11 

10 

8 

6 

4 

Min, 
utes 

Merid- 
ian 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

Alti-" 
tudes 

Declinations. 


Hour 
Angles 

36° 

37' 

'      38° 

39° 

40° 

41= 

>      42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angle 

/      II 

1 

//    /     // 

/      // 

1     II 

1 

//    /      // 

/      // 

/      // 

I     II 

/     // 

Min. 

Min, 

4 

3  34 

2  55 

2  28 

2  07 

1  51 

139 

4 

8* 

14  16 

11  42 

9  53 

8  30 

7  25 

6  34 

8 

12 

32  05 

26  20 

22  14 

19  08 

16  43 

14  47 

12 

16 

46  48 

39  30 

34  00 

29  41 

26  17 

16 

20 

53  08 

46  24 

4104 

20 

24 

59  09 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

It 

II 

II 

Aih 

13.37 

10.97 

9.26 

7.97 

6.96 

6.16 

Aih 

Log. 

1.126 
13 

1.040 
21 

0.966 
61 

0.901 
46 

0.842 
61 

0.789 
58 

Log. 

Limit 

2 

0 

2 

4 

6 

8 

10 

12 

14 

15 

17 

19 

Min- 
utes 

Merid- 
ian 

89° 

90^ 

89° 

88° 

87° 

86' 

'      85° 

84° 

83° 

82° 

81° 

80° 

Alti- 
tudes 

Latitude  37°  Decimation  Same  Name. 


Declixatioxs. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

1     II 

/  // 

/  " 

Min. 

Min. 

4 

1  28 

1  19 

1  11 

105 

0  59 

0  54 

0  51 

0  46 

0  43 

0  40 

0  37 

0  35 

4 

8 

5  52 

5  16 

4  47 

4  21 

4  00 

3  39 

3  21 

3  06 

2  52 

2  40 

2  28 

2  18 

8 

12 

13  12 

11  53 

10  46 

9  48 

8  57 

8  13 

7  33 

6  59 

6  27 

6  00 

5  34 

5  11 

12 

16 

23  28 

21  07 

19  06 

17  24 

15  55 

14  35 

13  27 

12  25 

11  29 

10  40 

9  54 

9  13 

16 

20 

36  40 

33  00 

29  52 

27  12 

24  52 

22  48 

2100 

19  24 

17  56 

16  40 

15  28 

14  24 

20 

24 

52  48 

47  31 

42  59 

39  10 

35  48 

32  50 

30  15 

27  56 

25  50 

24  00 

22  17 

20  45 

24 

28 

71  52 

64  41 

58  33 

53  19 

48  45 

44  42 

4109 

38  02 

35  09 

32  40 

30  19 

28  13 

28 

32 

69  38 

63  40 

58  22 

53  45 

49  40 

45  54 

42  40 

39  35 

36  51 

32 

36 

68  03 

62  51 

58  07 

54  00 

50  07 

46  40 

36 

40 

7144 

66  40 

6152 

57  36 

40 

44 

74  52 

69  42 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

A,h 

5.50 

4.95 

4.48 

4.08 

3.73 

3.42 

3.15 

2.91 

2.69 

2.50 

2.32 

2.16 

A,h 

Log. 

0.740 

0.694 

0.651 

0.610 

0.571 

0.534 

0.498 

0.463 

0.429 

0.397 

0.365 

0.334 

Log. 

36 

61 

28 

66 

71 

03 

31 

89 

75 

94 

49 

45 

Limit 

21 

23 

24 

25 

27 

29 

30 

31 

32 

34 

36 

38 

Min- 
utes 

Merid- 
ian 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

/  // 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 

II 
1.51 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1     II 

0  32 

2  08 
4  48 
8  32 
13  20 
19  12 
26  08 
34  08 
43  12 
53  20 
64  32 
76  48 

II 
2.00 

/   // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

3155 

40  24 

49  52 

60  21 

71  48 

84  16 

II 
1.87 

/  // 

0  28 

152 

4  11 

7  25 

1136 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

II 
1.74 

/  II 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

II 
1.62 

/  // 

0  22 
130 
3  22 

5  58 
9  20 
13  26 
18  18 
23  54 
30  14 
37  20 
45  10 
53  46 
63  06 
73  10 

84  00 

II 

1.40 

1     II . 

0  21 

1  24 
3  08 
5  36 
8  44 

12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

1.31 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

1     II 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 

68  24 

II 

1.14 

/  // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
II 

1.06 

/  // 

0  15 

1  02 

2  22 
4  10 
6  32 
9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 
II 

0.98 

/  // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

11  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

" 
0.90 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.301 
03 

0.271 

84 

0.240 
55 

0.209 
52 

0.178 
98 

48 

0.146 
13 

0.117 
27 

0.086 
36 

0.056 
90 

0.025 
31 

9.991 
23 

9.954 
24 

Log. 

Limit 

41 

42 

44 

46 

49 

51 

53 

55 

57 

59 

61 

Min- 
utes 

Merid- 
ian 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

56° 

Alti- 
tudes 

Latitude  37°  Declination  Contrary  Name. 


223 


Declix.\tioxs 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5°        6° 

7° 

8°        9° 

10°      11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/        n 

0  42 
2  47 
6  15 
1109 
17  24 
25  04 
34  06 
44  32 
56  23 
69  36 
84  13 

II 
2.61 

0  41 
2  43 
6  07 
10  53 
17  00 
24  29 
33  19 
43  31 
55  05 
68  00 
82  17 

II 
2.55 

1          H 

0  39 
2  40 
5  59 
10  37 
16  36 
23  54 
32  33 
42  30 
53  47 
66  24 
80  20 
95  37 

II 
2.49 

/     II 

0  39 
2  37 
5  52 
10  24 
16  16 
23  25 
3153 
41  39 
52  42 
65  04 
78  43 
93  42 

II 
2.44 

0  38 

2  32 

5  43 

10  09 

15  52 

22  51 

3106 

40  37 

51  25 

63  28 

76  48 

9123 

107  15 

II 
2.38 

/     // 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

II 
2.33 

/      // 

0  36 

2  27 

5  30 

9  46 

15  16 

21  59 

29  56 

39  05 

49  28 

61  04 

73  53 

87  56 

103  12 

II 
2.29 

/      // 

0  36 

2  24 

5  23 

9  33 

14  56 

2130 

29  16 

38  14 

48  23 

59  44 

72  16 

86  01 

100  57 

II 
2.24 

/     // 

0  35 

2  21 
5  17 
9  23 
14  40 
21  07 
28  45 
37  33 
47  31 
58  40 
70  59 
84  29 
99  09 

2.20 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

1     II 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

// 
2.11 

/      // 

0  33 
2  13 

•4  58 
8  50 
13  48 
19  52 
27  03 
35  20 
44  43 
55  12 
66  48 
79  29 
93  17 

II 
2.07 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.416    0.406 
64        54 

0.396 
20 

0.387 
39 

0.376 
58 

0.367 
36 

0.359 
84 

0.350 
25 

0.342 
42 

0.332 
44 

0.324 

28 

0.315 
97 

Log. 

litmit 

39 

39 

40 

41 

42 

43 

43 

44 

44 

45 

46        46 

Min- 
utes 

Merid- 
ian 

53° 

52° 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/       n 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  32 

0  31 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

4  - 

8 

2  10 

2  07 

2  05     2  02 

2  01 

158 

156 

155 

153 

151 

149 

1  47 

8  - 

12 

4  52 

4  47     4  43     4  37 

4  32 

4  26 

4  22 

4  18 

4  14 

4  09 

4  05 

4  00 

12  . 

16 

8  40 

8  29     8  21|     8  11 

8  04 

7  54 

7  46 

7  38 

7  30 

7  23 

7  15 

7  08 

16-. 

20 

13  32 

13  16|   13  041  12  48 

12  36 

12  20 

12  08 

1156 

11.44 

1132 

11  20 

11  08 

20.. 

24 

19  29 

19  06    18  49'   18  26'  18  09 

17  46 

17  29    17  11 

16  54 

16  36 

16  19 

16  02 

24 

28 

26  32 

26  01    25  37    25  06    24  42 

24  10 

23  47    23  24 

2^00 

22  37    22  13    21  49 

28 

32 

34  39:  33  58    33  27    32  46    32  15 

3134 

31  03;  30  33 

30  02 

29  32    29  or  28  30 

32 

36 

43  5l|  42  59i  42  20    41  28    40  50 

39  58 

39  19    38  40    38  01 

37  22    36  43    36  05 

36 

40 

54  08 

53  04|  52  16    51  12 

50  24 

49  20 

48  32 

47  44 

46  56 

46  08    45  20    44  32 

40 

44 

65  30 

64  12    63  14,  61  57 

60  59 

59  42 

58  44 

57  45 

56  47 

55  49 

54  51J  53  54 

44 

48 

77  57 

76  25    75  16'  73  44]  72  34 

7102 

69  53 

68  42 

67  33 

66  24 

65  15i  64  07 

48 

52 

9129 

89  41,  8820'  86  32 

85  10 

83  22 

82  01 

80  40 

79  19 

77  58 

76  37 

75  15 

52 

56 

106  06 

104  01 

102  26 

100  21 

98  47 

96  42 

95  08 

93  33 

9159 

90  25 

88  51 

87  18 

56 

60 

113  24 

11100 

109  12 

107  24 

105  36 

103  48 

102  00 

100  12 

60 

// 

// 

II 

II 

II 

II 

II 

II 

II 

// 

// 

II 

A,h 

2.03 

1.99 

1.96 

1.92 

1.89 

1.85 

1.82 

1.79 

1.76 

1.73 

1.70 

1.67 

A,h 

Log. 

0.307 

0.298   0.292   0.283 

0.276 

0.267 

0.260 

0.252 

0.245 

0.238|  0.230|  0.222 

Log. 

50 

85        26        30 

46 

17 

07 

85 

51 

05 

45 

72 

Limit 

47 

48    1    49        50 

1 

50 

51 

52 

53 

53 

54 

55 

56 

Min- 
utes 

Merid- 
ian 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

-  •( 
7 


224 


Latitude  37°  Declination  ODntrary  Name 

Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

/        n 

1     II 

/     II 

/       n 

/     II 

/     // 

/     /' 

/     // 

/     // 

Min. 

Min. 

4 

0  27 

0  26 

0  25 

0  25 

0  25 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

4 

8 

145 

1  42 

141 

139 

1  38 

136 

135 

133 

131 

130 

128 

126 

8 

12 

3  56 

3  50 

3  48 

3  43 

3  40 

3  36 

3  34 

3  29 

3  25 

3  22 

3  19 

3  14 

12 

16 

7  00 

6  50 

6  44 

6  37 

6  32 

6  24 

6  18 

6  11 

6  03 

5  58 

5  53 

5  46 

16 

20 

10  56 

10  40 

10  32 

10  20 

10  12 

10  00 

9  52 

9  40 

9  28 

9  20 

9  12 

9  00 

20 

24 

15  45 

15  22 

15  10 

14  53 

14  41 

14  24 

14  12 

13  55 

13  38 

13  26 

13  15 

12  58 

24 

28 

21  25 

20  54 

20  39 

20  15 

20  00 

19  36 

19  21 

18  57 

18  34 

18  18 

18  02 

17  38 

28 

32 

27  59 

27  18 

26  58 

26  27 

26  07 

25  36 

25  16 

24  45 

24  14 

23  54 

23  33 

23  02 

32 

36 

35  26 

34  34 

34  08 

33  29 

33  03 

32  24 

3158 

31  19 

30  40 

30  14 

29  49 

29  10 

36 

40 

43  44 

42  40 

42  08 

41  20 

40  48 

40  00 

39  28 

38  40 

37  52 

37  20 

36  48 

36  00 

40 

44 

52  55 

5138 

50  59 

50  01 

49  22 

48  24 

47  45 

46  47 

45  49 

45  10 

44  32 

43  34 

44 

48 

62  58 

61  26 

60  40 

59  31 

58  45 

57  36 

56  50 

55  41 

54  32 

53  46 

52  59 

5150 

48 

52 

73  54 

72  06 

71  12 

69  51 

68  57 

67  36 

66  42 

65  21 

64  00 

63  06 

62  11 

60  50 

52 

56 

85  43 

83  38 

82  35 

8101 

79  58 

78  24 

77  21 

75  47 

74  13 

73  10 

72  08 

70  34 

56 

60 

98  24 

96  00 

94  48 

93  00 

9148 

90  00 

88  48 

87  00 

85  12 

84  00 

82  48 

8100 

60 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

A,h 

1.64 

1.60 

1.58 

1.55 

1.53 

1.50 

1.48 

1.45 

1.42 

1.40 

1.38 

1.35 

A,h 

Log. 

0.214 

0.204 

0.198 

0.190 

0.184 

0.176 

0.170 

0.161 

0.152 

0.146 

0.139 

0.130 

Log. 

84 

12 

66 

33 

69 

09 

26 

37 

29 

13 

88 

33 

Limit 

57 

58 

58 

59 

60 

61 

62 

62 

63 

64 

65 

66 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42°      43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  22 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 

II 

1.33 

/      // 

0  21 

1  23 
3  07 
5  33 

8  40 
12  29 
16  59 
22  11 
28  05 
34  40 
4157 
49  55 
58  35 
67  57 
78  50 

1.30 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 

It 

1.28 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

2120 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 

1.25 

/      // 

0  20 

1  19 

2  57 
5  15 
8  12 

11  48 
16  05 
2100 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 
73  48 

1.23 

/     // 

0  19 

1  18 

2  54 
5  10 
8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

/     // 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
71  24 

1.19 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

II 

1.17 

/      // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 
69  00 

1.15 

/     // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

1.12 

/     // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

/      // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 

II 

1.08 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.123 
85 

0.113 
94 

0.107 
21 

0.096 
91 

0.089 
91 

0.082 
79 

0.075 
55 

0.068 
19 

0.060 
70 

0.049 
22 

0.041 
39 

0.033 
42 

Log. 

Limit 

67 

68 

69 

71 

72 

73 

74 

75 

76 

76 

77 

77 

Min- 
utes 

Merid- 
ian 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

Alti- 
tudes 

Latitude  37°  Decimation  ConttSLty  Name. 

Declinations.  —  Inferior  Meridian. 


225 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

" 
1.05 

0  17 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
// 

1.03 

1 

// 

// 

II 

// 

1 
II 

// 

1 
II 

// 

1 
II 

// 

II 

// 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

/     // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 

II 

0.81 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

liOg. 

0.021 
19 

0.012 

84 

9.919 
08 

9.908 
49 

Log. 

Limit 

78 

78 

80 

81 

Min- 
utes 

Merid- 
ian 

5° 

4^ 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

4 

8 

0  51 

0  50 

0  48 

0  47 

0  45 

0  43 

0  41 

0  39 

0  38 

0  37 

0  36 

0  35 

8 

12 

1  54 

151 

147 

145 

141 

1  38 

133 

129 

126 

124 

1  21 

1  18 

12 

16 

3  22 

3  17 

3  09 

3  07 

2  59 

2  54 

2  47 

2  39 

2  34 

2  28 

2  23 

2  18 

16 

20 

5  16 

5  08 

4  56 

4  52 

4  40 

4  32 

4  20 

4  08 

4  00 

3  52 

3  44 

3  36 

20 

24 

7  35 

7  23 

7  06 

7  00 

6  43 

6  32 

6  15 

5  58 

5  46 

5  32 

5  23 

5  11 

24 

28 

10  20 

10  04 

9  40 

9  33 

9  09 

8  53 

8  29 

8  06 

7  50 

7  35 

7  19 

7  03 

28 

32 

13  29 

13  09 

12  38 

12  28 

1157 

11  36 

11  05 

10  34 

10  14 

9  54 

9  33 

9  13 

32 

36 

17  04 

16  38 

15  59 

15  46 

15  07 

14  42 

14  03 

13  24 

12  58 

12  32 

12  06 

11  40 

36 

40 

2104 

20  32 

19  44 

19  28 

18  40 

18  08 

17  20 

16  32 

16  00 

15  28 

14  56 

14  24 

40 

44 

25  29 

24  51 

23  52 

23  33 

22  35 

21  57 

20  59 

20  01 

19  22 

18  43 

18  04 

17  25 

44 

48 

30  18 

29  32 

28  23 

28  00 

26  51 

26  08 

24  57 

23  48 

23  02 

22  16 

2130 

20  44 

48 

52 

35  36 

34  42 

33  21 

32  54 

3133 

30  38 

29  17 

27  56 

27  02 

26  08 

25  14 

24  20 

52 

56 

41  17 

40  15 

38  40 

38  09 

36  35 

35  33 

33  59 

32  25 

3122 

30  19 

29  16 

28  13 

56 

60 

47  24 

46  12 

44  24 

42  36 

42  00 

40  48 

39  00 

37  12 

36  00 

34  48 

33  36 

32  24 

60 

II 

" 

II 

II 

II 

II 

// 

II 

" 

II 

II 

Ajh 

0.79 

0.77 

0.75 

0.73 

0.70 

0.68 

0.65 

0.62 

0.60 

0.58 

0.56 

0.54 

A,h 

Log. 

9.897 

9.886 

9.875 

9.863 

9.845 

9.832 

9.812 

9.792 

9.778 

9.763 

9.748 

9.732 

Log. 

63 

49 

06 

32 

10 

51 

91 

39 

15 

43 

19 

39 

Limit 

82 

83 

84 

84 

85 

85 

86 

86 

86 

87 

87 

87 

Min- 
utes 

Merid- 
ian 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

Alti- 
tudes 

226 


Latitude  38°  Declination  Same  Name. 


Declinations. 


Hour 

Angles 

1    0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/     // 

Min. 

Min. 

4 

0  40 

0  41 

0  42 

0  43 

0  44 

0  45 

0  46 

0  47 

0  49 

0  51 

0  52 

0  54 

4 

8 

2  41 

2  45 

2  48 

2  52 

2  57 

3  01 

3  05 

3  10 

3  16 

3  21 

3  28 

3  34 

8 

12 

6  01 

6  10 

6  18 

6  27 

6  38 

6  47 

6  58 

7  10 

7  21 

7  33 

7  48 

8  02 

12 

16 

10  43 

10  58 

11  14 

11  29 

11  46 

12  05 

12  22 

12  42 

13  03 

13  27 

13  52 

14  18 

16 

20 

16  44 

17  08 

17  32 

17  56 

18  24 

18  52 

19  20 

19  52 

20  24 

2100 

21  40 

22  20 

20 

24 

24  06 

24  40 

25  15 

25  50 

26  30 

27  10 

27  50 

28  36 

29  23 

30  15 

31  12 

32  10 

24 

28 

32  48 

33  35 

34  22 

35  09 

36  04 

36  59 

37  54 

38  57 

39  59 

4109 

42  28 

43  46 

28 

32 

42  50 

43  52 

44  53 

45  54 

47  06 

48  18 

49  30 

50  52 

52  13 

53  45 

55  28 

57  10 

32 

36 

54  13 

55  31 

56  49 

58  07 

59  37 

61  08 

62  38 

64  22 

66  06 

68  03 

70  12 

72  22 

36 

40 

.66  56 

68  32 

70  08 

71  44 

73  36 

75  28 

77  20 

79  28 

8136 

84  00 

86  40 

89  20 

40 

44 

80  59 

82  56 

84  52 

86  48 

44 

48 

96  23 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

» 

Ajh 

2.51 

2.57 

2.63 

2.69 

2.76 

2.83 

2.90 

2.98 

3.06 

3.15 

3.25 

3.35 

Ajh 

Log. 

0.399 

0.409 

0.419 

0.429 

0.440 

0.451 

0.462 

0.474 

0.485 

0.498 

0.511 

0.525 

Log. 

67 

93 

96 

75 

91 

79 

40 

22 

72 

31 

88 

04 

Limit 

40 

40 

39 

39 

38 

37 

37 

36 

36 

35 

34 

33 

Min- 
utes 

Merid- 
ian 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/        n 

/     // 

t     11 

/     // 

/      II 

/      // 

/     II 

/      // 

/      // 

/      // 

1     It 

1       n 

Min. 

4 

0  55 

0  57 

0  59 

101 

103 

106 

109 

1  11 

1  15 

1  18 

1  23 

128 

4 

8 

3  41 

3  49 

3  56 

4  05 

4  14 

4  24 

4  35 

4  48 

5  01 

5  16 

5  33 

5  52 

8 

12 

8  17 

8  34 

8  51 

9  10 

9  32 

9  54 

10  19 

10  47 

11  17 

11  52 

12  29 

13  12 

12 

16 

14  43 

15  14 

15  45 

16  18 

16  56 

17  38 

18  21 

19  09 

20  03 

21  04 

22  11 

23  28 

16 

20 

23  00 

23  48 

24  36 

25  28 

26  28 

27  32 

28  40 

29  56 

3120 

32  56 

34  40 

36  40 

20 

24 

33  07 

34  16 

35  26 

36  41 

38  06 

39  39 

41  17 

43  05 

45  07 

47  25 

49  55 

52  48 

24 

28 

45  05 

46  39 

48  13 

49  55 

51  53 

53  58 

56  11 

58  41 

61  25 

64  33 

67  57 

71  52 

28 

32 

58  53 

60  56 

62  58 

65  11 

67  46 

70  29 

73  23 

76  38 

80  13 

32 

36 

74  31 

77  07 

79  43 

36 

40 

92  00 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

3.45 

3.57 

3.69 

3.82 

3.97 

4.13 

4.30 

4.49 

4.70 

4.94 

5.20 

5.50 

A,h 

Log. 

0.537 

0.552 

0.567 

0.582 

0.598 

0.615 

0.633 

0.652 

0.672 

0.693 

0.716 

0.740 

Log. 

82 

67 

03 

06 

79 

95 

47 

25 

10 

73 

00 

36 

Limit 

32 

31 

30 

30 

29 

28 

27 

26 

25 

24 

23 

22 

Min- 
utes 

Merid- 
ian 

64° 

65° 

66° 

67" 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

Alti- 
tudes 

Latitude  38°  Declination  Same  Name. 

Declinations. 


227 


Hour 

Angles 

24°  !   25° 

26° 

27° 

28° 

29°      30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
73^      20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

134 
6  14 
14  01 
24  55 
38  56 
56  04 
76  18 

5.84 

1' 

6 
14 
26 

dT 

59 
81 

6.2 

10 
39 
57 

i2 

25 

3 

1 

7 

16 

28 

^44 

64 

n 

6.6 

// 

17 
38 
33 
33 
36 
14 

3 

1 

7 
17 
30 

48 

II 
7.2 

// 

56 
13 
21 
51 
12 

3 

1 

1 
3 
5 

7 

2( 

8 

8. 

3 

2 

// 
.8 

// 

36 
24 
53 
35 

28 

1 

2 

9 

20 
36 
57 

8.6 

// 

19 
13 
15 
55 
10 

5 

2 
10 
23 
41 

9.6 

34 

16 
36 
36 

3 

2 
11 
26 
46 

II 
10.8 

58 
36 
37 
25 

3 

/     // 

3  21 
13  23 
30  07 

II 
12.55 

/     // 

3  58 
15  53 
35  44 

II 
14.89 

• 
/ 

// 

II 

// 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.766 
41 

0.794 
49 

0.825 
43 

0.859 
14 

0.895 
97 

0.937 
02 

0.983 
63 

1.036 
63 

1.098 
64 

1.172 
89 

Log. 

Limit 

21 

20 

18 

17 

16 

15 

14 

13 

12 

10 

8 

6 

Min- 
utes 

Merid- 
ian 

76° 

77° 

78° 

79^ 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

i    36° 

37° 

38 

=      39 

0      40O 

41 

°      42 

0        430 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/     II 

/ 

//    / 

//    /      // 

1 

//    / 

//     /       // 

/     II 

/     // 

/     // 

/     // 

Min. 

4 

3  27 

2  51 

2  23 

2  03 

149 

4 

8 

.      13  50 

11  21 

9  34 

8  14 

7  12 

8 

12 

31  10 

25  33 

2134 

18  32 

16  12 

12 

16 

45  27 

38  18 

32  56 

28  48 

16 

20 

45  00 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

Ajh 

12.98 

10.65 

8.98 

7.72 

6.75 

A,h 

Log. 

1.113 
27 

1.027 
35 

0.953 
29 

0.887 
62 

0.829 
30 

Log. 

Limit 

4 

2 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

Min- 
utes 

Merid- 
ian 

88° 

89° 

90° 

89° 

1   88° 

87° 

86= 

85° 

84°  1 

83° 

82° 

81° 

Alti- 
tudeg 

228 


Latitude  38°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

1 

6 
14 
25 
39 
57 

It 
5.9( 

// 

35 
21 
19 
25 
44 
13 

3 

1 
5 
12 
22 
35 
50 

II 
5.3 

25 
40 
44 
40 
24 
59 

I 

f 

1 
5 
11 
20 
31 
45 
62 

II 
4.7 

16 
06 
29 
23 
52 
53 
26 

1 

1 
4 
10 
18 
28 
41 
56 

II 
4.3 

// 

09 
37 
23 
29 
52 
34 
35 

3 

1 
4 
9 
16 
26 
37 
51 
67 

3.9 

03 
12 

28 
48 
16 
49 
29 
15 

i 

0 
3 
8 
15 
24 
34 
47 
61 

3.6 

// 

58 
50 
38 
22 
00 
34 
D2 
26 

3 

0 
3 
7 
14 
22 
31 
43 
56 
71 

II 
3.3 

// 

53 
31 
55 
05 
00 
41 
07 
19 
17 

0 

1 

0 
3 

7 
12 
20 
29 
39 
51 
65 

II 
3.0 

// 

49 
15 

18 
58 
16 

53 
10 

i 

/     // 

0  45 
2  59 
6  43 
1157 
18  40 
26  53 
36  35 
47  47 
60  29 
74  40 

II 
2.80 

/     // 

0  42 
2  46 
6  13 
1103 
17  16 
24  52 
"33  51 
44  12 
55  57 
69  04 

II 
2.59 

/     // 

0  38 
2  34 
5  46 
10  14 
16  00 
23  02 
31  22 
40  58 
5150 
64  00 
77  26 

2.40 

/     // 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

7138 

II 
2.22 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.775 
25 

0.725 
09 

0.679 
43 

0.636 
49 

0.595 
50 

0.556 
30 

0.518 
51 

0.482 
87 

0.447 
16 

0.413 
30 

0.380 
21 

0.346 
35 

Log. 

Limit 

20 

22 

23 

24 

26 

28 

29 

30 

32 

34 

36 

38 

Min- 
utes 

Merid- 
ian 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

/     /' 

/      // 

/     // 

/      // 

/     // 

/     // 

'      '> 

/     // 

/     // 

r       II 

/     // 

JNlin. 

4 

0  33 

0  30 

0  28 

0  27 

0  25 

0  23 

0  22 

0  20 

0  19 

0  17 

0  16 

0  14 

4 

8 

2  13 

2  02 

155 

146 

139 

133 

126 

120 

1  13 

109 

104 

0  58 

8 

12 

4  58 

4  37 

4  18 

3  59 

3  43 

3  24 

3  13 

2  59 

2  45 

2  36 

2  24 

2  13 

12 

16 

8  50 

811 

7  38 

7  05 

6  37 

6  06 

5  43 

5  17 

4  55 

4  36 

4  16 

3  55 

16 

20 

13  48 

12  48 

1156 

1104 

10  20 

9  32 

8  56 

8  16 

7  40 

7  12 

6  40 

6  08 

20 

24 

19  52 

18  26 

17  11 

15  57 

14  53 

13  43 

12  52 

11  54 

1103 

10  22 

9  36 

8  50 

24 

28 

27  03 

25  06 

23  24 

2141 

20  15 

18  42 

17  30 

16  12 

15  01 

14  07 

13  04 

12  02 

28 

32 

35  20 

32  46 

30  33 

28  19 

26  27 

24  25 

22  52 

21  10 

19  37 

18  26 

17  04 

15  42 

32 

36 

44  43 

41  28 

38  40 

35  52 

33  29 

30  53 

28  57 

26  47 

24  51 

23  20 

2136 

19  52 

36 

40 

55  12 

51  12 

47  44 

44  16 

41  20 

38  08 

35  44 

33  04 

30  40 

28  48 

26  40 

24  32 

40 

44 

66  48 

61  57 

57  45 

53  34 

50  01 

46  08 

43  14 

40  00 

37  07 

34  51 

32  16 

29  41 

44 

48 

79  29 

73  44 

68  42 

63  44 

59  31 

54  55 

51  27 

47  37 

44  09 

41  28 

38  24 

35  20 

48 

52 

86  32 

80  40 

74  48 

69  51 

64  27 

60  23 

55  53 

5149 

48  40 

45  04 

4128 

52 

56 

8101 

74  44 

70  02 

64  48 

60  07 

56  27 

52  16 

48  05 

56 

60 

84  24 

74  24 

69  00 

64  48 

60  00 

55  12 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

2.07 

1.92 

1.79 

1.66 

1.55 

1.43 

1.34 

1.24 

1.15 

1.08 

1.00 

0.92 

Ajh 

Log. 

0.315 

0.283 

0.252 

0.220 

0.190 

0.155 

0.127 

0.093 

0.060 

0.033 

0.00 

9.963 

Log. 

97 

30 

85 

11 

33 

34 

10 

42 

70 

42 

79 

Limit 

40 

42 

44 

46 

47 

48 

50 

52 

54 

56 

58 

60 

Min- 
utes 

Merid- 
ian 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

57° 

Alti- 
tudes 

Latitude  38"  Declination  Contrary  Name. 

229 

Declinations. 

Hour 
Angles 

0°    1    1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9°       10° 

11° 

Hour 
Angles 

Min. 

/        H  \  1        n     1        It 

/       n 

/     // 

/     II 

/     // 

/     // 

/       n 

1          H       1          II 

/      II 

Min. 

4 

0  40     0  39     0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  34 

0  33!     0  33 

0  32 

4 

8 

2  41      2  38     2  35     2  31 

2  28 

2  25 

2  22 

2  19 

2  16 

2  14 

2  11 

209 

8 

12 

6  01      5  55     5  47|     5  40 

5  32 

5  26 

5  20 

5  12 

5  06 

5  01 

4  55 

4  49      12 

16 

10  43    10  291  10  17    10  04 

9  52 

9  38 

9  28 

9  16 

9  06!     8  55 

8  45 

8  35      16 

20 

16  44    16  24'  16  04    15  44|  15  24 

15  04 

14  48    14  28    14  12    13  56 

13  40 

13  24[     20 

24 

24  06    23  37    23  08,  22  40    22  11 

21  42 

21  19    20  50    20  27    20  04    19  41 

19  18     24 

28 

32  48    32  09 

31  30l  30  50    30  10 

29  32 

29  01    28  21    27  50    27  19    26  47 

26  16     28 

32 

42  50   41  59 

41  08!  40  16!  39  25 

38  34 

37  53i  37  02    36  2r  35  40    34  59 

34  18     32 

36 

54  13    53  08    52  03!  50  59    49  54 

48  49 

47  57    46  53    46  01    45  09    44  17 

43  25,     36 

40 

66  56    65  36    64  16    62  56    61  36 

60  16 

59  12    57  52 

56  48   55  44,  54  40 

53  36!     ^'^ 

44 

80  59    79  22    77  45    76  09'  74  32 

72  55 

71  38!  70  02 

68  44    67  26    66  09 

64  51      44 

48 

96  23    94  28   92  33   90  37    88  42 

86  47 

85  15   83  19 

81  46|  80  15,  78  43 

77  11,     48 

52 

106  21  104  06 

10151 

100  03 

97  47   95  59 

94  11 

92  23 

90  35      52 

56 

. . . 

56 

60 

60 

// 

n 

n 

// 

" 

II 

// 

II 

//  ■ 

II 

II 

II 

Ajh 

2.51 

2.46 

2.41      2.36     2.31 

2.26 

2.22     2.17 

2.13 

2.09 

2.05 

2.01 

A,h 

I-og, 

0.399    0.390   0.382   0.372,  0.363 

0.354 

0.346    0.336 

0.328 

0.320    0.311 

20|        ^ 

67        94        02 

91 

61 

11 

35 

46 

38 

15 

75 

Limit 

40 

40    1    41 

42 

43 

43 

44 

45 

45 

46 

47 

48       ^^^'*" 
*°       utes 

Merid- 
ian 

52°  ;   51°      50°  !   49° 

48° 

47° 

46°  !   45° 

44° 

43°  1   42° 

41°  1  ^l*'' 
*-^      1  tudes 

Decx,inations. 

Hour 
Angles 

12°  1    13°      14° 

15° 

16° 

17° 

18°      19° 

20° 

21° 

22° 

rjQo    :  Hour 
^^       Angles 

aiin. 

'       n     1       t     r       I' 

/     // 

/     // 

/     // 

/     // 

/     II 

/     // 

/     // 

/     // 

'       "      Min. 

4 

0  31     0  31     0  30 

0  30 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

0  26        4 

'    8 

2  06     2  04     2  02 

2  00      1  58 

156 

154 

•   152 

150 

1  48      1  46 

144|       8 

12 

4  46     4  40     4  35 

4  29 

4  25 

4  20 

4  16 

4  11 

.  4  06 

4  03      3  59 

3  54      12 

16 

8-26     8  16:     8  09 

7  59 

7  51 

7  44 

7  33 

7  25 

7  18 

7  13     7  05 

6  58!     1^ 

20 

13  12    12  56    12  44    12  28 

12  16 

12  04 

1148 

1136 

11  24    11  16]  11  04 

10  52     20 

24 

19  00    18  37    18  20    17  57    17  40 

17  23 

16  59 

16  42'   16  25!  16  HJ  15  57 

15  39      24 

28 

25  53    25  21'  24  58!  24  26   24  02 

23  39 

23  08    22  44    22  21    22  Oo'  21  41 

21  18     28 

32 

33  48;  33  07    32  36    31  55    31  24 

30  53 

30  13!  29  42    29  11    28  50 

28  19 

27  49      32 

36 

42  46    41  54    41  15    40  24   39  45 

39  06 

38  14j  37  35    36  56    36  31 

35  52 

35  13      36 

40 

52  48    51  44   50  56    49  52    49  04 

48  16 

47  12    46  24:  45  36    45  04'  44  16 

43  28      40 

44 

63  53    62  35    61  37    60  21    59  22 

58  24 

57  07    56  08    55  lOj  54  32,  53  34 

52  36:     44 

48 

76  02    74  30    73  2l'  7148    70  39 

69  30 

67  56    66  47    65  38    64  53    63  44 

62  35      48 

52 

89  14,  87  26   86  05:  84  16    82  55 

8134 

79  46    78  25    77  04    76  09    74  48 

73  271     52 

56 

103  29 

101  23   99  49!  97  45   96  10 

94  36 

92  31    90  56    89  22:  88  20    86  46 

85  12      56 

60 

114  36  112  12  110  24 

108  36 

106  12  104  24  102  36  10124   99  36 

97  48      60 

// 

// 

n 

n 

II 

II 

// 

II 

II 

II 

II 

"      1 

A,h 

1.98 

1.94 

1.91 

1.87 

1.84 

1.81 

1.77 

1.74 

1.71 

1.69 

1.66 

1.63 

A,h 

Log. 

0.296    0.287   0.281 

0.271    0.264 

0.257 

0.247    0.240    0.233    0.227 

0.220 

0.212 

■      67        80        03 

84        82 

68 

97        55        00        89 

11 

19 1    ""^• 

Limit 

49    !    50        51 

51 

51 

52 

53 

54       54        54 

55 

56 

Min- 
utes 

Merid- 
ian 

40°  i"  39° 

38° 

37° 

36° 

35°. 

34°      33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

230 


Latitude  38°  Declination  Contrary  Name. 
Declinations. 


Hour 
Aiigles 

24°  1   25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Mill. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 

n 

1.60 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 
94  12 

1.57 

/     // 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

4104 

49  41 

59  08 

69  24 

80  29 

92  24 
II 

1.54 

/     // 

0  24 

1  37 
•3  39 

6  29 
10  08 
14  36 
19  52 
25  56 
32  50 
40  32 
49  03 
58  22 
68  30 
79  27 

91  12 

II 

1.52 

'     II 

0  23 

1  36 
3  35 
6  21 
9  56 

14  18 

19  29 

25  26 

32  11 

39  44 

48  04 

57  13 

67  09 

77  52 

89  24 
II 

1.49 

1     II 

0  23 

1  35 
3  32 
6  16 
9  48 

14  06 
19  13 
25  06 
31  45 
39  12 
47  26 
56  27 
66  15 
76  50 
88  12 

1.47 

1     II 

0  23 

1  33 
3  29 
6  11 
9  40 

13  55 
18  57 
24  45 
31  19 
38  40 
46  47 
55  41 
65  21 
75  47 

87  00 

II 

1.45 

0  22 

1  31 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30.40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
II 

1.42 

/     // 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

/     // 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
II 

1.37 

/      // 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

51  50 

60  58 

70  34 

8100 
II 

1.35 

'     II 

0  22 

1  25 
3  11 
5  41 
8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 
II 

1.33 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.204 
12 

0.195 
90 

0.187 
52 

0.181 
84 

0.173 
19 

0.167 
32 

0.161 
37 

0.152 
29 

0.146 
13 

0.136 

72 

0.130 
33 

0.123 

85 

Log. 

Limit 

57 

58 

59 

60 

61 

62 

62 

63 

64 

65 

66 

67 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
A  ngles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  21 

123 

3  07 

5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 

1.30 

/     // 

0  20 
122 
3  05 

5  27 

8  32 

12  17 

16  44 

'2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

/      // 

0  20 
121 
3  02 
5  22 

8  24 
12  06 
16  28 
21  30 
27  13 
33  36 
40  38 
48  23 
56  47 
65  51 

75  36 

II 

1.26 

0  20 

1  20 

2  59 
5  17 
8  16 

11  54 
16  12 
21  10 
26  47 
33  04 
40  00 
47  37 
55  53 
64  48 

74  24 

II 

1.24 

0  19 

1  18 

2  54 
5  10 
8  04 

11  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

II 

1.21 

/     // 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 
15  33 
20  18 
25  43 
31  44 
38  24 
45  41 
53  37 
62  12 

71  24 

II 

1.19 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

II 

1.17 

/      // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 
69  00 

1.15 

0  19 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 
67  48 

1.13. 

/     // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

1.11 

/      // 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 
14  07 
18  26 
23  20 
28  48 
34  51 
41  28 
48  40 
56  27 
64  48 

1.08 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,ll 

Log. 

0.113 
94 

0.107 
21 

0.100 
37 

0.093 
42 

0.082 
79 

0.075 
55 

0.068 
19 

0.060 
70 

0.053 
08 

0.045 
32 

0.033 
42 

0.025 
31 

Log. 

Limit 

67 

68 

69 

70 

72 

73 

74 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

16° 

15° 

14° 

13° 

12° 

IP  1 

10° 

9° 

go            70 

6°        5° 

Alti- 
tude! 

Latitude  38°  Declination  Contrary  Name. 
Declinations.  — Inferior  Meridian 


231 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Anglos 

Mill. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

/ 

// 

/ 
/ 

// 

t 

n 

// 

1/ 

/ 

// 

/ 

// 

// 

1 

w 

r 

II 

/ 

// 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 
50  24 

0.84 

1     If 

0  13 
0  52 
158 
3  30 

5  28 
7  53 
10  43 
13  59 
17  43 
21  52 
26  28 
31  29 
36  57 
42  52 
49  12 

0.82 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
41  49 

48  00 

II 

0.80 

Mln. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.924 

28 

9.913 
81 

9.903 
09 

Log. 

Limit 

78 

79 

81 

Min- 
utes 

Merid- 
ian 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

40 

5° 

6° 

70 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

/     // 

0  12 

0  49 

150 

-   3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  44 

45  36 
II 

0.76 

/     // 

0  12 

0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 

0.74 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 
43  12 

0.72 

1     II 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

1146 

14  55 

18  24 

22  16 

26  29 

3105 

36  04 

41  24 

II 

0.69 

/     // 

Oil 

0  43 

1  36 

2  52 
4  28 
6  26 
8  45 

1126 
14  29 
17  52 
2138 
25  43 
30  11 
35  02 
40  12 

0.67 

/     // 

Oil 

0  41 

133 

2  47 

4  20 

6  15 

8  29 

1105 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 

II 

0.65 

0  10 
0  39 
129 
2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 

37  12 

II 

0.62 

t     II 

0  10 

0  28 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 
12  58 
16  00 
19  22 
23  02 
27  02 
3122 
36  00 

0.60 

/     // 

0  09 

0  37 

1  24 

2  28 

3  52 
5  32 
7  35 
9  54 

12  32 
15  28 
18  43 
22  16 
26  08 
30  19 
34  48 

0.58 

/     // 

0  09 

0  36 

1  21 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
2130 
25  14 
29  16 
33  36 

0.56 

/     // 

0  09 

0  35 

1  18 

2  18 

3  36 
5  11 
7  03 
9  13 

11  40 
14  24 
17  25 
20  44 
24  20 
28  13 

32  24 

II 

0.54 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.892 
09 

9.880 
81 

9.869 
23 

9.857 
33 

9.838 
85 

9.826 
07 

9.812 
91 

9.792 
39 

9.778 
15 

9.763 
43 

9.748 
19 

9.732 
39 

Log. 

Limit 

82 

83 

83 

84 

84 

85 

85 

85 

86 

86 

87 

88 

Min- 
utes 

Merid- 
ian 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

Alti-j 
tudes 

232 


Latitude  39**  Declination  Same  Namc« 


Declinations. 


Hour 
Angles 

0" 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      II 

0  38 
2  35 
5  49 
10  19 
16  08 
23  14 
31  38 
41  18 
52  16 
64  32 
78  05 
92  56 

2.42 

/       u 

0  39 
2  39 
5  58 
10  34 
16  32 
23  48 
32  25 
42  20 
53  34 
66  08 
80  01 
95  14 

II 
2.48 

/     // 

0  40 
2  42 
6  04 
10  48 
16  52 
24  17 
33  04 
43  11 
54  39 
67  28 
8138 

2.53 

/     // 

0  41 
2  46 
6  13 
11  03 
17  16 
24  52 
33  51 
44  12 
55  57 
69  04 
83  34 

II 
2.59 

0  43 
2  49 
6  21 
11  19 
17  40 
25  27 
34  37 
45  13 
57  15 
70  40 
85  31 

II 
2.65 

/     // 

0  43 
2  54 
6  32 
11  36 
18  08 
26  07 
35  33 
46  25 
58  45 
72  32 
87  46 

2.72 

0' 
2. 
6' 

11. 

18 

26 

36 

47 

60 

74 

II 
2.7 

n 

i4 
39 
12 
54 
36 
17 
28 
Yl 
16 
24 

5 

1 

1 
1 
2 
3 
4 
6 
7 

2 

0' 
3( 
6. 

2 

9( 

1  . 

1  . 

8 

1 

6 

// 

.8 

n 

16 
)3 
52 
12 
)4 
28 
22 
18 
17 
16 

5 

/ 

1 
1 
2 

3 
5 
6 

7 

2 

0^ 

3( 

7( 

2. 

9. 

8( 

8 

0( 

3 

8( 

// 
.9 

II 

16 

)7 
)2 
50 
32 
)7 
18 
31 
17 
)8 

3 

/     II 

0  48 
3  13 
7  13 
12  51 
20  04 
28  54 
39  20 
51  22 
65  01 
80  16 

3.01 

0  50 
3  18 
7  26 
13  14 
20  40 
29  46 
40  30 
52  54 
66  58 
82  40 

II 
3.10 

0  51 
3  24 
7  39 
13  37 
21  16 
30  38 
41  41 
54  26 
68  55 
85  04 

II 
3.19 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.383 
82 

0.394 
45 

0.403 
12 

0.413 
30 

0.423 
25 

0.434 
57 

0.445 
60 

0.456 
37 

0.466 
87 

0.478 
57 

0.491 
36 

0.503 
79 

Log. 

Limit 

41 

41 

40 

39 

39 

38 

38 

37 

36 

36 

35 

34 

Min- 
utes 

Merid- 
ian 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

1     II 

1     II 

1     II 

/     II 

1      II 

/      // 

1     II 

1     II 

Min. 

Min. 

4 

0  52 

0  54 

0  56 

0  58 

100 

102 

105 

107 

1  10 

1  14 

1  18 

122 

4 

8 

3  31 

3  37 

3  44 

3  51 

4  00 

4  09 

4  19 

4  30 

4  42 

4  55 

5  10 

5  26 

8 

12 

7  54 

8  08 

8  24 

8  41 

9  00 

9  22 

9  43 

10  08 

10  34 

1103 

11  37 

12  14 

12 

16 

14  02 

14  z8 

14  56 

15  27 

16  00 

16  38 

17  17 

18  00 

18  46 

19  41 

20  39 

21  46 

16 

20 

21  56 

22  36 

23  20 

24  08 

25  00 

26  00 

27  00 

28  08 

29  20 

30  44 

32  16 

34  00 

20 

24 

31  35 

32  33 

33  36 

34  46 

36  00 

37  26 

38  53 

40  31 

42  14 

44  16 

46  28 

48  58 

24 

28 

43  00 

44  18 

45  44 

47  18 

49  00 

50  58 

52  55 

55  09 

57  30 

60  14 

63  14 

66  38 

28 

32 

56  09 

57  51 

59  44 

61  46 

64  00 

66  34 

69  07 

72  01 

75  06 

78  40 

82  36 

32 

36 

7104 

73  14 

75  36 

78  12 

36 

40 

87  44 

90  24 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

A,h 

3.29 

3.39 

3.50 

3.62 

3.75 

3.90 

4.05 

4.22 

4.40 

4.61 

4.84 

5.10 

Ajh 

Log. 

0.517 

0.530 

0.544 

0.558 

0.574 

0.591 

0.607 

0.625 

0.643 

0.663 

0.684 

0.707 

Log. 

20 

20 

07 

71 

03 

06 

46 

31 

45 

70 

85 

57 
24 

Limit 

33 

32 

31 

31 

31 

30 

29 

28 

27 

26 

25 

Min- 
utes 

Merid- 
ian 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

Alti- 
tudes 

Latitude  39°  Declination  Same  Name. 

Declinations. 


233 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angle* 

Mia. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

5 
12 
23 
35 
51 
70 

5.3 

26 
46 
56 
00 
56 
45 
26 

9 

1 

1. 

6( 
13^ 
24! 
38  ( 
54. 

5.7 

// 

U 
)6 
14 
24 
)8 
55 

2 

/ 

1     V 

6; 

14. 
26  ( 
40' 

58. 

6.1 

J8 
JO 
}8 
)2 
10 
54 

0 

1 

1  ^ 
6. 

15' 

27. 

43. 

62' 

6.5 

15 
)9 
12 
54 
J6 
17 

4 

1  . 

7; 

16. 
30  { 
47  ( 

// 
7.0 

53 
}2 
57 
)7 
)4 

5 

2( 

8 

18  i 
32' 
51 

11 
7.6 

)3 
2 

27 
19 
16 

3 

1 

2 

9( 
20 
36  ( 
56  i 

II 
8.4 

5 
)1 
17 
)3 
JO 

5 

2; 

10  ( 
22; 
40  ( 

II 
9.4 

II 

50 
)2 
$4 
)6 

3 

I  II 

2  50 

II  19 
25  29 
45  19 

10.62 

/      // 

3  16 
13  04 
29  23 

II 
12.24 

/     // 

3  52 
15  29 
34  49 

II 
14.51 

II 

II 

Min, 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.731 
59 

0.757 
40 

0.785 
33 

0.815 

58 

0.848 
80 

0.885 
93 

0.926 
86 

0.973 
13 

1.026 
12 

1.087 

78 

1.161 
67 

Log. 

Limit 

23 

21 

20 

19 

18 

17 

16 

15 

14 

12 

10 

8 

Min- 
utes 

Merid- 
ian 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/ 

1 

// 

II 

// 

1 

1 

// 

1 

1 

// 

1 

II 

II 

// 

1 
II 

// 

1 

3 
13 
30 

12.5{ 

// 

21 
26 
13 

) 

/ 
2 
11 
24 
44 

10.3i 

45 
OO 
i6 
D2 

I 

/ 
2 
9 

20 
37 

II 
8 

// 

19 
17 
53 
07 

?0 

/ 

1 

7 

17 

31 

49 

II 
7.4 

59 
59 
56 
52 

48 

1 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.100 
03 

1.013 
68 

0.939 
52 

0.873 
32 

Log. 

Limit 

6 

4 

2 

0 

2 

4 

6 

8 

10 

12 

14 

16 

Min- 
utes 

Merid- 
ian 

87° 

88° 

89° 

90° 

89^ 

88° 

87° 

86° 

85° 

84° 

83' 

82° 

Alti- 
tudes 

234 


Latitude  39°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/  // 

/  " 

/  /' 

/  n 

/  // 

1     II 

/  // 

1     II 

/  // 

/  // 

Min. 

Min. 

4 

144 

132 

123 

1  14 

107 

101 

0  55 

0  51 

0  46 

0  43 

0  39  0  37 

4 

8 

6  57 

6  09 

5  29 

4  55 

4  27 

4  03 

3  42 

3  23 

3  06 

2  52 

2  39  2  27 

8 

12 

15  39 

13  50 

12  20 

1105 

10  02 

9  07 

8  20 

7  38 

7  01 

6  27 

5  58  5  31 

12 

16 

27  49 

24  34 

2156 

19  43 

17  50 

16  13 

14  48 

13  34 

12  27 

1129 

10  34  9  49 

16 

20 

43  38 

38  24 

34  16 

30  48 

27  52 

25  20 

23  08 

21  12 

19  28 

17  56 

16  32  15  20 

20 

24 

62  36 

55  18 

49  21 

44  22 

40  08 

36  29 

33  18 

30  32 

28  02 

25  50 

23  48  22  05 

24 

28 

60  22 

54  37 

49  39 

45  21 

41  33 

38  10 

35  09 

32  25  30  03 

28 

32 

64  51 

59  14 

54  16 

49  50 

45  54 

42  20  39  15 

32 

36 

68  42 

63  04 

58  07 

53  34  49  41 

36 

40 

7144 

66  08 

61  20 

40 

44 

80  01 

74  13 

44 

48 

48 

52 

52 

56 

56 

60 

60 

i> 

11 

n 

II 

II 

It 

// 

II 

II 

II 

// 

II 

Ajh 

6.52 

5.76 

5.14 

4.62 

4.18 

3.80 

3.47 

3.18 

2.92 

2.69 

2.48 

2.30 

A,h 

0.814 

0.760 

0.710 

0.664 

0.621 

0.579 

0.540 

0.502 

0.465 

0.429 

0.394 

0.361 

Log. 

Log. 

25 

42 

96 

64 

18 

78 

33 

43 

38 

75 

45 

73 

Limit 

18 

20 

21 

22 

24 

26 

28 

29 

31 

33 

35 

37 

Min- 
utes 

Merid- 
ian 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

/  // 
0  19 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 

/   // 
0  34 

/  // 
0  31 

1     II 
0  30 

/  // 
0  27 

0  25 

/  // 
0  23 

0  22 

1     II 
0  20 

t     II 
0  17 

0  16 

/  // 
0  14 

Min. 
4 

8 

2  16 

2  06 

1  57 

149 

141 

135 

128 

121 

1  15 

1  10 

1  05 

0  59 

8 

12 

5  06 

4  44 

4  23 

4  05 

3  48 

3  32 

3  17 

3  02 

2  48 

2  37 

2  25 

2  14 

12 

16 

9  06 

8  24 

7  49 

7  15 

6  44 

6  16 

5  51 

5  22 

5  00 

4  39 

4  19 

3  58 

16 

20 

14  12 

13  08 

12  12 

1120 

10  32 

9  48 

9  08 

8  24 

7  48 

7  16 

6  44 

6  12 

20 

24 

20  27 

18  44 

17  34 

16  19 

15  10 

14  06 

13  09 

12  06 

11  14 

10  28 

9  42 

8  55 

24 

28 

27  50 

25  45 

23  55 

22  13 

20  39 

19  13 

17  54 

16  28 

15  17 

14  15 

13  12 

12  10 

28 

32 

36  21 

33  38 

31  14 

29  01 

26  58 

25  06 

23  23 

21  30 

19  58 

18  36 

17  14 

15  53 

32 

36 

46  01 

42  33 

39  32 

36  43 

34  08 

3145 

29  36 

27  13 

25  17 

23  33 

21  49 

20  05 

36 

40 

56  48 

52  32 

48  48 

45  20 

42  08 

39  12 

36  32 

33  36 

31  12 

29  04 

26  56 

24  48 

40 

44 

68  44 

63  34 

59  03 

54  51 

50  59 

47  26 

44  13*  40  39 

37  46 

35  10 

32  35 

30  00 

44 

48 

75  39 

70  16 

65  15 

60  40 

56  27 

52  36 

48  23 

44  55 

41  51 

38  47 

35  43 

48 

52 

82  28 

76  37 

71  12 

66  15 

6144 

56  47 

52  43 

49  07 

45  31 

41  55 

52 

56 

88  51 

82  35 

76  50 

7137 

65  51 

61  10 

56  58 

52  47 

48  36 

56 

60 

82  12 

75  36 

70  12 

65  24 

60  36 

55  48 

60 

II 

II 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

A,h 

2.13 

1.97 

1.83 

1.70 

1.58 

1.47 

1.37 

1.26 

1.17 

1.09 

1.01 

0.93 

A,h 

0.328 

0.294 

0.262 

0.230 

0.198 

0.167 

0.136 

0.100 

0.068 

0.037 

0.004 

9.968 

Log. 

Log. 

38 

47 

45 

45 

66 

32 

72 

37 

19 

43 

32 

48 

Limit 

39 

41 

43 

45 

47 

48 

49 

51 

53 

55 

57 

59 

]\Iin- 
utes 

Merid- 
ian 

69° 

68°' 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

58° 

Alti- 
tudes 

Latitude  39°  Declination  Contrary  Name. 


235 


Decuxations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

/       // 

/     // 

/     // 

/     // 

/      // 

/      // 

/     // 

/     // 

r       II 

/     // 

/     // 

/     // 

Min. 

4 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  35 

0  34 

0  33 

0  32 

0  31 

0  31 

4 

8 

2  35 

2  32 

2  28 

2  26 

2  23 

2  20 

2  17 

2  15 

2  13 

2  10 

2  07 

2  05 

8 

12 

5  49 

5  41 

5  34 

5  29 

5  21 

5  15 

5  09 

5  03 

4  58 

4  52 

4  47 

4  43 

12 

16 

10  19 

10  07 

9  54 

9  43 

9  31 

9  21 

9  11 

9  01 

8  50 

8  40 

8  29 

8  21 

16 

20 

16  08 

15  48 

15  28 

15  12 

14  52 

14  36 

14  20 

14  04 

13  48 

13  32 

13  16 

13  04 

20 

24 

23  14 

22  45 

22  17 

2153 

2124 

2102 

20  39 

20  16 

19  52 

19  29 

19  06 

18  49 

24 

28 

3138 

30  58 

30  19 

29  48 

29  09 

28  37 

28  05 

27  34 

27  03 

26  32 

26  01 

25  37 

28 

32 

41  18 

40  27 

39  35 

38  55 

38  04 

37  22 

36  41 

36  00 

35  20 

34  39 

33  58 

33  27 

32 

36 

52  16 

51  12 

50  07 

49  15 

48  10 

47  19 

46  27 

45  35 

44  43 

43  51 

42  59 

42  20 

36 

40 

64  32 

63  12 

61  52 

60  48 

59  28 

58  24 

57  20 

56  16 

55  12 

54  08 

53  04 

52  16 

40 

44 

78  05 

76  39 

74  52 

73  34 

7157 

70  40 

69  23 

68  05 

66  48 

65  30 

64  12 

63  14 

44 

48 

92  56 

9100 

89  05 

87  33 

85  38 

84  05 

82  33 

81  01 

79  29 

77  57 

76  25 

75  16 

48 

52 

106  48 

104  33 

102  45 

100  30 

98  41 

96  53 

95  05 

93  17 

9129 

89  41 

88  20 

52 

56 

56 

60 

60 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.42 

2.37 

2.32 

2.28 

2.23 

2.19 

2.15 

2.11 

2.07 

2.03 

1.99 

1.96 

A,h 

Log. 

0.383 

0.374 

0.365 

0.357 

0.348 

0.340 

0.332 

0.324 

0.315 

0.307 

0.298 

0.292 

Log. 

82 

75 

49 

93 

30 

44 

44 

28 

97 

50 

85 

26 

Limit 

41 

41 

42 

43 

44 

45 

45 

46 

46 

47 

48 

48 

Min- 
utes 

Merid- 
ian 

51° 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      /' 

/     // 

/     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  30 

0  30 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

0  27 

0  26 

0  25 

4 

8 

2  02 

2  01 

158 

156 

1  55 

153 

151 

1  49 

147 

145 

1  43 

1  42 

8 

12 

4  37 

4  32 

4  26 

4  22 

4  18 

4  14 

4  09 

■  4  05 

4  00 

3  56 

3  53 

3  49 

12 

16 

8  11 

8  04 

7  54 

7  46 

7  38 

7  30 

7  23 

7  15 

7  08 

7  00 

6  55 

6  47 

16 

20 

12  48 

12  36 

12  20 

12  08 

1156 

1144 

1132 

11  20 

11  08 

10  56 

10  48 

10  36 

20 

24 

18  26 

18  09 

17  46 

17  29 

17  11 

16  54 

16  36 

16  19 

16  02 

15  45 

15  34 

15  16 

24 

28 

25  06 

24  42 

24  10 

23  47 

23  24 

23  00 

22  37 

22  13 

21  49 

2125 

21  10 

20  47 

28 

32 

32  46 

32  15 

3134 

3103 

30  33 

30  02 

29  32 

29  01 

28  30 

27  59 

27  38 

27  08 

32 

36 

41  28 

40  50 

39  58 

39  19 

38  40 

38  01 

37  22 

36  43 

36  05 

35  26 

35  00 

34  21 

36 

40 

51  12 

50  24 

49  20 

48  32 

47  44 

46  56 

46  08 

45  20 

44  32 

43  44 

43  12 

42  24 

40 

44 

61  57 

60  59 

59  42 

58  44 

57  45 

56  47 

55  49 

54  51 

53  54 

52  55 

52  17 

51  18 

44 

48 

73  44 

72  34 

7102 

69  53 

68  42 

67  33 

66  24 

65  15 

64  07 

62  58 

62  12 

6103 

48 

52 

86  32 

85  10 

83  22 

82  01 

80  40 

79  19 

77  58 

76  37 

75  15 

73  54 

73  00 

71  39 

52 

56 

100  21 

98  47 

96  42 

95  08 

93  33 

9159 

90  25 

88  51 

87  18 

85  43 

84  41 

83  06 

56 

60 

113  24 

11100 

109  12 

107  24 

105  36 

103  48 

102  00 

100  12 

98  24 

97  12 

95  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.92 

1.89 

1.85 

1.82 

1.79 

1.76 

1.73 

1.70 

1.67 

1.64 

1.62 

1.59 

A,h 

Log. 

0.283 

0.276 

0.267 

0.260 

0.252 

0.245 

0.238 

0.230 

0.222 

0.214 

0.209 

0.201 

Log. 

30 

46 

17 

07 

85 

51 

05 

45 

72 

84 

52 

40 

Limit 

49 

50 

51 

52 

52 

53 

54 

55 

55 

56 

57 

58 

Min- 
utes 

Merid- 
ian 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

Alti- 
tudes 

236 


Latitude  39°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

/       // 

/     It 

/      // 

1     II 

/     // 

/     // 

/     // 

/     // 

/       n 

/     // 

/     // 

/      II 

Min. 

4 

0  25 

0  25 

0  24 

0  23 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

4 

8 

140 

138 

137 

1  36 

134 

133 

131 

1  29 

1  28 

126 

125 

1  23 

8 

12 

3  45 

3  40 

3  37 

3  35 

3  31 

3  28 

3  25 

3  20 

3  17 

3  14 

3  11 

3  07 

12 

16 

6  39 

6  32 

6  27 

6  21 

6  13 

6  08 

6  03 

5  56 

5  51 

5  46 

5  41 

5  33 

16 

20 

10  24 

10  12 

10  04 

9  56 

9  44 

9  36 

9  28 

9  16 

9  08 

9  00 

8  52 

8  40 

20 

24 

14  59 

14  41 

14  30 

14  18 

14  01 

13  49 

13  38 

13  21 

13  09 

12  58 

12  46 

12  29 

24 

28 

20  23 

20  00 

19  44 

19  29 

19  05 

18  49 

18  34 

18  10 

17  54 

17  38 

17  23 

16  59 

28 

32 

26  37 

26  07 

25  46 

25  26 

24  55 

24  35 

24  14 

23  43 

23  23 

23  02 

22  42 

22  11 

32 

36 

33  42 

33  03 

32  37 

32  11 

3132 

3106 

30  40 

30  02 

29  36 

29  10 

28  44 

28  05 

36 

40 

4136 

40  48 

40  16 

39.44 

38  56 

38  24 

32  52 

37  04 

36  32 

36  00 

35  28 

34  40 

40 

44 

50  20 

49  22 

48  43 

48  04 

47  06 

46  27 

45  49 

44  51 

44  13 

43  34 

42  55 

4157 

44 

48 

59  54 

58  45 

57  59 

57  13 

56  04 

55  18 

54  32 

53  22 

52  36 

5150 

5104 

49  55 

48 

52 

70  18 

68  57 

68  03 

67  09 

65  48 

64  54 

64  00 

62  38 

61  44 

60  50 

59  56 

58  35 

52 

56 

8132 

79  58 

78  55 

77  52 

76  18 

75  15 

74  13 

72  39 

7137 

70  34 

69  31 

67  57 

56 

60 

93  36 

9148 

90  36 

89  24 

87  36 

86  24 

85  12 

83  24 

82  12 

8100 

79  48 

78  00 

60 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.56 

1.53 

1.51 

1.49 

1.46 

1.44 

1.42 

1.39 

1.37 

1.35 

1.33 

1.30 

Aih 

0.193 

0.184 

0.178 

0.173 

0.164 

0.158 

0.152 

0.143 

0.136 

0.130 

0.123 

0.113 

Log. 

12 

69 

98 

19 

35 

36 

29 

01 

72 

33 

85 

94 

Limit 

59 

59 

59 

60 

61 

62 

63 

63 

64 

65 

66 

67 

Min- 
utes 

Merid- 
ian 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

1     II 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

2130 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 

II 

1.26 

1     II 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

/     // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

/      // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

3144 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

/      // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

/     // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 
69  00 

1.15 

0  19 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

/     // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 
65  24 

n 

1.09 

/     // 

0  17 

109 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
II 

1.07 

II 

// 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.107 
21 

0.100 
37 

0.089 
91 

0.082 
79 

0.075 
55 

0.068 
19 

0.060 
70 

0.053 
08 

0.045 
32 

0.037 
43 

0.029 
38 

Log. 

Limit 

68 

69 

70 

71 

73 

74 

75 

76 

77 

77 

77 

Min- 
utes 

Merid- 
ian 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

Alti- 
tudes 

Latitude  39°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


237 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

1 

n 

/ 

// 

// 

// 

/ 

// 

// 

II 

ti 

II 

n 

f 

II 

// 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

51  36 
II 

0.86 

/     // 

0  14 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 
14  10 
17  56 
22  08 
26  47 
31  52 
37  24 
43  23 
49  48 

0.83 

/     // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

31  06 

36  30 

42  20 

48  36 
II 

0.81 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.934 
50 

9.919 
08 

9.908 
49 

9.897 
63 

Log. 

Limit 

76 

78 

79 

81 

Min- 
utes 

Merid- 
ian 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

Alti- 
tudes 

Declinations 

).  —  Inferior  Meridian. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64°  !    65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/      /' 

/     // 

/     // 

/      //    /     // 

/     // 

/      // 

/      // 

/     // 

/     // 

/     // 

Min. 

4 

0  12 

0  12 

0  12 

Oil 

Oil      Oil 

Oil 

0  10 

0  09 

0  09 

0  09 

0  09 

4 

8 

0  50 

0  49 

0  47 

0  46 

0  44;     0  42 

0  41 

0  39 

0  38 

0  37 

0  35 

0  34 

8 

12 

151 

150 

145 

142 

1  39 

135 

132 

127 

125 

122 

1  19 

1  16 

12 

16 

3  17 

3  14 

3  07 

3  02 

2  57 

2  49 

2  44 

2  37 

2  31 

2  26 

2  21 

2  16 

16 

20 

5  08 

5  04 

4  52 

4  44 

4  36 

4  24 

4  16 

4  04 

3  56 

3  48 

3  40 

3  32 

20 

24 

7  23 

7  18 

7  00 

6  49 

6  38 

6  21 

6  09 

5  52 

5  40 

5  28 

5  17 

5  05 

24 

28 

10  04 

9  56 

9  33 

9  17 

9  01 

8  37 

8  21 

7  58 

7  43 

7  27 

7  11 

6  56 

28 

32 

13  09 

12  58 

12  28 

12  07 

1146 

11  15 

10  55 

10  24 

10  04 

9  44 

9  23 

9  03 

32 

36 

16  38 

16  25 

15  46 

15  20 

14  55 

14  16 

13  50 

13  11 

12  45 

12  19 

1153 

11  27 

36 

40 

20  32 

20  16 

19  28 

18  56 

18  24 

17  36 

17  04 

16  16 

15  44 

15  12 

14  40 

14  08 

40 

44 

24  51 

24  31 

23  33 

22  54 

22  16 

21  18 

20  39 

19  41 

19  02 

18  24 

17  45 

17  06 

44 

48 

29  32 

29  09 

28  00 

27  14 

26  29,  25  20 

24  34 

23  25 

22  39 

2153 

2107 

20  21 

48 

52 

34  42 

34  15 

32  54 

32  00 

31  05 

29  44 

28  50 

27  29 

26  35 

25  41 

24  47 

23  53 

52 

56 

40  15 

39  44 

38  09 

37  06 

36  04 

34  30 

33  27 

31  53 

30  50 

29  48 

28  45 

27  42 

56 

60 

46  12 

45  36 

43  48 

42  36 

41  24 

39  36 

38  24 

36  36 

35  24 

34  12 

33  00 

3148 

60 

II 

" 

// 

" 

II 

II 

II 

II 

II 

» 

II 

II 

A,h 

^ni 

0.76 

0.73 

0.71 

0.69 

0.66 

0.64 

0.61 

0.59 

0.57 

0.55 

0.53 

Ajh 

Log. 

9.886 

9.880 

9.863 

9.851 

9.838 

9.819 

9.806 

9.785 

9.770 

9.755 

9.740 

9.724 

49 

81 

32 

26 

85!        54 

18 

33 

85 

87 

36 

28 

Log. 

Limit 

82 

83 

83 

84 

84 

85 

85 

85 

86 

86 

87 

87 

Min- 
utes 

Merid- 
ian 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

Alti- 
tudes 

238 


Latitude  40°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       // 

1      II 

/     // 

/      // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     II 

/     // 

/     // 

Min. 

4 

0  38 

0  38 

0  39 

0  40 

0  41 

0  42 

0  43 

0  44 

0  45 

0  46 

0  47 

0  49 

4 

8 

2  30 

2  33 

2  37 

2  40 

2  43 

2  47 

2  51 

2  56 

3  00 

3  04 

3  09 

3  15 

8 

12 

5  37 

5  44 

5  52 

6  00 

6  07 

6  15 

6  26 

6  35 

6  44 

6  55 

7  07 

7  19 

12 

16 

9  59 

10  12 

10  24 

10  40 

10  53 

11  09 

1126 

11  41 

12  00 

12  17 

12  37 

13  01 

16 

20 

15  36 

15  56 

16  16 

16  40 

17  00 

17  24 

17  52 

18  16 

18  44 

19  12 

19  44 

20  20 

20 

24 

22  28 

22  57 

23  25 

24  00 

24  29 

25  04 

25  44 

26  18 

26  59 

27  39 

28  25 

29  17 

24 

28 

30  34 

31  14 

31  53 

32  40 

33  19 

34  06 

35  01 

35  48 

36  43 

37  38 

38  41 

39  51 

28 

32 

39  56 

40  47 

41  39 

42  40 

43  31 

44  32 

45  44 

46  46 

47  57 

49  09 

50  31 

52  03 

32 

36 

50  33 

51  38 

52  42 

54  00 

55  05 

56  23 

57  54 

59  11 

60  42 

62  13 

63  56 

65  53 

36 

40 

62  24 

63  44 

65  04 

66  40 

68  00 

69  36 

71  28 

73  04 

74  56 

76  48 

78  56 

81  20 

40 

44 

75  30 

77  07 

78  43 

80  40 

82  17 

84  13 

86  29 

88  24 

44 

48 

89  51 

91  46 

93  42 

96  00 

48 

52 

105  27 

107  42 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

" 

Ajh 

2.34 

2.39 

2.44 

2.50 

2.55 

2.61 

2.68 

2.74 

2.81 

2.88 

2.96 

3.05 

A,h 

Log. 

0.369 

0.378 

0.387 

0.397 

0.406 

0.416 

0.428 

0.437 

0.448 

0.459 

0.471 

0.484 

Log. 

22 

40 

39 

94 

54 

64 

13 

75 

71 

39 

29 

30 

Limit 

42 

42 

41 

41 

40 

39 

39 

38 

37 

37 

36 

35 

Min- 
utes 

Merid- 
ian 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/      // 

/      // 

Min. 

Min. 

4 

0  50 

0  51 

0  53 

0  55 

0  57 

0  59 

101 

103 

106 

109 

1  12 

1  16 

4 

8 

3  20 

3  27 

3  33 

3  41 

3  47 

3  55 

4  05 

4  14 

4  24 

4  36 

4  49 

5  04 

8 

12 

7  30 

7  45 

7  59 

8  16 

8  31 

8  50 

9  11 

9  32 

9  54 

10  20 

10  49 

11  23 

12 

16 

13  22 

13  47 

14  13 

14  40 

15  09 

15  42 

16  18 

16  56 

17  38 

18  24 

19  15 

20  13 

16 

20 

20  52 

2132 

22  12 

22  56 

23  40 

24  32 

25  28 

26  28 

27  32 

28  44 

30  04 

3136 

20 

24 

30  03 

31  00 

31  58 

33  01 

34  05 

35  20 

36  41 

38  06 

39  39 

4123 

43  18 

45  30 

24 

28 

40  54 

42  13 

43  31 

44  57 

46  23 

48  05 

49  55 

51  53 

53  58 

56  19 

58  56 

6154 

28 

32 

53  25 

55  08 

56  50 

58  43 

60  35 

62  48 

65  11 

67  46 

70  29 

73  33 

76  58 

80  54 

32 

36 

67  37 

69  46 

7156 

74  18 

76  41 

79  30 

36 

40 

83  28 

86  08 

88  48 

91  44 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

// 

II 

" 

II 

II 

II 

II 

II 

A,h 

3.13 

3.23 

3.33 

3.44 

3.55 

3.68 

3.82 

3.97 

4.13 

4.31 

4.51 

4.74 

A,h 

Log. 

0.495 

0.509 

0.522 

0.536 

0.550 

0.565 

0.582 

0.598 

0.615 

0.634 

0.654 

0.675 

Log. 

54 

20 

44 

56 

23 

85 

06 

79 

95 

48 

18 

78 

Limit 

34 

33 

32 

32 

32 

31 

30 

29 

28 

27 

26 

25 

Min- 
utes 

Merid- 
ian 

62°  1   63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

Alti- 
tudes 

Latitude  40°  Declination  Same  Name. 


239 


Declinations. 


Hoar 
Angles 

24° 

25° 

26° 

27°      28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      // 

1  19 
5  19 
1159 
21  17 
33  16 
47  54 
65  11 

4.99 

1 

5 
12 
22 
35 
50 
68 

// 
5.2' 

// 

24 

38 
39 
29 
08 
35 
52 

I 

1 

5 
13 
23 
37 
53 
73 

// 
5.5c 

// 

29 

58 
25 
51 
16 
40 
01 

) 

1 
6 

14 

25 
39 
57 

» 
5.9( 

35 
21 

19 
25 
44 
13 

) 

1 
6 

15 

27 

42 

61 

If 
6.35 

42 
49 
20 
16 
36 
21 

) 

1  50 
7  21 
16  34 
29  26 
46  00 
66  14 

// 
6.90 

2 

8 
18 
32 
50 

7.5( 

00 
00 
00 
00 
00 

) 

/      // 

2  12 

8  48 

19  47 

35  09 

54  56 

8.24 

/     // 

2  27 

9  46 

21  59 

39  05 

II 
9.16 

2  46 
11  02 
24  50 
44  10 

10.35 

/     // 

3  11 
12  13 
28  38 

II 
11.93 

/     // 

3  47 
15  05 
33  56 

II 
14.14 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Log. 

0.698 
10 

0.721 
81 

0.747 
41 

0.775 
25 

0.805 
50 

0.838 
85 

0.875 
06 

0.915 
93 

0.961 
90 

1.014 
94 

1.076 
64 

1.150 
45 

Log. 

Limit 

24 

23 

22 

21 

20 

19 

17 

16 

15 

14 

12 

10 

Min- 
utes 

Merid- 
ian 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

/     // 
II 

II 

1 

n 

/ 

II 

II 

II 

II 

/     // 
II 

/      // 

/      // 

3  15 
13  01 
29  17 

II 
12.20 

/ 

2 

10- 
24 
42 

10.0( 

40 
40 
00 
40 

) 

1 

2 

8 
20 
35 

II 
8.4: 

14 
59 
13 
55 

J 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.086 
36 

1.00 

0.925 
31 

Log. 

Limit 

8 

6 

4 

2 

0 

2 

4 

6 

8 

10 

12 

14 

Min- 
utes 

Merid- 
ian 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86°      85° 

84° 

83° 

Alti- 
tudes 

240 


Latitude  40°  Decimation  Same  Name. 


Declinations. 


Hour  1    4^«o 
Angles     *° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Mill. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

7 
17 
30 
48 

rr 

7.2> 

55 
43 

21 
51 
12 

J 

1 

1 

6 

15 

26 

42 

II 
6.3 

n 

41 

44 
08 
56 
04 

I 

1 

1 
5 
13 
23 
37 
53 

II 
5.5 

29 
57 

22 
16 

08 
28 

1 

1     II 

1  19 
5  17 
1155 
2109 
33  04 
47  37 

II 
4.96 

1 

1 
4 
10 
18 
29 
42 
58 

" 
4.4 

11 
45 
11 
59 
iO 
13 
09 

3 

1 
4 
9 
17 
26 
38 
52 
68 

II 
4.0 

04 
17 
39 
09 
48 
36 
32 
36 

2 

/        n 

0  59 
3  53 
8  45 
15  35 
24  20 
35  03 
47  41 
62  17 

3.65 

1 

2 
3 
4 
5 

7 

3 

0 
3 
7 
4 
2 
1 
3 
6 
1 

// 
.3 

H 

52 
32 
59 
13 
12 
58 
31 
50 
56 

3 

1     II 

0  49 
3  15 
7  19 
13  01 
20  20 
29  17 
39  51 
52  03 
65  53 

II 
3.05 

1     II 

0  45 
2  59 
6  43 
1157 
18  40 
26  53 
36  35 
47  47 
60  29 
74  40 

II 
2.80 

/     // 

0  41 

2  45 

6  12 

1100 

17  12 

24  46 

33  43 

44  02 

55  44 

68  48 

II 
2.58 

1       n 

0  38 
2  32 
5  43 
10  09 
15  52 
22  51 
3106 
40  37 
51  25 
63  28 
76  48 

II 
2.38 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.859 
14 

0.800 
03 

0.745 
86 

0.695 
48 

0.648 
36 

0.604 
23 

0.562 
29 

0.522 
44 

0.484 
30 

0.447 
16 

0.411 
62 

0.376 
58 

Log. 

Limit 

16 

18 

20 

21 

23 

25 

27 

28 

30 

32 

34 

36 

Min- 
utes 

Merid- 
ian 

82' 

81= 

> 

80' 

1 

79° 

78' 

> 

77' 

) 

76° 

'i 

^5' 

' 

74 

3 

73 

} 

72 

} 

71° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

Min. 

4 

0  35 

0  33 

0  30 

0  28 

0  26 

0  24 

0  22 

0  21 

0  19 

0  18 

0  16 

0  15 

4 

'8 

2  21 

2  10 

2  01 

152 

143 

136 

130 

123 

1  17 

1  10 

106 

101 

8 

12 

5  17 

4  52 

4  32 

4  12 

3  53 

3  36 

3  22 

3  06 

2  53 

2  39 

2  28 

2  17 

12 

16 

9  23 

8  40 

8  04 

7  28 

6  55 

6  24 

5  58 

5  30 

5  07 

4  45 

4  24 

4  03 

16 

20 

14  40 

13  32 

12  36 

1140 

10  48 

10  00 

9  20 

8  36 

8  00 

7  24 

6  52 

6  20 

20 

24 

2107 

19  29 

18  09 

16  48 

15  34 

14  24 

13  26 

12  23 

11  31 

10  40 

9  53 

9  07 

24 

28 

28  45 

26  32 

24  42 

22  52 

21  10 

19  36 

18  18 

16  52 

15  41 

14  30 

13  28 

12  25 

28 

32 

37  33 

34  39 

32  15 

29  52 

27  38 

25  36 

23  54 

22  01 

20  29 

18  56 

17  35 

16  13 

32 

36 

47  31 

43  51 

40  50 

37  48 

34  00 

32  24 

30  14 

27  52 

25  55 

23  59 

22  15 

20  31 

36 

40 

58  40 

54  08 

50  24 

46  20 

43  12 

40  00 

37  20 

34  24 

32  00 

29  36 

27  28 

25  20 

40 

44 

70  59 

65  30 

60  59 

56  28 

52  17 

48  24 

45  10 

4137 

38  43 

35  49 

33  14 

30  39 

44 

48 

77  57 

72  34 

67  10 

62  12 

57  36 

53  46 

49  32 

46  05 

42  37 

39  33 

36  29 

48 

52 

85  10 

78  52 

73  00 

67  36 

63  06 

58  08 

54  05 

50  01 

46  25 

42  49 

52 

56 

78  24 

73  10 

67  25 

62  43 

58  01 

53  50 

49  39 

56 

60 

77  24 

72  00 

66  36 

61  48 

57  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

It 

Aih 

2.20 

2.03 

1.89 

1.75 

1.62 

1.50 

1.40 

1.29 

1.20 

1.11 

1.03 

0.95 

A,h 

Log. 

0.342 

0.307 

0.276 

0.243 

0.209 

0.176 

0.146 

0.110 

0.079 

0.045 

0.012 

9.977 

Log. 

42 

50 

46 

04 

52 

09 

13 

59 

18 

32 

84 

72 

Limit 

38 

40 

42 

44 

45 

46 

48 

50 

52 

54 

56 

57 

Min- 
utes 

Merid- 
ian 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

59° 

Alti- 
tudes 

Latitude  40°  Declination  Contrary  Name« 


241 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  38 

2  30 

5  37 

9  59 

15  36 

22  28 

30  34 

39  56 

50  33 

62  24 

75  30 

89  51 

105  27 

II 
2.34 

/     // 

0  36 

2  27 

5  30 

9  46 

15  16 

2159 

29  56 

39  05 

49  28 

6104 

73  53 

87  56 

103  12 

II 
2.29 

/      /' 

0  36 

2  24 

5  24 

9  36 

15  00 

21  36 

29  24 

38  24 

48  36 

60  00 

72  36 

86  24 

10124 

II 
2.25 

0  35 

2  21 
5  17 
9  23 
14  40 
21  07 
28  45 
37  33 
47  31 
58  40 
70  59 
84  29 
99  09 

II 
2.20 

/     // 

0  35 

2  18 
5  11 
9  13 
14  24 
20  45 
28  13 
36  51 
46  40 
57  36 
69  42 
82  56 
97  20 

II 
2.16 

/     // 

0  34 
2  15 
5  05 
9  03 

14  08 
20  22 
27  42 
36  10 
45  48 
56  32 
68  25 
8124 
95  32 

II 
2.12 

/     // 

0  33 

2  13 

5  00 

8  52 

13  52 

19  58 

27  11 

35  30 

44  56 

55  28 

67  07 

79  52 

93  44 

II 
2.08 

/     // 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

44  04 

54  24 

65  49 

78  20 

9156 

106  37 

II 
2.04 

/     // 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

104  32 

II 
2.00 

/      // 

0  31 
2  05 
4  44 

8  24 
13  08 
18  54 
25  45 
33  38 
42  33 
52  32 
63  34 
75  39 
88  47 
102  57 

1.97 

/     // 

0  30 

2  03 

4  38 

8  14 

■12  52 

18  31 

25  14 

32  57 

4141 

5128 

62  16 

74  07 

86  59 

100  52 

II 
1.93 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

41  02 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 
II 

1.90 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.369 
22 

0.359 
84 

0.352 

18 

0.342 
42 

0.334 
45 

0.326 
34 

0.318 
06 

0.309 
63 

0.301 
03 

0.294 
47 

0.285 
56 

0.278 
75 

Log. 

Limit 

42 

42 

43 

43 

44 

45 

45 

46 

47 

48 

49 

49 

Min- 
utes 

Merid- 
ian 

50° 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       n 

f     II 

1     II 

/      II 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  30 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

0  26 

0  26 

0  25 

0  25 

4 

8 

2  00 

158 

1  55 

1  54 

152 

150 

148 

146 

144 

1  42 

141 

1  39 

8 

12 

4  29 

4  25 

4  19 

4  16 

4  11 

4  08 

4  03 

3  59 

3  54 

3  51 

3  48 

3  43 

12 

16 

7  59 

7  51 

7  41 

7  33 

7  25 

7  20 

7  13 

7  05 

6  58 

6  53 

6  44 

6  37 

16 

20 

12  28 

12  16 

12  00 

1148 

1136 

1128 

11  16 

11  04 

10  52 

10  44 

10  32 

10  20 

20 

24 

17  57 

17  40 

17  17 

16  59 

16  42 

16  31 

16  14 

15  57 

15  39 

15  28 

15  10 

14  53 

24 

28 

24  26 

24  02 

23  31 

23  08 

22  44 

22  29 

22  05 

21  41 

21  18 

21  02 

20  39 

20  15 

28 

32 

3155 

3124 

30  43 

30  13 

29  42 

29  21 

28  50 

28  19 

27  49 

27  28 

26  58 

26  27 

32 

36 

40  24 

39  45 

38  53 

38  14 

37  35 

37  09 

36  31 

35  52 

35  13 

34  47 

34  08 

33  29 

36 

40 

49  52 

49  04 

48  00 

47  12 

46  24 

45  52 

45  04 

44  16 

43  28 

42  56 

42  08 

41  20 

40 

44 

60  21 

59  22 

58  05 

57  07 

56  08 

55  30 

54  32 

53  34 

52  36 

51  57 

50  59 

50  01 

44 

48 

7148 

70  39 

69  07 

67  56 

66  47 

66  01 

64  53 

63  44 

62  35 

61  49 

60  40 

59  31 

48 

52 

84  16 

82  55 

8107 

79  46 

78  25 

77  31 

76  09 

74  48 

73  27 

72  33 

71  12 

69  51 

52 

56 

97  45 

96  10 

94  05 

92  31 

90  56 

89  54 

88  20 

86  46 

85  12 

84  09 

82  35 

8101 

56 

60 

112  12 

110  24 

108  00 
II 

106  12 
II 

104  24 

II 

103  12 

II 

101  24 
II 

99  36 
II 

97  48 

II 

96  36 
II 

94  48 
II 

93  00 

II 

60 

A,h 

1.87 

1.84 

1.80 

1.77 

1.74 

1.72 

1.69 

1.66 

1.63 

1.61 

1.58 

1.55 

A,h 

Log. 

0.271 

0.264 

0.255 

0.247 

0.240 

0.235 

0.227 

0.220 

0.212 

0.206 

0.198 

0.190 

Log. 

84 

82 

27 

97 

55 

53 

89 

11 

19 

83 

66 

33 

Limit 

50 

51 

51 

52 

52 

53 

54 

55 

56 

56 

57 

58 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

Alti- 
tudes 

242 


Latitude  40°  Decimation  Contrary  Name. 


Declination.s. 

Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35'= 

Hour 
Angles 

Min. 

/      '/ 

/     // 

/      // 

/     " 

/     // 

/     // 

/     // 

/     // 

/      '/ 

/      // 

1     II 

1     II 

Min. 

4 

0  24 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

4 

8 

138 

1  36 

135 

134 

1  32 

130 

129 

1  27 

1  26 

124 

123 

122 

8 

12 

3  40 

3  36 

3  34 

3  31 

3^ 

3  23 

3  20 

3  16 

3  13 

3  10 

3  07 

3  05 

12 

16 

6  32 

6  24 

6  18 

6  13 

6  06 

6  01 

5  56 

5  48 

5  43 

5  38 

5  33 

5  27 

16 

20 

10  12 

10  00 

9  52 

9  44 

9  32 

9  24 

9  16 

9  04 

8  56 

8  48 

8  40 

8  32 

20 

24 

14  41 

14  24 

14  12 

14  01 

13  43 

13  32 

13  21 

13  04 

12  52 

12  41 

12  29 

12  17 

24 

28 

20  00 

19  36 

19  21 

19  05 

18  42 

18  26 

18  10 

17  46 

17  30 

17  15 

16  59 

16  44 

28 

32 

26  07 

25  36 

25  16 

24  55 

24  25 

24  04 

23  43 

23  12 

22  52 

22  31 

22  11 

2151 

32 

36 

33  03 

32  24 

3158 

31  32 

30  53 

30  27 

30  02 

29  23 

28  57 

28  31 

28  05 

27  39 

36 

40 

40  48 

40  00 

39  28 

38  56 

38  08 

37  36 

37  04 

36  16 

35  44 

35  12 

34  40 

34  08 

40 

44 

49  22 

48  24 

47  45 

47  06 

46  08 

45  29 

44  51 

43  53 

43  14 

42  36 

4157 

41  18 

44 

48 

58  45 

57  36 

56  50 

56  04 

54  55 

54  09 

53  22 

52  13 

5127 

50  41 

49  55 

49  09 

48 

52 

68  57 

67  36 

66  42 

65  48 

64  27 

63  33 

62  38 

61  17 

60  23 

59  29 

58  35 

57  41 

52 

56 

79  58 

78  24 

77  21 

76  18 

74  44 

73  41 

72  39 

7105 

70  02 

69  00 

67  57 

66  54 

56 

60 

9148 

90  00 

88  48 

87  36 

85  48 

84  36 

83  24 

81  36 

80  24 

79  12 

78  00 
II 

76  48 

II 

60 

Ajh 

1.53 

1.50 

1.48 

1.46 

1.43 

1.41 

1.39 

1.36 

1.34 

1.32 

1.30 

1.28 

A,h 

0.184 

0.176 

0.170 

0.164 

0.155 

0.149 

0.143 

0.133 

0.127 

0.120 

0.113 

0.107 

Log. 

Log. 

69 

09 

26 

35 

34 

22 

01 

54 

10 

57 

94 

21 

Limit 

59 

60 

60 

61 

62 

63 

64 

64 

65 

66 

67 

68 

Min- 
utes 

Merid- 
ian 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      /' 

/     // 

/      // 

/     // 

/            H 

/     // 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

Min. 

4 

0  20 

0  20 

0  19 

0  19 

0  19 

0  19 

0  18 

0  18 

0  17 

0  17 

4 

8 

1  21 

120 

1  17 

1  16 

1  15 

1  13 

1  12 

1  11 

1  10 

108 

8 

12 

3  02 

2  59 

2  54 

2  51 

2  48 

2  45 

2  42 

2  39 

2  37 

2  34 

12 

16 

5  22 

5  17 

5  10 

5  05 

5  00 

4  55 

4  50 

4  45 

4  39 

4  34 

16 

20 

8  24 

8  16 

8  04 

7  56 

7  48 

7  40 

7  32 

7  24 

7  16 

7  08 

20 

24 

12  06 

1154 

1137 

11  26 

11  14 

1103 

10  51 

10  40 

10  28 

10  16 

24 

28 

16  28 

16  12 

15  49 

15  33 

15  17 

15  01 

14  46 

14  30 

14  15 

13  59 

28 

32 

21  30 

21  10 

20  39 

20  18 

19  58 

19  37 

19  17 

18  56 

18  36 

18  16 

32 

36 

27  13 

26  47 

26  08 

25  43 

25  17 

24  51 

24  25 

23  59 

23  33 

23  07 

36 

40 

33  36 

33  04 

32  16 

31  44 

31  12 

30  40 

30  08 

29  36 

29  04 

28  32 

40 

44 

40  38 

40  00 

39  02 

38  24 

37  46 

37  07 

36  28 

35  49 

35  10 

34  32 

44 

48 

48  23 

47  37 

46  28 

45  41 

44  55 

44  09 

43  23 

42  37 

41  51 

4105 

48 

52 

56  47 

55  53 

54  32 

53  37 

52  43 

5149 

50  55 

50  01 

49  07 

48  13 

52 

56. 

65  51 

64  48 

63  14 

62  12 

61  10 

60  07 

59  04 

58  01 

56  58 

55  56 

56 

60 

75  36 

74  24 

72  36 

71  24 

70  12 

69  00 

67  48 

66  36 

65  24 

64  12 

60 

II 

n 

n 

n 

n 

" 

n 

II 

II 

II 

II 

II 

A,h 

1.26 

1.24 

1.21 

1.19 
0.075 

1.17 

1.15 

1.13 

1.11 

1.09 

1.07 

A,h 

Log.' 

0.100 

0.093 

0.082 

0.068 

0.060 

0.053 

0.045 

0.037 

0.029 

Log. 

37 

42 

79 

55 

19 

70 

08 

32 

43 

38 

Limit 

69 

70 

71 

72 

74 

75 

76 

77 

78 

78 

Min- 
utes 

Merid- 
ian 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

Alti- 
tudes 

Latitude  40°  Decimation  Contrary  Name. 


243 


Declinations.  - 

— 

Infe 

RioR  Meridian 

Hour 
Angles 

48°      49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

MiD. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

1 

// 

n 

// 

/ 

n 

i> 

II 

/ 

II 

// 

II 

// 

I  II 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

II  22 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  29 

52  12 
II 

0.87 

1     II 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 
50  24 

0.84 

/     II 

0  13 
0  52 
158 
3  30 

5  28 
7  53 
10  43 
13  59 
17  43 
21  52 
26  28 
31  29 
36  57 
42  52 
49  12 

0.82 

/     II 

0  13 

0  51 

1  55 
3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

1      II 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

II 

0.78 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.939 
52 

9.924 

28 

9.913 
81 

9.903 
09 

9.892 
09 

Log. 

Limit 

77 

77 

78 

79 

81 

Min- 
utes 

Merid- 
ian 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  12 

0  50 

1  51 
3  17 
5  08 
7  23 

10  04 
13  09 
16  38 
20  32 
24  51 
29  32 
34  42 
40  15 

46  12 

II 

0.77 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

0.75 

/      // 

Oil 
0  46 
144 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 

43  12 

II 

0.73 

/      // 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 

II 

0.70 

/     // 

Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 
II 

0.68 

I  II 

Oil 
0  42 
135 
2  49 
4  24 
6  21 
8  37 

II  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 

39  36 

It 

0.66 

/     // 

0  11 

0  40 

132 

2  44 

4  16 

6  09 

8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
II 

0.64 

/      // 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 

13  11 

16  16 

19  41 

23  25 

27  29 

31  53 

36  36 
II 

0.61 

0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

/     // 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
2154 
25  41 
29  48 

34  12 

II 

0.57 

/      // 

0  09 

0  35 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

1153 

14  40 

17  45 

2107 

24  47 

28  45 

33  00 
II 

0.55 

0  09 

0  34 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

11  27 
14  08 
17  06 
20  21 
23  53 
27  42 
31  48 

0.53 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.886 
49 

9.875 
06 

9.863 
32 

9.845 
10 

9.832 
51 

9.819 
54 

9.806 
18 

9.785 
33 

9.770 
85 

9.755 
87 

9.740 
36 

86 

9.724 

28 

Log. 

Limit 

82 

82 

82 

83 

83 

84 

84 

83 

85 

86 

87 

Min- 
utes 

Merid- 
ian 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

Alti- 
tudes 

244 


Latitude  4J°  Declination  Same  Name. 


Declinations. 


Hour 
Angle? 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 

/   // 
0  36 

/  11 
0  37 

/  n 

0  38 

/  n 

0  38 

1       n 

0  39 

/  // 
0  40 

/  It 
0  41 

/  n 
0  42 

/  // 
0  43 

/  // 
0  44 

/   // 
0  45 

0  46 

Min. 
4 

8 

2  25 

2  28 

2  30 

2  34 

2  38 

2  41 

2  45 

2  48 

2  52 

2  57 

3  01 

3  06 

8 

12 

5  26 

5  32 

5  38 

5  46 

5  55 

6  01 

6  10 

6  18 

6  27 

6  38  6  47 

6  59 

12 

16 

9  38 

9  52 

10  02 

10  14 

10  29 

10  43 

10  58 

11  14 

1129 

11  46  12  05 

12  25 

16 

20 

15  04 

15  24 

15  40 

16  00 

16  24 

16  44 

17  08 

17  32 

17  56 

18  24 

18  52 

19  24 

20 

24 

21  42 

22  11 

22  34 

23  02 

23  37 

24  06 

24  40 

25  15 

25  50 

26  30 

27  10 

27  56 

24 

28 

29  32 

30  11 

30  42 

3122 

32  09 

32  48 

33  35 

34  22 

35  09 

36  04 

36  59 

38  02 

28 

32 

38  34 

39  25 

40  06 

40  58 

41  59 

42  50 

43  52 

44  53 

45  54 

47  06 

48  18 

49  40 

32 

36 

48  49 

49  54 

50  46 

5150 

53  08 

54  13 

55  31 

56  49 

58  07 

59  37 

61  08 

62  51 

36 

40 

60  16 

61  36 

62  40 

64  00 

65  36 

66  56 

68  32 

70  08 

71  44 

73  36 

75  28 

77  36 

40 

44 

72  55 

74  32 

75  50 

77  26 

79  22 

80  59 

82  56 

84  52 

86  48 

44 

48 

86  47 

88  42 

90  14 

92  10 

94  28 

96  33 

48 

52 

101  51 

104  06 

105  54 

108  10 

52 

56 

56 

60 

60 

// 

It 

II 

II 

II 

" 

II 

II 

II 

// 

II 

II 

A,h 

2.26 

2.31 

2.35 

2.40 

2.46 

2.51 

2.57 

2.63 

2.69 

2.76 

2.83 

2.91 

A,h 

Log. 

0.354 

0.363 

0.371 

0.380 

0.390 

0.399 

0.409 

0.419 

0.429 

0.440 

0.451 

0.463 

Log. 

11 

61 

07 

21 

94 

67 

93 

96 

75 

91 

79 

89 

Limit 

43 

42 

41 

41 

40 

40 

39 

38 

38 

37 

37 

36 

Min- 
utes 

Merid- 
ian 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/  // 

1      II 

1     II 

/  // 

1     II 

/  II 

/    H 

1     II 

/  II 

/   n 

/  II 

1     II 

Min. 

4 

0  47 

0  49 

0  51 

0  52 

0  54 

0  55 

0  58 

100 

102 

105 

107 

1  10 

4 

8 

3  11 

3  17 

3  23 

3  30 

3  36 

3  43 

3  51 

4  00 

4  09 

4  19 

4  30 

4  43 

8 

12 

7  11 

7  24 

7  36 

7  51 

8  05 

8  22 

8  39 

8  59 

9  20 

9  42 

10  08 

10  35 

12 

16 

12  45 

13  08 

13  32 

13  57 

14  23 

14  50 

15  25 

15  57 

16  36 

17  14 

18  00 

18  49 

16 

20 

19  56 

20  32 

2108 

2148 

22  28 

23  12 

24  04 

24  56 

25  56 

26  56 

28  08 

29  24 

20 

24 

28  42 

29  34 

30  26 

3123 

32  21 

33  24 

34  40 

35  54 

37  21 

68  47 

40  31 

42  20 

24 

28 

39  05 

40  15 

4125 

42-44 

44  02 

45  29 

47  10 

48  52 

50  50 

52  47 

55  09 

57  38 

28 

32 

5102 

52  34 

54  06 

55  49 

57  31 

59  24 

6136 

63  50 

66  23 

68  57 

72  01 

75  16 

32 

36 

64  35 

66  32 

68  29 

70  38 

72  48 

75  10 

77  59 

36 

40 

79  44 

82  08 

84  32 

87  12 

89  52 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Aih 

2.99 

3.08 

3.17 

3.27 

3.37 

3.48 

3.61 

3.74 

3.89 

4.04 

4.22 

4.41 

A,h 

Log 

0.475 

0.488 

0.501 

0.514 

0.527 

0.541 

0.557 

0.572 

0.589 

0.606 

0.625 

0.644 

Log. 

67 

55 

06 

55 

63 

58 

51 

87 

95 

38 

31 

44 

Limit 

35 

34 

33 

33 

32 

31 

30 

29 

29 

28 

27 

26 

Min- 
utes 

Merid- 
ian 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68 

0 

69 

} 

70 

3 

71 

3 

72 

3 

Alti- 
tudes 

Latitude  4J°  Decimation  Same  Name, 


245 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 
4 

11 

19 

30 

44 

60 

79 

4.6 

// 

15 
56 

36 
i6 
52 
27 
30 
31 

3 

/ 

1 
5 

20 
32 
46 
63 

ti 
4.8 

// 

18 
12 
41 

i7 
28 
i5 
38 

1 

/ 

1 
2 

3 

4 

6 

5 

1 
5 
2 

1 
4 
9 

7 

// 
.1 

// 

23 
30 
21 
59 
20 
27 
17 

5 

/ 

1 
5 

13 

23 

36 

52 

II 
5.4 

// 

27 
50 
37 
17 
24 
25 

5 

1 

6 
13 
24 
38 
55 

II 

5.8 

33 
12 

58 
50 
i8 
53 

2 

/ 

1 
2 

4 
5 

6 

1 
6 
4 
6 
1 
9 

// 
.2 

// 

iO 
39 
57 
35 
32 
i8 

3 

1 

1 

7 

16 
28 
44 
64 

II 
6.7 

// 

i8 
11 
39 
i3 
52 
36 

3 

1. 

7' 
17 
31 
48 

7.3 

11 

57 
18 
32 
12 
14 

1 

1      II 

2  08 

8  34 

19  14 

34  16 

53  32 

II 
8.03 

/     // 

2  22 

9  31 

2126 

38  06 

II 
8.93 

/     // 

2  41 
10  45 
24  12 
43  00 

II 
10.08 

/      // 

3  06 
12  23 
27  51 

11.61 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.665 
58 

0.687 
53 

0.711 
81 

0.737 
19 

0.764 
92 

0.794 
49 

0.828 
02 

0.863 
92 

0.904 
72 

0.950 

85 

1.003 
46 

1.064 
83 

Log. 

Limit 

25 

24 

23 

22 

21 

20 

18 

17 

16 

15 

14 

13 

Min- 
utes 

Merid- 
ian 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40  • 
44 
48 
52 
56 
60 

Aih 

// 
13.7 

5 

/ 

II 

// 

II 

// 

t 
II 

// 

II 

// 

II 

// 

/ 

II 
II 

II 

// 

3 
12 
28 

II 
11.8( 

09 
35 
19 

) 

/ 

2 
10 

23 

J 

II 
9.6 

n 

35 
19 
12 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.138 
30 

• 

1.071 

88 

0.985 
43 

Log. 

Limit 

10 

8 

6 

4 

2 

0 

2 

4 

6 

9 

11 

13 

Min- 
utes 

Merid- 
ian 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

Alti- 
tudes 

246 


Latitude  4i°  Decimation  Same  Name. 


Declinations. 


48= 


2  10 

8  41 

19  32 

34  44 

54  16 


14 


0.910 
62 


49° 


1  51 

7  26 

16  46 

29  46 

46  32 


6.98 


0.843 
86 


50° 


1  37 
6  30 
14  37 
25  59 
40  36 
58  28 


6.09 


0.784 
62 


51° 


1  26 
5  44 
12  53 
22  55 
35  48 
51  33 


5.37 


0.729 
97 


52° 


1  16 
5  06 
11  29 
20  23 
31  52 
45  53 


78 


0.679 
43 


53° 


1  08 
4  35 
10  18 
18  18 
28  36 
41  li 
56  04 


54° 


1  02 
4  08 
9  1/ 
16  31 
25  48 
37  09 
50  34 
66  03 


4.29 


0.632 
46 


3  87 


0.587 
71 


55° 


0  56 
3  45 
8  25 
14  59 
23  24 
33  42 
45  52 
59  54 


3.51 


0.545 
31 


56° 


0  51 
3  25 
7  41 
13  39 
21  20 
30  43 
41  49 
54  37 
69  07 


3.20 


0.505 
15 


57° 


0  47 
3  07 
7  02 
12  30 
19  32 
28  07 
38  18 
50  01 
63  17 


2.93 
0.466 

87 


58° 


0  43 
2  51 
6  26 
11  26 
17  52 
25  44 
35  01 
45  44 
57  54 
71  28 


0.428 
13 


59° 


0  39 
2  39 
5  56 
10  32 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 


2.47 


0.392 
70 


Hour 

Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 


Log. 


15 


17 


19 


20 


22 


24 


26 


27 


29 


31 


32 


34 


Min- 
utes 


83° 


82= 


81° 


80° 


79° 


78° 


77° 


76° 


75° 


74° 


73° 


72° 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 
4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  37 

2  26 

5  29 

9  43 

15  12 

21  53 

29  48 

38  55 

49  15 

60  48 

73  34 

II 
2.28 

/     // 

0  34 

2  14 

5  02 

8  58 

14  00 

20  10 

27  26 

35  50 

45  22 

56  00 

67  46 

II 
2.10 

1     II 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

5144 

62  35 

74  30 

II 
1.94 

/      // 

0  29 

155 

4  19 

7  41 

12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

8107 

II 
1.80 

/      // 

0  27 

1  46 
3  59 
7  05 

1104 
15  57 
21  41 
28  19 
35  52 
44  16 
53  34 
63  44 
74  48 

II 
1.66 

0  25 

1  39 
3  42 
6  34 

10  16 
14  47 
20  07 
26  17 
33  16 
41  04 
49  41 
59  08 
69  24 
80  29 

II 
1.54 

0  23 

1  32 
3  24 
6  06 
9  32 

13  43 
18  42 
24  25 
30  53 
38  08 
46  08 
54  55 
64  27 
74  44 

II 
1.43 

/     // 

0  21 
124 
3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
II 

1.32 

I  II 

0  19 

1  18 

2  56 
5  12 
8  08 

II  43 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

/     II 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 
II 

1.04 

/     // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

II 

0.95 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.357 
93 

0.322 
22 

0.287 
80 

0.255 
27 

0.220 
11 

0.187 
52 

0.155 
34 

0.120 
57 

0.086 
36 

0.053 
08 

0.017 
03 

9.977 
72 

Log. 

Limit 

36 

38 

40 

42 

44 

45 

47 

49 

51 

53 

56 

59 

Min- 
utes 

Merid- 
ian 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

60° 

Alti- 
tudes 

Latttode  41°  Declination  Gjntrary  Name. 


247 


Declinations. 


Hour 
Angles 

0° 

1° 

2°    '     3° 

4° 

5° 

6°    1     7° 

8° 

9° 

10° 

IP 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  36 

2  25 

5  26 

9  38 

15  04 

21  42 

29  32 

38  34 

48  49 

60  16 

72  55 

86  47 

10151 

2.26 

0  35 
2  22 
5  18 
9  26 

14  44 
21  13 
28  53 
37  43 
47  44 
58  56 
71  18 
84  52 
99  36 

2.21 

1       n 

0  35 
2  19 
5  12 
9  16 

14  28 
20  50 
28  21 
37  02 
46  53 
57  52 
70  02 
83  19 
97  47 

II 
2.17 

/     It 

0  34 

2  16 
5  06 
9  06 
14  12 
20  27 
27  50 
36  21 
46  01 
56  48 
68  44 
81  46 
95  59 

II 
2.13 

/       n 

0  33 
2  14 
5  01 

8  55 
13  56 
20  04 
27  19 
35  40 
45  09 
55  44 
67  26 
80  15 
94  11 

II 
2.09 

/       n 

0  33 

2  11 
4  55 
8  45 
13  40 
19  41 
26  47 
34  59 
44  17 
54  40 
66  09 
78  43 
92  23 

II 
2.05 

/          H 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

91  02 

105  35 

II 
2.02 

t        n 

0  31 

2  06 

4  46 

8  26 

13  12 

19  00 

25  53 

33  48 

42  46 

52  48 

63  53 

76  02 

89  14 

103  29 

II 
1.98 

/     // 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

51  44 

62  35 

74  30 

87  26 

10123 

1.94 

/     II 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

61  37 

73  21 

86  05 

99  49 

114  36 
II 

1.91 

/     // 

0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

98  15 

112  48 
// 

1.88 

0  30 

158 

4  26 

7  54 

12  20 

17  46 

24  10 

3134 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 

II 

1.85 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.354    0.344 

11         39 

0.336 
46 

0.328 
38 

0.320 
15 

0.311 
75 

0.305 
35 

0.296J  0.287 
67i        80 

0.281 
03 

0.274    0.267 
16         17 

Log. 

Limit 

43        43 

44 

44 

45 

46 

46 

47 

47 

48 

49 

49 

Min- 
utes 

Merid- 
ian 

49°      48° 

47°  1   46° 

45° 

44° 

43° 

42°  1   41° 

40° 

39° 

38° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       /' 

/      // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

/      // 

/     // 

/      // 

/      // 

Min. 

4 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

0  27     0  26 

0  25 

0  25 

0  25 

0  24 

4 

8 

156 

154 

153 

151 

149 

147 

1  45      1  43 

142 

1  41 

139 

137 

8 

12 

4  20 

4  17 

4  14 

4  09 

4  05 

4  00 

3  56      3  53 

3  49 

3  46 

3  42 

3  39 

12 

16 

744 

7  35 

7  30 

7  23 

7  15 

7  08 

7  00|     6  55 

6  47 

6  42 

6  34 

6  29 

16 

20 

12  04 

11  52 

11  44 

11  32 

11  20 

11  08 

10  56,   10  48 

10  36 

10  28 

10  16 

10  08 

20 

24 

17  23 

17  05 

16  54 

16  36 

16  19 

16  02 

15  45;  15  34 

15  16 

15  04 

14  47 

14  36 

24 

28 

23  39 

23  16 

23  00 

22  37 

22  13 

2149 

I  21  25|  21  10 

20  47 

20  31 

20  07 

19  52 

28 

32 

30  53 

30  23 

30  02 

29  32 

29  01 

28  30 

27  59,  27  38 

27  08 

26  48 

26  17 

25  56 

32 

36 

39  06 

38  27 

38  01 

37  22 

36  43 

36  05 

35  261  35  00 

34  21 

33  55 

33  16 

32  50 

36 

40 

48  16 

47  28 

46  56 

46  08 

45  20 

44  32 

43  44'  43  12 

42  24 

41  52 

4104 

40  32 

40 

44 

58  24 

57  26 

56  47 

55  49 

54  51 

53  54 

52  55    52  17 

51  18 

50  40 

49  41 

49  03 

44 

48 

69  30 

68  19 

67  33 

66  24 

65  15 

64  07 

62  58'  62  12 

61  03 

60  17 

59  08 

58  22 

48 

52 

81  34 

80  13 

79  19 

77  58 

76  37 

75  15 

73  54    73  00 

71  39 

70  45 

69  24 

68  30'     52 

56 

94  36 

93  02 

9159 

90  25 

88  51 

87  18 

85  43    84  41 

83  06 

82  04 

80  29 

79  27     56 

60 

108  36 

II 

106  48 

II 

105  36 

103  48 

102  00 

100  12 

98  24 
II 

97  12 
II 

95  24 
II 

94  12 

92  24 
II 

91  12 
II 

60 

Ajh 

1.81 

1.78 

1.76 

1.73 

1.70 

1.67 

1.64 

1.62 

1.59 

1.57 

1.54 

1.52 

Ajh 

Log. 

0.257 

0.250 

0.245 

0.238 

0.230 

0.222 

0.214 

0.209 

0.201 

0.195 

0.187 

0.181 

Log. 

68 

42 

51 

05 

45 

72 

84 

52 

40 

90 

52 

84 

Limit 

50 

51 

52 

53 

53 

54 

55 

56 

57 

57 

58 

59 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

248 


Latitude  4l°  Decimation  Contrary  Name* 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/        n 

/     // 

/     // 

/     /' 

/     // 

1     II 

1     II 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  23 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  20 

4 

8 

136 

134 

133 

131 

130 

128 

127 

1  25 

124 

123 

122 

120 

8 

12 

3  35 

3  31 

3  28 

3  25 

3  22 

3  19 

3  16 

3  11 

3  08 

3  06 

3  03 

3  00 

12 

16 

6  21 

6  13 

6  08 

6  03 

5  58 

5  53 

5  48 

5  41 

5  36 

5  30 

5  25 

5  20 

16 

20 

9  56 

9  44 

9  36 

9  28 

9  20 

9  12 

9  04 

8  52 

8  44 

8  36 

8  28 

8  20 

20 

24 

14  18 

14  01 

13  49 

13  38 

13  26 

13  15 

13  04 

12  46 

12  35 

12  23 

12  11 

12  00 

24 

28 

19  29 

19  05 

18  49 

18  34 

18  18 

18  02 

17  46 

17  23 

17  07 

16  52 

16  36 

16  20 

28 

32 

25  26 

24  55 

24  35 

24  14 

23  54 

23  33 

23  12 

22  42 

22  21 

22  01 

21  41 

2120 

32 

36 

32  11 

31  32 

3106 

30  40 

30  14 

29  49 1  29  23 

28  44 

28  18 

27  52 

27  26 

27  00 

36 

40 

39  44 

38  56 

38  24 

37  52 

37  20 

36  48    36  16 

35  28 

34  56 

34  24 

33  52 

33  20 

40 

44 

48  04 

47  06 

46  27 

45  49 

45  10 

43  32    43  53 

42  55 

42  16 

4137 

40  59 

40  20 

44 

48 

57  13 

56  04 

55  18 

54  32 

53  46 

52  59    52  13 

5104 

50  18 

49  32 

48  45 

48  00 

48 

52 

67  09 

65  48 

64  54 

64  00 

63  06 

62  11    61  17 

59  56 

59  02 

58  08 

57  14 

56  20 

52 

56 

77  52 

76  18 

75  15 

74  13 

73  10 

72  08    71  05 

69  31 

68  28 

67  25 

66  23 

65  20 

56 

60 

89  24 

87  36 
II 

86  24 
II 

85  12 

84  00 

II 

82  48 

8136 
II 

79  48 

78  36 
II 

77  24 

II 

76  12 

75  00 

60 

Ajh 

1.49 

1.46 

1.44 

1.42 

1.40 

1.38 

1.36 

1.33 

1.31 

1.29 

1.27 

1.25 

A,h 

Log. 

0.173 

0.164 

0.158 

0.152 

0.146 

0.139 

0.133 

0.123 

0.117 

0.110 

0.103 

0.096 

Log. 

19 

35 

36 

29 

13 

88 

54 

85 

27 

59 

80 

91 

Limit 

60 

61 

61 

62 

63 

64 

65 

65 

66 

67 

68 

69 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

/     // 
0  20 

/     // 
0  19 

/  -    // 
0  19 

/      // 
0  19 

/     // 
0  19 

/     // 
0  19 

/     // 
0  18 

/      // 
0  17 

0  17 

/     // 

/     // 

/      // 

Min. 
4 

8 

1  19 

1  18 

1  16 

1  15 

1  13 

1  12 

1  11 

1  10 

109 

8 

12 

2  57 

2  54 

2  51 

2  48 

2  45 

2  42 

2  39 

2  37 

2  34 

12 

16 

5  15 

5  10 

5  05 

5  00 

4  55 

4  50 

4  45 

4  39 

4  34 

16 

20 

8  12 

8  04 

7  56 

7  48 

7  40 

7  32 

7  24 

7  16 

7  08 

20 

24 

1148 

11  37 

1126 

11  14 

1103 

10  51 

10  40 

10  28 

10  16 

24 

28 

16  05 

15  49 

15  33 

15  17 

15  01 

14  46 

14  30 

14  15 

13  59 

28 

32 

2100 

20  39 

20  18 

19  58 

19  37 

19  17 

18  56 

18  36 

18  16 

32 

36 

26  34 

26  08 

25  43 

25  17 

24  51 

24  25 

23  59 

23  33 

23  07 

36 

40 

32  48 

32  16 

31  44 

31  12 

30  40 

30  08 

29  36 

29  04 

28  32 

40 

44 

39  41 

39  02 

38  24 

37  46 

37  07 

36  28 

35  49 

35  10 

34  32 

44 

48 

47  14 

46  28 

45  41 

44  55 

44  09 

43  23 

42  37 

4151 

4105 

48 

52 

55  26 

54  32 

53  37 

52  43 

51  49 

50  55 

50  01 

49  07 

48  13 

52 

56 

64  17 

63  14 

62  12 

61  10 

60  07 

59  04 

58  01 

56  58 

55  56 

56 

60 

73  48 

72  36 

7124 

70  12 

69  00 

67  48 

66  36 

65  28 

64  12 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

/ 

A,h 

1.23 

1.21 

1.19 

1.17 

1.15 

1.13 

1.11 

1.09 

1.07 

Ajh 

0.089 

0.082 

0.075 

0.068 

0.060 

0.053 

0.045 

0.037 

0.029 

Log. 

Log. 

91 

79 

55 

19 

70 

08 

32 

43 

38 

Limit 

70 

71 

72 

73 

75 

76 

77 

78 

78 

Min- 
utes 

Merid- 
ian 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2 

0 

Alti- 
tudes 

Latitude  41°  Declination  Contrary  Name. 
Declinations.  —  Infehior  Meridian. 


249 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

II 

1 
1 

// 

II 

// 

II 

// 

1 

/ 

/  // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 
52  48 

0.88 

/  // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 
II 

0.83 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

/  // 

0  12 

0  51 

154 

3-22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

/  // 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.944 
48 

9.929 
42 

9.919 
08 

9.908 
49 

9.897 
63 

9.892 
09 

Log. 

Limit 

73 

74 

76 

77 

•79 

80 

Min- 
utes 

Merid- 
ian 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/   // 

0  12 

0  49 

1  50 
3  14 
5  04 
7  18 
9  56 

12  58 
16  25 
20  16 
24  31 
29  09 
34  15 
39  44 

45  36 

II 

0.76 

/  // 

0  12 
0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 

15  59 

19  44 

23  52 

28  23 

33  21 

38  40 

44  24 
II 

0.74 

Oil 
0  46 
142 

3  02 

4  44 
6  49 
9  17 

12  07 

15  20 

18  56 

22  54 

27  14 

32  00 

37  06 

42  36 
II 

0.71 

Oil 

0  44 

1  39 

2  57 
4  36 
6  38 
9  01 

1146 
14  55 
18  24 
22  16 
26  29 
3105 
36  04 
4124 

0.69 

/  // 

Oil 

0  43 

1  36 

2  52 
4  28 
6  26 
8  45 

11  26 

14  29 

17  52 

21  38 

25  43 

30  11 

35  02 

40  12 
II 

0.67 

/  // 

Oil 

0  41 

1  33 

2  47 
4  20 
6  15 
8  29 

1105 
14  03 
17  20 
20  59 
24  57 
29  17 
33  59 
39  00 

0.65 

/  // 

0  10 

0  40 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
II 

0.63 

/  // 

0  10 

0  38 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 

12  58 

16  00 

19  22 

23  02 

27  02 

31  22 

36  00 
II 

0.60 

/  // 

0  09 

0  37 

1  24 

2  28 

3  52 
5  34 
7  35 
9  54 

12  32 

15  28 

18  43 

22  16 

26  08 

30  19 

34  48 
II 

0.58 

/  // 

0  09 

0  36 

1  21 

2  23 

3  44 
5  23 
7  19 
9  53 

12  06 
14  56 
18  04 
21  30 
25  14 
29  16 
33  36 

0.56 

/  // 

0  09 

0  35 

1  18 

2  18 

3  36 
5  11 
7  03 
9  13 

1140 
14  24 
17  25 
20  44 
24  20 
28  13 

32  24 

II 

0.54 

/  // 

0  08 

0  33 

1  15 

2  13 

3  28 

5  00 

6  48 
8  52 

11  14 

13  52 

16  47 

19  58 

23  26 

27  11 

31  12 
// 

0.52 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.880 
81 

9.869 
23 

9.851 
26 

9.838 
85 

9.826 
07 

9.812 
91 

9.799 
34 

9.778 
15 

9.763 
43 

9.748 
19 

9.732 
39 

9.716 
00 

Log. 

Limit 

81 

82 

82 

83 

83 

83 

84 

84 

85 

85 

86 

86 

Min- 
utes 

Merid- 
ian 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

Alti- 
tudes 

250 


Latitude  42°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5°    6° 

7° 

8° 

9° 

10°   11° 

Hour 
Angles 

Mis. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  1' 

0  35 

2  19 

5  14 

9  18 

14  32 

20  56 

28  29 

37  12 

47  06 

58  08 

70  21 

83  42 

98  14 

2.18 

/  n 

0  35 

2  22 

5  20 

9  28 

14  48 

21  19 

29  01 

37  53 

47  57 

59  12 

7138 

85  15 

100  03 

II 
2.22 

/   // 

0  36 

2  26 

5  27 

9  41 

15  08 

2147 

29  40 

38  45 

49  02 

60  32 

73  15 

87  10 

102  18 

II 
2.27 

/  // 

0  37 

2  28 

5  34 

9  54 

15  28 

22  17 

30  19 

39  35 

50  07 

61  52 

74  52 

89  05 

104  33 

II 
2.32 

/  // 

0  38 

2  31 

5  40 

10  04 

15  44 

22  40 

30  50 

40  16 

50  59 

62  56 

76  09 

90  37 

106  21 

II 
2.36 

/  // 

0  38 
2  35 
5  49 
10  19 
16  08 
23  14 
3138 
41  18 
52  16 
64  32 
78  05 
92  56 

// 
2.42 

/  // 

0  39 
2  39 
5  56 
10  32 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 
94  51 

II 
2.47 

/   // 

0  40 
2  42 
6  04 
10  48 
16  52 
24  17 
33  04 
43  11 
54  39 
67  28 
8138 

II 
2.53 

/  // 

0  41 
2  45 
6  12 
1100 
17  12 
24  46 
33  43 
44  02 
55  44 
68  48 
83  15 

2.58 

/  II 

0  43 
2  49 
6  21 
11  19 
17  40 
25  27 
34  37 
45  13 
57  15 
70  40 
85  31 

II 
2.65 

/  // 

0  43 
2  54 
6  30 
11  34 
18  04 
26  01 
35  25 
46  15 
58  32 
72  16 
87  26 

It 
2.71 

/  // 

0  44 

2  58 

6  41 

11  51 

18  32 
26  41 
36  20 
47  27 
60  03 
74  08 

II 
2.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log 

0.338 
46 

0.346 
35 

0.356 
03 

0.365 
49 

0.372 
91 

0.383 
82 

0.392 
70 

0.403 
12 

0.411 
62 

0.423 
25 

0.432 
97 

0.444 
04 

Log. 

Limit 

44 

43 

42 

42 

41 

41 

40 

40 

39 

39 

38 

37 

Min- 
utes 

Merid- 
ian 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Alti 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/  // 

/  // 

/  // 

/  n 

/  II 

/  // 

Min. 

Min. 

4 

0  46 

0  46 

0  48 

0  50 

0  51 

0  53 

0  54 

0  56 

0  59 

101 

103 

106 

4 

8 

3  02 

3  07 

3  13 

3  18 

3  25 

3  31 

3  39 

3  46 

3  54 

4  03 

4  13 

4  24 

8 

12 

6  50 

7  02 

7  15 

7  26 

7  41 

7  55 

8  11 

8  28 

8  47 

9  07 

9  31 

9  54 

12 

16 

12  10 

12  30 

12  53 

13  14 

13  39 

14  05 

14  33 

15  04 

15  37 

16  13 

16  53 

17  38 

16 

20 

19  00 

19  32 

20  08 

20  40 

21  20 

22  00 

22  44 

23  32 

24  24 

25  20 

26  24 

27  32 

20 

24 

27  22 

28  07 

29  00 

29  46 

30  43 

3141 

32  44 

33  53 

35  09 

36  29 

38  01 

39  39 

24 

28 

37  14 

38  18 

39  28 

40  30 

41  49 

43  07 

44  34 

46  08 

47  49 

49  39 

51  45 

53  58 

28 

32 

48  38 

50  01 

51  32 

52  54 

54  37 

56  19 

58  12 

60  15 

62  27 

64  51 

67  35 

70  29 

32 

36 

61  34 

63  17 

65  14 

66  58 

69  07 

71  17 

73  39 

76  15 

79  04 

36 

40 

76  00 

78  08 

80  32 

82  40 

85  20 

88  00 

90  56 

40 

44 

44 

48 

48 

52 

N    •  •  . 

52 

56 

'l  .  . 

56 

60 

60 

II 

II 

II 

n 

n 

II 

II 

II      \ 

n 

II 

II 

II 

A,h 

2.85 

2.93 

3.02 

3.10 

3.20 

3.30 

3.41 

3.53 

3.66 

3.80 

3.96 

4.13 

A,h 

Log. 

0.454 

0.466 

0.480 

0.49ll  0.505 

0.518 

0.532 

0.547 

0.563 

0.579 

0.597 

0.615 

Log. 

84 

87 

01 

36 

15 

51 

75 

77 

48 

78 

70 

95 

Limit 

36 

35 

34 

34 

34 

33 

32 

31 

31 

29 

28 

27 

Min- 
utes 

Merid- 
ian 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Alti- 
tudes 

Lathucie  42°  Declination  Same  Name. 


251 


De(XINATION8. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

1     II 

/      // 

/      // 

Ujn. 

Min. 

4 

1  10 

1  12 

1  16 

1  20 

126 

1  31 

137 

1  45 

154 

2  05 

2  19 

2  37 

4 

8 

4  36 

4  49 

5  05 

5  21 

5  41 

6  03 

6  29 

7  00 

7  36 

8  20 

9  16 

10  28 

8 

12 

10  20 

10  51 

11  26 

12  03 

12  47 

13  36 

14  36 

15  45 

17  06 

18  46 

20  51 

23  32 

12 

16 

18  24 

19  17 

20  18 

21  25 

22  45 

2ii2 

25  56 

27  59 

30  26 

33  22 

37  05 

4152 

16 

20 

28  44 

30  08 

31  44 

33  28 

35  32 

(37  3| 

40  32 

43  44 

47  32 

52  08 

57  56 

20 

24 

41  23 

43  24 

45  42 

48  12 

51  10 

M26 

58  22 

24 

28 

56  19 

59  04 

62  10 

65  36 

69  39 

74  05 

28 

32 

73  33 

77  08 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

" 

" 

II 

" 

" 

II 

II 

II 

" 

II 

II 

A,h 

4.31 

4.52 

4.76 

5.02 

5.33 

5.67 

6.08 

6.56 

7.13 

7.82 

8.69 

9.81 

A,h 

Log. 

0.634 

0.655 

0.677 

0.700 

0.726 

0.753 

0.783 

0.816 

0.853 

0.893 

0.939 

0.991 

Log. 

48 

14 

61 

70 

73 

58 

90 

90 

09 

21 

02 

67 

Limit 

26 

25 

24 

23 

22 

21 

20 

18 

17 

16 

15 

14 

Min- 
utes 

Merid- 
ian 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

3 

12  1 
27  ( 

11.2 

DO 
33 
36 

/ 

3 

14 
32 

II 
13.3 

// 

34 
16 
35 

7 

/ 

// 

// 

// 

/ 

// 

/ 

// 

// 

1 
II 

// 

1 
II 

// 

/ 

// 

1 

// 

1 

3 

12 
27 

11.4 

02 
U 
23 

1 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

1.052 
69 

1.126 
13 

1.057 
29 

Log. 

Limit 

12 

10 

8 

6 

4 

2 

0 

2 

4 

6 

8 

10 

Min- 
utes 

Merid- 
ian 

84= 

85' 

> 

£ 

16= 

> 

8' 

?° 

8) 

5° 

8< 

)° 

{ 

)0 

5 

89 

3 

81 

}° 

87 

J 

8f 

3° 

85 

3 

Alti- 
tudes 

252 


Latitude  42°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


48° 


Log. 


Limit 

Merid- 
ian 


2  29 

9  58 

22  25 

39  51 


49"= 


9.34 


0.970 
35 


13 


84° 


2  06 

8  22 

18  50 

33  30 

52  20 


7.85 


0.894 
87 


15 


83° 


50°  I   51° 


1  48 

7  12 

16  11 

28  45 

44  56 


6.74 


0.828 
66 


17 


82° 


134 
6  16 
14  05 
25  03 
39  08 
56  21 


5.87 


0.768 
64 


19 


81= 


52° 


123 
5  31 
12  24 
22  04 
34  28 
49  38 


5.17 


0.713 
49 


21 


80° 


53= 


1  14 
4  54 
11  02 
19  38 
30  40 
44  10 
60  06 


4.60 


0.662 
76 


23 


79° 


54° 


1  06 
4  23 
9  53 
17  35 
27  28 
39  34 
53  50 


4.12 


0.614 
90 


24 


78° 


55° 


0  59 
3  58 
8  56 
15  52 
24  48 
35  43 
48  37 
63  29 


3.72 


0.570 
54 


26 


77° 


56° 


0  54 
3  36 
8  05 
14  23 
22  28 
32  21 
44  02 
57  31 
72  48 


3.37 


0.527 
63 


28 


76° 


57° 


0  49 
3  17 
7  22 
13  06 
20  28 
29  28 
,40  07 
52  24 
66  19 


58° 


0  45 
2  59 
6  43 
11  57 
18  40 
26  53 
36  35 
47  47 
60  29 
74  40 


3.07 


0.487 
14 


30 


75° 


2.80 


0.447 
16 


32 


74° 


59° 


Hour 

Angles 


0  41 
2  45 
6  12 
11  00 
17  12 
24  46 
33  43 
44  03 
55  44 
68  48 


2.58 


0.411 
62 


34 


73° 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Min- 
utes 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1        n 

/     // 

1     II 

/     // 

/     // 

/      // 

/     // 

1     II 

/     // 

/     II 

/     // 

/      // 

Min. 

4 

0  38 

0  35 

0  32 

0  30 

0  27 

0  25 

0  23 

0  22 

0  20 

0  19 

0  17 

0  15 

4 

8 

2  31 

2  19 

2  08 

158 

150 

1  41 

134 

126 

1  20 

1  13 

108 

102 

8 

12 

5  40 

5  12 

4  48 

4  26 

4  06 

3  48 

3  31 

3  14 

3  00 

2  45 

2  33 

2  20 

12 

16 

10  04 

9  16 

8  32 

7  54 

7  18 

6  44 

6  13 

5  46 

5  20 

4  55 

4  31 

4  08 

16 

20 

15  44 

14  28 

13  20 

12  20 

1124 

10  32 

9  44 

9  00 

8  20 

7  40 

7  04 

6  28 

20 

24 

22  40 

20  50 

19  12 

17  46 

16  25 

15  10 

14  01 

12  58 

12  00 

1103 

10  11 

9  18 

24 

28 

30  50 

28  21 

26  08 

24  10 

22  21 

20  39 

19  05 

17  38 

16  20 

15  01 

13  51 

12  41 

28 

32 

40  16 

37  02 

34  08 

3134 

29  11 

26  58 

24  55 

23  02 

21  20 

19  37 

18  05 

16  34 

32 

36 

50  59 

46  53 

43  12 

39  58 

36  56 

34  08 

31  32 

29  10 

27  00 

24  51 

22  54 

20  57 

36 

40 

62  56 

57  52 

53  20 

49  20 

45  36 

42  08 

38  56 

36  00 

33  20 

30  40 

28  16 

25  52 

40 

44 

70  02 

64  32 

59  42 

55  10 

50  59 

47  06 

43  34 

40  20 

37  07 

34  12 

31  18 

44 

.   48 

76  48 

7102 

65  38 

60  40 

56  04 

5150 

48  00 

44  09 

40  42 

37  15 

48 

52 

77  04 

71  12 

65  48 

60  50 

56  20 

51  49 

47  46 

43  43 

52 

56 

76  18 

70  34 

65  20 

60  07 

55  24 

50  42 

56 

60 

8100 

75  00 

69  00 

63  36 

58  12 

60 

It 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.36 

2.17 

.2.00 

1.85 

1.71 

1.58 

1.46 

1.35 

1.25 

1.15 

1.06 

0.97 

A,h 

Log. 

0.372 

0.336 

0.301 

0.267 

0.233 

0.198 

0.164 

0.130 

0.096 

0.060 

0.025 

9.986 

Log. 

91 

46 

03 

17 

00 
43 

66 

35 

33 

91 

70 

31 

77 

Limit 

35 

37 

39 

41 

44 

46 

48 

50 

52 

55 

58 

Min- 
utes 

Merid- 
ian 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61° 

Alti- 
tudes 

Latitude  42°  Declination  Contfary  Name. 


263 


Declinations. 

Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/      // 

/     // 

/     // 

/     II 

/     // 

/      // 

/     // 

/     // 

'      " 

/     // 

/     // 

/     // 

Min. 

4 

0  35 

0  35 

0  34 

0  33 

0  32 

0  31 

0  31 

0  30 

0  30 

0  30 

0  29 

0  28 

4 

8 

2  19 

2  17 

2  14 

2  12 

2  09 

2  07 

2  04 

2  02 

2  01 

158 

1  56 

155 

8 

12 

5  14 

5  08 

5  02 

4  57 

4  51 

4  47 

4  41 

4  37 

4  32 

4  26 

4  22 

4  18 

12 

16 

9  18 

9  08 

8  58 

8  47 

8  37 

8  29 

8  19 

8  11 

8  04 

7  54 

7  46 

7  38 

16 

20 

14  32 

14  16 

14  00 

13  44 

13  28 

13  16 

13  00 

12  48 

12  36 

12  20 

12  08 

1156 

20 

24 

20  56 

20  33 

20  10 

19  47 

19  24 

19  06 

18  43 

18  26 

18  09 

17  46 

17  29 

17  11 

24 

28 

28  29 

27  57 

27  26 

26  55 

26  24 

26  01 

25  29 

25  06 

24  42 

24  10 

23  47 

23  24 

28 

32 

37  12 

36  31 

35  50 

35  09 

34  28 

33  58 

33  17 

32  46 

32  15 

3134 

3103 

30  33 

32 

36 

47  06 

46  14 

45  22 

44  30 

43  38 

42  59 

42  07 

41  28 

40  50 

39  58 

39  19 

38  40 

36 

40 

58  08 

57  04 

56  00 

54  56 

53  52 

53  04 

52  00 

51  12 

50  24 

49  20 

48  32 

47  44 

40 

44 

70  21 

69  03 

67  46 

66  28 

65  11 

64  12 

62  55 

6157 

60  59 

59  42 

58  44 

57  45 

44 

48 

83  42 

82  10 

80  38 

79  06 

77  34 

76  25 

74  53 

73  44 

72  34 

7102 

69  53 

68  42 

48 

52 

98  14 

96  26 

94  38 

92  50 

9102 

89  41 

87  53 

86  32 

85  10 

83  22 

82  01 

80  40 

52 

56 

105  35 

104  01 

10155 

100  21 

98  47 

96  42 

95  08 

93  33 

56 

60 

113  24 

11100 

109  12 

107  24 

60 

// 

II 

II 

" 

" 

II 

II 

" 

II 

II 

" 

II 

A,h 

2.18 

2.14 

2.10 

2.06 

2.02 

1.99 

1.95 

1.92 

1.89 

1.85 

1.82 

1.79 

Aih 

Log. 

0.338 

0.330 

0.322 

0.313 

0.305 

0.298 

0.290 

0.283 

0.276 

0.267 

0.260 

0.252 

Log. 

46 

41 

22 
45 

87 

35 

85 

03 

30 

46 

17 

07 

85 

Limit 

44 

44 

45 

46 

47 

47 

48 

48 

49 

50 

50 

Min- 
utes 

Merid- 
ian 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  28 

153 

4  14 

7  30 

11  44 

16  54 

23  00 

30  02 

38  01 

46  56 

56  47 

67  33 

79  19 

91  59 

105  36 
// 

1.76 

/     // 

0  28 

1  52 
4  11 
7  25 

11  36 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 
90  56 
104  24 

1.74 

/     // 

0  27 

150 

4  06 

7  18 

11  24 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 

II 

1.71 

/      // 

0  27 

147 

4  02 

7  10 

11  12 

16  08 

2157 

28  40 

36  18 

44  48 

54  13 

64  30 

75  42 

87  49 

100  48 
II 

1.68 

/     // 

0  27 

145 

3  57 

7  03 

1100 

15  51 

21  33 

28  09 

35  39 

44  00 

53  15 

63  21 

74  21 

86  15 

99  00 

II 

1.65 

/     // 

0  26 

1  44 
3  54 
6  58 

10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 
97  48 

1.63 

1     II 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 

II 

1.60 

1     II 

0  25 

1  41 
3  48 
6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/     // 

0  25 

1  39 
3  43 
6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

8101 

93  00 
II 

1.55 

/     // 

0  24 

1  38 
3  40 
6  32 

10  12 
14  41 
20  00 
26  07 
33  03 
40  48 
49  22 
58  45 
68  57 
79  58 
9148 

1.53 

1     II 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 
90  36 

1.51 

/      // 

0  23 

1  35 
3  34 
6  18 
9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
II 

1.48 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.245 
51 

0.240 
55 

0.233 
00 

0.225 
31 

0.217 

48 

0.212 
19 

0.204 
12 

0.198 
66 

0.190 
33 

0.184 
69 

0.178 
98 

0.170 
26 

Log. 

Limit 

51 

52 

53 

54 

54 

55 

56 

57 

58 

58 

59 

60 

Min- 
utes 

Merid- 
ian 

36°  1   35° 

34° 

33° 

32° 

31° 

30°      29° 

28° 

27° 

26° 

25° 

Alti- 
tudes 

254 


Latitude  42°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Miu. 

/       n 

/       n 

/       n 

/     // 

/     It 

/      II 

1     II 

/     II 

/     '/ 

/      // 

/     // 

/       n 

Min. 

4 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

0  20 

0  20 

0  19 

4 

8 

134 

132 

1  30 

129 

128 

126 

125 

1  23 

123 

121 

120 

1  19 

8 

12 

3  31 

3  24 

3  23 

3  20 

3  17 

3  14 

3  11 

3  08 

3  06 

3  03 

2  59 

2  57 

12 

16 

6  13 

6  06 

6  01 

5  56 

5  51 

5  46 

5  41 

5  36 

5  30 

5  25 

5  17 

5  15 

16 

20 

9  44 

9  32 

9  24 

9  16 

9  08 

9  00 

8  52 

8  44 

8  36 

8  28 

8  16 

8  12 

20 

24 

14  01 

13  43 

13  32 

13  21 

13  09 

12  58 

12  46 

12  35 

12  23 

12  11 

1154 

1148 

24 

28 

19  05 

18  42 

18  26 

18  10 

17  54 

17  38 

17  23 

17  07 

16  52 

16  36 

16  12 

16  05 

28 

32 

24  55 

24  25 

-24  04 

23  43 

23  23 

23  02 

22  42 

22  21 

22  01 

21  41 

21  10 

2100 

32 

36 

31  32 

30  53 

30  27 

30  02 

29  36 

29  10 

28  44 

28  18 

27  52 

27  26 

27  47 

26  34 

36 

40 

38  56 

38  08 

37  36 

37  04 

36  32 

36  00 

35  28 

34  56 

34  24 

33  52 

33  04 

32  48 

40 

44 

47  06 

46  08 

45  29 

44  51 

44  13 

43  34 

42  55 

42  16 

41  37 

40  59 

40  00 

39  41 

44 

48 

56  04 

54  55 

54  09 

53  22 

52  36 

5150 

51  04 

50  18 

49  32 

48  46 

47  37 

47  14 

48 

52 

65  48 

64  27 

63  33 

62  38 

61  44 

60  50 

59  56 

59  02 

58  08 

57  14 

55  53 

55  26 

52 

56 

76  18 

74  44 

73  41 

72  39 

71  37 

70  34 

69  31 

68  28 

67  25 

66  23 

64  48 

64  17 

56 

60 

87  36 

85  48 

84  36 

83  24 

82  12 

81  00 

79  48 

78  36 

77  24 

76  12 

II 

74  24 

73  48 

II 

60 

A,h 

1.46 

1.43 

1.41 

1.39 

1.37 

1.35 

1.33 

1.31 

1.29 

1.27 

1.24 

1.23 

A,h 

Log. 

0.164 

0.155 

0.149 

0.143 

0.36 

0.130 

0.123 

0.117 

0.110 

0.103 

0.093 

0.089 

Log. 

35 

34 

22 

01 

72 

33 

85 

27 

59 

80 

42 

91 

Limit 

61 

62 

62 

63 

64 

65 

66 

66 

67 

68 

69 

70 

Min- 
utes 

Merid- 
ian 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

/     // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

31  44 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

1.17 

/      // 

0  19 

1  13 

2  45 
4  55 
7  40 

11  03 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 

69  00 

II 

1.15 

1     II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 

67  48 

II 

1.13 

/     // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

41  51 

49  07 

56  58 

65  24 
II 

1.09 

/     // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

II 

1.07 

/ 

// 

// 

1 

1 

// 

■/ 

II 

II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.082 
79 

0.075 
55 

0.068 
19 

0.060 
70 

0.053 
08 

0.045 
32 

0.037 
43 

0.029 
38 

Log. 

Limit 

71 

72 

73 

74 

75 

77 

78 

78 

Min- 
utes 

Merid- 
ian 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

no     i      10        Alti- 
^      1     ^        tudes 

Latitude  42°  Decimation  Contrary  Name. 
Declinations.  —  Infeuior  Meridian. 


256 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55°' 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/     // 
It 

/     // 
If 

t     II 

/     // 

1 
II 

II 

I  II 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

II  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

/     // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

5136 
II 

0.86 

/     // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

57  51 

43  54 

50  24 
II 

0.84 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 
II 

0.82 

9.913 

81 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

2120 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/     II 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

/     // 

0  12 
0  50 
151 
3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
// 

0.77 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.944 
48 

9.934 
50 

9.924 
28 

9.903 
09 

9.892 
09 

9.886 
49 

80 

Log. 

Limit 

72 

73 

74 

75 

76 

78 

Min- 
utes 

Merid- 
ian 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11°  1  ^^f- 
■'•■'•     1  tude8 

Declinations 

,.  —  Inferior  Meridian 

. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

/      // 

/     // 

/      // 

/     // 

/     // 

/      // 

/     // 

/     // 

/      // 

1      II 

/      // 

Min. 

4 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  08 

4 

8 

0  48 

0  47 

0  45 

0  43 

0  42 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  33 

8 

12 

148 

145 

1  41 

137 

135 

132 

129 

126 

124 

121 

1  18 

1  15 

12 

16 

3  12 

3  07 

2  59 

2  54 

2  49 

2  44 

2  39 

2  34 

2  28 

2  23 

2  18 

2  13 

16 

20 

5  00 

4  52 

4  40 

4  32 

4  24 

4  16 

4  08 

4  00 

3  52 

3  44 

3  36 

3  28 

20 

24 

7  12 

7  00 

6  43 

6  32 

6  21 

6  09 

5  58 

5  46 

5  34 

5  23 

5  11 

5  00 

24 

28 

9  48 

9  33 

9  09 

8  53 

8  37 

8  21 

8  06 

7  50 

7  35 

7  19 

7  03 

6  48 

28 

32 

12  48 

12  28 

1157 

11  36 

11  15 

10  55 

10  34 

10  14 

9  54 

9  33 

9  13 

8  52 

32 

36 

16  12 

15  46 

15  07 

14  42 

14  16 

13  50 

13  24 

12  58 

12  32 

12  06 

1140 

11  14 

36 

40 

20  00 

19  28 

18  40 

18  08 

17  36 

17  04 

16  02 

16  00 

15  28 

14  56 

14  24 

13  52 

40 

44 

24  12 

23  33 

22  35 

21  57 

21  18 

20  39 

20  01 

19  22 

18  43 

18  04 

17  25 

16  47 

44 

48 

28  46 

28  00 

26  51 

26  08 

25  20 

24  34 

23  48 

23  02 

22  16 

2130 

20  44 

19  58 

48 

52 

33  48 

32  54 

31  33 

30  38 

29  44 

28  50 

27  56 

27  02 

26  09 

25  14 

24  20 

23  26 

52 

56 

39  12 

38  09 

36  35 

35  33 

34  30 

33  27 

32  25 

3122 

30  19 

29  16 

28  13 

27  11 

56 

60 

45  00 

43  48 

42  00 

40  48 

39  36 

38  24 

37  12 

36  00 

34  48 

33  36 

32  24 

31  12 

60 

II 

II 

// 

" 

II 

// 

" 

" 

II 

II 

II 

II 

Ajh 

0.75 

0.73 

0.70 

0.68 

0.66 

0.64 

0.62 

0.60 

0.58 

0.56 

0.54 

0.52 

Ajh 

9.875 

9.863 

9.845 

9.832 

9.819 

9.806 

9.792 

9.778 

9.763 

9.748 

9.732 

9.716 

Log. 

Log. 

06 

32 

10 

51 

54 

18 

39 

15 

43 

19 

39 

00 

Limit 

81 

81 

82 

83 

83 

83 

84 

84 

85 

85 

85 

86 

Min- 
utes 

Merid- 
ian 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Alti- 
tudes 

256 


Latitude  43°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

HTour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

81  01 

95  05 

It 
2.11 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

1     II 

0  35 

2  20 

5  15 

9  21 

14  36 

2102 

28  37 

37  22 

47  19 

58  24 

70  40 

84  05 

98  41 

2.19 

1     II 

0  35 

2  23 

5  21 

9  31 

14  52 

21  24 

29  09 

38  04 

48  10 

59  28 

7157 

85  38 

100  30 

2.23 

0  36 

2  26 

5  29 

9  43 

15  12 

2153 

29  48 

38  55 

49  15 

60  48 

73  34 

87  33 

102  45 

2.28 

0  37 

2  28 

5  34 

9  54 

15  28 

22  17 

30  19 

39  35 

50  07 

61  52 

74  52 

89  05 

104  33 

II 
2.32 

/     // 

0  38 

2  32 

5  41 

10  07 

15  48 

22  45 

30  58 

40  27 

51  12 

63  12 

76  39 

9100 

106  48 

II 
2.37 

/      // 

0  38 
2  35 
5  49 
10  19 
16  08 
23  14 
3138 
41  18 
52  16 
64  32 
78  05 
92  56 

II 
2.42 

0  39 
2  39 
5  58 
10  34 
16  32 
23  48 
32  25 
42  20 
53  34 
66  08 
80  01 
95  14 

II 
2.48 

1     II 

0  41 
2  43 
6  06 
10  50 
16  56 
24  23 
33  11 
43  21 
54  52 
67  44 
8157 
97  32 

II 
2.54 

0  42 
2  46 
6  14 
1106 
17  20 
24  58 
33  58 
44  22 
56  10 
69  20 
83  54 
99  50 

2.60 

/     // 

0  43 
2  50 
6  23 
1121 
17  44 
25  33 
34  45 
45  23 
57  28 
70  56 
85  50 

2.66 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.324 
28 

0.332 
44 

0.340 
44 

0.348 
30 

0.357 
93 

0.365 
49 

0.374 
75 

0.383 
82 

0.394 
45 

0.404 
83 

0.414 
97 

0.424 

88 

Log. 

Limit 

45 

44 

43 

42 

42 

42 

41 

41 

40 

40 

39 

38 

Min- 
utes 

Merid- 
ian 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1       II 

/      // 

/      // 

/      II 

/     // 

t     II 

1     II 

1      II 

/      II 

/      // 

t     II 

1     11 

Min. 

4 

0  43 

0  45 

0  46 

0  47 

0  49 

0  50 

0  51 

0  54 

0  55 

0  57 

0  59 

102 

4 

8 

2  55 

2  59 

3  04 

3  09 

3  15 

3  20 

3  27 

3  34 

3  41 

3  49 

3  59 

4  07 

8 

12 

6  33 

6  43 

6  53 

7  05 

7  18 

7  30 

7  45 

8  01 

8  17 

8  36 

8  56 

9  16 

12 

16 

1139 

1157 

12  15 

12  35 

12  58 

13  22 

13  47 

14  15 

14  43 

15  16 

15  52 

16  28 

16 

20 

18  12 

18  40 

19  08 

19  40 

20  16 

20  52 

21  32 

22  16 

23  00 

23  52 

24  48 

25  44 

20 

24 

26  12 

26  53 

27  33 

28  19 

29  11 

30  03 

31  00 

32  04 

33  07 

34  22 

35  43 

37  04 

24 

28 

35  41 

36  35 

37  30 

38  33 

39  43 

40  54 

42  13 

43  38 

45  05 

46  47 

48  37 

50  26 

28 

32 

46  36 

47  47 

48  59 

50  21 

51  53 

53  25 

55  08 

57  00 

58  53 

61  06 

63  29 

65  52 

32 

36 

58  58 

60  29 

62  00 

63  43 

65  40 

67  37 

69  46 

72  09 

74  31 

77  20 

36 

40 

72  48 

74  40 

76  32 

78  40 

8104 

83  28 

86  08 

89  04 

92  00 

40 

44 

88  05 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

ir 

II 

Ajh 

2.73 

2.80 

2.87 

2.95 

3.04 

3.13 

3.23 

3.34 

3.45 

3.58 

3.72 

3.86 

A,h 

Log. 

0.436 

0.447 

0.457 

0.469 

0.482 

0.495 

0.509 

0.523 

0.537 

0.553 

0.570 

0.586 

Log. 

16 

16 

88 

82 

87 

54 

20 

75 

82 

88 

54 

59 
29 

Limit 

37 

36 

36 

35 

35 

34 

33 

32 

32 

31 

30 

Min- 
utes 

Merid- 
ian 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

Alti- 
tudes 

Latitude  43°  Declination  Same  Name. 


267 


Declinations. 


Hoar 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

S 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 
4 
9 

17 

26 

38 

52 

68 

4.o: 

// 

04 

18 
40 
12 
52 
41 
40 
47 

5 

1 

1 

4 
10 
17 
28 
40 
55 
71 

II 
4.2 

// 

07 
30 
06 

58 
04 
25 
01 
51 

I 

1 

1 
4 
10 
18 
29 
42 
57 
75 

II 
4.4 

// 

10 
43 
35 
49 
24 
20 
38 
16 

L 

1 

1 
4 

11 

19 

30 

44 

60 

79 

II 
4.6' 

// 

15 
57 
08 
48 
56 
33 
37 
11 

1 

/ 

1 

5 
11 
20 
32 
47 
64 

4.9( 

18 
13 
46 
54 
40 
02 
02 

) 

/      // 

1  23 
5  32 
12  27 
22  09 
34  36 
49  50 

II 
5.19 

/     // 

1  29 
5  55 
13  16 
23  36 
36  52 
53  05 

II 
5.53 

/     // 

1  34 
6  18 
14  13 
25  15 
39  28 
56  50 

II 
5.92 

/      // 

142 
6  48 
15  19 
27  13 
42  32 
61  15 

II 
6.38 

/      // 

151 

7  24 

16  40 

29  36 

46  16 

II 
6.94 

/     // 

2  02 

8  07 

18  15 

32  29 

50  44 

II 
7.61 

/      // 

2  15 

9  01 

20  17 

36  03 

56  20 

II 
8.45 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.605 
31 

0.624 
28 

0.644 
44 

0.666 
52 

0.690 
20 

0.715 
17 

0.742 
73 

0.772 
32 

0.804 
82 

0.841 
36 

0.881 
38 

0.926 
86 

Log. 

Limit 

28 

27 

26 

25 

24 

22 

21 

20 

19 

18 

17 

16 

Min- 
utes 

Merid-;    rj-to 
ian    I    '  ^ 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40 

0      41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/             // 

/      // 

/      // 

/     // 

1 

//    /     // 

/      // 

/     // 

Min. 

Min, 

4 

2  32 

2  55 

3  27 

4 

8 

10  10 

1142 

13  50 

8 

12 

22  52 

26  20 

31  10 

12 

16 

40  40 

46  48 

16 

20 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

t . . 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

ft 

ft 

Ajh 

9.53 

10.97 

12.98 

Ajh 

0.979 

1.040 

1.113 

Log. 

09 

21 

27 

Log. 

Limit 

14 

12 

10 

8 

7 

4 

2 

0 

2 

4 

7 

9 

Min- 
utes 

Merid- 
ian 

83° 

84° 

85° 

86° 

87= 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

Alti- 
tudes 

258 


Latitude  43°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Mill. 

/       // 

/      // 

1     II 

1     II 

/      // 

/      // 

/      // 

/      // 

'        n 

1     II 

1     II 

1     II 

Min. 

4 

2  56 

2  24 

2  01 

143 

1  31 

120 

1  10 

103 

0  58 

0  51 

0  49 

0  43 

4 

8 

11  45 

9  37 

8  05 

6  56 

6  01 

5  18 

4  43 

4  13 

3  49 

3  27 

3  08 

2  51 

8 

12 

26  27 

21  37 

18  10 

15  35 

13  33 

11  58 

10  37 

9  31 

8  34 

7  45 

7  04 

6  26 

12 

16 

38  27 

32  18 

27  41 

24  07 

21  14 

18  51 

16  53 

15  14 

13  47 

12  32 

1126 

16 

20 

50  28 

43  16 

37  40 

33  12 

29  28 

26  24 

23  48 

21  32 

19  36 

17  52 

20 

24 

47  48 

42  26 

38  01    34  16 

3100 

28  13 

25  44 

24 

28 

51  45'  46  39 

42  13 

38  25 

35  01 

28 

32 

60  56 

55  08 

50  11 

45  44 

32 

36 

63  30 

57  44 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

n 

II 

" 

// 

II 

n 

II 

II 

II 

II 

II 

A,h 

11.02 

9.01 

ijn 

6.49 

5.65 

4.98 

4.42 

3.96 

3.57 

3.23 

2.94 

2.68 

A,h 

Log. 

1.042 

0.954 

0.879 

0.812 

0.752 

0.697 

0.645 

0.597 

0.552 

0.509 

0.468 

0.428 

Log. 

18 

72 

10 

\ 

24 

05 

23 

42 

70 

67 

20 

35 

13 
32 

Limit 

11 

13 

15 

16 

18 

20 

22 

24 

26 

28 

30 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

Declinations. 

Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

/     // 

/      // 

/     // 

/     // 

/      // 

/      // 

/      // 

/      // 

/     // 

/      // 

Min. 

Min. 

4 

0  39 

0  36 

0  33 

0  30 

0  28 

0  26 

0  24 

0  22 

0  20 

0  19 

0  17 

0  15 

4 

8 

2  38 

2  24 

2  13 

2  02 

153 

143 

1  36 

1  28 

122 

1  15 

109 

103 

8 

12 

5  55 

5  24 

4  58 

4  35 

4  14 

3  53 

3  36 

3  17 

3  03 

2  48 

2  36 

2  33 

12 

16 

10  29 

9  36 

8  50 

8  09 

7  30 

6  55 

6  21 

5  51 

5  25 

5  00 

4  36 

4  13 

16 

20 

16  24 

15  00 

13  48 

12  44 

1144 

10  48 

9  56 

9  08 

8  28 

7  48 

7  12 

6  36 

20 

24 

23  37 

21  36 

19  52 

18  20 

16  54 

15  04 

14  18 

13  09 

12  11 

11  14 

10  22 

9  30 

24 

28 

32  09 

29  24 

27  03 

24  58 

23  00 

21  10 

19  29 

17  54 

16  36 

15  17 

14  07 

12  57 

28 

32 

4159 

38  24 

35  20 

32  36 

30  02 

27  38 

25  26 

23  23 

21  41 

19  58 

18  26 

16  54 

32 

36 

53  08 

48  36 

44  43 

41  15 

38  01 

35  00 

31  11 

29  36 

27  26 

25  17 

23  20 

21  23 

36 

40 

65  36 

60  00 

55  12 

50  56 

46  56 

43  12 

39  44 

36  32 

33  52 

31  12 

28  48 

26  24 

40 

44 

72  36 

66  48 

6137 

56  47 

52  17 

48  04 

44  13 

40  59 

37  46 

34  51 

3156 

44 

48 

73  21 

67  33 

62  12 

57  13 

52  36 

48  46 

44  55 

41  28 

38  01 

48 

52 

79  19 

73  00 

67  09 

61  44 

57  14 

52  43 

48  40 

44  37 

52 

56 

77  52 

7137 

66  23 

61  10 

56  27 

51  44 

56 

60 

76  12 

70  12 

64  48 

59  24 

60 

/' 

" 

II 

" 

II 

" 

" 

II 

" 

II 

II 

II 

A,h 

2.46 

2.25 

2.07 

1.91 

1.76 

1.62 

1.49 

1.37 

1.27 

1.17 

1.08 

0.99 

A,h 

Log. 

0.390   0.352 

0.315 

0.281 

0.245 

0.209 

0.173 

0.136 

0.103 

0.068 

0.033 

9.995 

Log. 

94 

18 

97 

03 

51 

52 

19 

72 

80 

19 

42 

64 

Limit 

34 

36 

38 

40 

42 

43 

45 

47 

49 

51 

54 

57 

Min- 
utes 

Merid- 
ian 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

Alti- 
tudes 

Latitude  43"  Declination  Contrary  Name. 


259 


Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

// 
2.11 

1     II 

0  33 
2  13 
4  58 
8  50 

13  48 
19  52 
27  03 
35  20 
44  43 
55  12 
66  48 
79  29 
93  17 

II 
2.07 

1     1' 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

9129 

106  06 

2.03 

1       n 

0  31 
2  07 

4  47 
8  29 
13  16 
19  06 
26  01 
33  58 
42  59 
53  04 
64  12 
76  25 
89  41 
104  01 

1.99 

/       n 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

1.96 

/       n 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

41  28 

51  12 

61  57 

73  44 

86  32 

100  21 

1.92 

/     // 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 

II 

1.89 

0  30 
159 

4  28 
7  56 
12  24 
17  52 
24  18 
3144 
40  11 
49  36 
60  01 
71  25 
83  49 
97  13 

11136 

II 

1.86 

0  29 
157 
4  23 

7  49 
12  12 
17  34 
23  55 
31  13 
39  32 
48  48 
59  03 
70  16 
82  28 
95  39 

109  48 

II 

1.83 

1       n     1       II 

0  29     0  28 

1  55      1  54 
4  19     4  16 
7  41      7  33 

12  00    1148 

17  17    16  59 

23  31    23  08 

30  43    30  13 

38  53    38  14 

48  00    47  12 

58  05    57  07 

69  07    67  56 

81  07j  79  46 

94  051  92  31 

108  00  106  12 
//          // 

1.80     1.77 

/      II 

0  28 

152 
4  11 
7  25 
11  36 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 
90  56 

104  24 

II 

1.74 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.324 

28 

0.315 
97 

0.307 
50 

0.298 

85 

0.292 
26 

0.283 
30 

0.276 
46 

0.269 
51 

0.262 
45 

0.255 
27 

0.247 
97 

0.240 
55 

Log. 

Limit 

45 

45 

46 

46 

47 

48 

48 

49 

49 

50 

51 

51 

Min- 
utes 

Merid- 
ian   1 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

'       // 

/      /' 

t      II 

/      // 

1     II 

1     II 

1     It 

1     II 

/      // 

/      II 

/     // 

/     // 

Min. 

4 

0  27 

0  27 

0  27 

0  27 

0  26 

0  25 

0  25 

0  25 

0  24 

0  23 

0  23 

0  23 

4 

8 

1  50 

148 

1  46      1  45 

142 

1  42 

140 

1  39 

1  36 

136 

134 

133 

8 

12 

4  06 

4  03 

3  59     3  56 

3  51 

3  49 

3  45 

3  42 

3  37 

3  35 

3  32 

3  29 

12 

16 

7  18 

7  13 

7  05 

7  00 

6  53 

6  47 

6  39 

6  34 

6  27 

6  21 

6  16 

6  11 

16 

20 

1124 

11  16 

1104 

10  56 

10  44 

10  36 

10  24 

10  16 

10  04 

9  56 

9  48 

9  40 

20 

24 

16  25 

16  14 

15  57 

15  45 

15  28 

15  16 

14  59 

14  47 

14  30 

14  18 

14  06 

13  55 

24 

28 

22  21 

22  05 

2141 

21  25 

2102 

20  47 

20  23 

20  07 

19  44 

19  29 

19  13 

18  57 

28 

32 

29  11 

28  50 

28  19 

27  59 

27  28 

27  08 

26  37 

26  17 

25  46 

25  26 

25  06 

24  45 

32 

36 

36  56 

36  31 

35  52 

35  26 

34  47 

34  21 

33  42 

33  16 

32  37 

32  11 

31  45 

31  19 

36 

40 

45  36 

45  04 

44  16 

43  44 

42  56 

42  24 

41  36 

41  04 

40  16 

39  44 

39  12 

38  40 

40 

44 

55  10 

54  32 

53  24 

52  55 

5157 

51  18 

50  20 

49  41 

48  43 

48  04 

47  26 

46  47 

44 

48 

65  38 

64  53 

63  44 

62  58 

6149 

6103 

59  54 

59  08 

57  59 

57  13 

56  27 

55  41 

48 

52 

77  04 

76  09 

74  48 

73  54 

72  33 

71  39 

70  18 

69  24 

68  03 

67  09 

66  15 

65  21 

52 

56 

89  22 

88  20 

86  46 

85  43 

84  09 

83  06 

81  32 

80  29 

78  55 

77  52 

76  50 

75  37 

56 

60 

102  36 
II 

10124 
II 

99  36 

98  24 

II 

96  36 

95  24 

93  36 
II 

92  24 
II 

90  36 

II 

89  24 

88  12 

87  00 

60 

Ajh 

1.71 

1.69 

1.66 

1.64 

1.61 

1.59 

1.56 

1.54 

1.51 

1.49 

1.47 

1.45 

A,h 

Log. 

0.233 

0.227 

0.220,  0.214 

0.206 

0.201 

0.193 

0.187 

0.178 

0.173 

0.167 

0.161 

00 

89 

11 

84 

83 

40 

12 

52 

98 

19 

32 

37 

Log. 

Limit 

52 

53 

54 

55 

55 

56 

57 

58 

58 

59 

60 

61 

Min- 
utes 

Merid- 
ian 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

260 


Latitude  43°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  23 

132 

3  24 

6  06 

9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
II 

1.43 

/  // 

0  22 

130 

3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 

II 

1.40 

/  // 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 
II 

1.38 

1     II 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

8136 

II 

1.36 

/  // 

0  22 

126 

3  13 

5  43 

8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

5127 

60  23 

70  02 

80  24 

II 

1.34 

/  // 

0  21 

124 

3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 

II 

1.32 

/  // 

0  21 
123 
3  07 
5  33 

8  40 
12  29 
16  59 
22  11 
28  05 
34  40 
4157 
49  55 
58  35 
67  57 

78  00 

II 

1.30 

/  // 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
II 

1.28 

/  // 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 

II 

1.26 

/   // 

0  20 

120 

2  59 

5  17 

8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
II 

1.24 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 

15  57 

20  49 

26  21 

32  32 

39  12 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

/   n 

0  19 

1  17 

2  53 
5  07 
8  00 

1131 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
II 

1.20 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.155 
34 

0.146 
13 

0.139 

88 

0.133 
54 

0.127 
10 

0.120 
57 

0.113 
94 

0.107 
21 

0.100 
37 

0.093 
42 

0.086 
36 

0.079 
18 

Log. 

Limit 

62 

62 

63 

64 

65 

66 

67 

67 

68 

69 

70 

71 

Min- 
uteH 

Merid- 
ian 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   // 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 

15  33 

20  18 

25  43 

31  44 

38  24 

45  41 

53  37 

62  12 

7124 
II 

1.19 

/  // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

1.17 

/  // 

0  19 

113 

2  45 

4  55 

7  40 

1103 

15  01 

19  37 

24  51 

30  40 

37  07 

42  09 

51  49 

60  07 

69  00 

II 

1.15 

1     II 

0  19 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  11 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 

67  48 

II 

1.13 

/  // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

1     II 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 

65  24 

II 

1.09 

/   // 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
41  05 
48  13 
55  56 

64  12 

II 

1.07 

II 

II 

// 

II 

// 

1 

1 

// 

/  // 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

0.075 
55 

0.068 
19 

0.060 
70 

0.053 
08 

0.045 
32 

0.037 
43 

0.029 
38 

Log. 

Limit 

72 

73 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

Alti- 
tudes 

Latitude  43°  Declination  Contrary  Name* 

Declinations.  —  Inferior  Meridian. 


261 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57°      58° 

59° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

It 

// 

1 

II 

// 

1     II 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

/     // 

0  14 
0  55 

2  05 

3  43 

5  48 
8  21 
11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

II 

0.87 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 
5100 

0.85 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

/     // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

3106 

36  30 

42  20 

48  36 

II 

0.81 

/     // 

0  12 

0  51 

1  54 
3  22 
5  16 
7  35 

10  20 
13  29 
17  04 
2104 
25  29 
30  18 
35  36 
41  17 

47  24 

II 

0.79 

/      // 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

II 

0  12 

0  49 

1  50 
3  14 
5  04 
7  18 
9  56 

12  58 
16  25 
20  16 
24  31 
29  09 
34  15 
39  43 

45  36 

II 

0.76 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.944 

48 

9.939 
52 

9.929 
42 

9.919 
08 

9.908 
49 

9.897 
63 

9.886 
49 

9.880 
81 

Log. 

Limit 

71 

71 

72 

73 

75 

77 

78 

80 

Min- 
utes 

Merid- 
ian 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/      // 

/     // 

/      // 

/      // 

1     II 

/     // 

/     // 

/      // 

/     // 

Min. 

Min. 

4 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

0  10 

0  09 

0  09 

0  09 

0  09 

0  08 

4 

"     8 

0  47 

0  46 

0  44 

0  42 

0  41 

0  40 

0  39 

0  38 

0  37 

0  35 

0  34 

0  33 

8 

12 

147 

1  44 

1  39 

136 

133 

1  30 

127 

125 

122 

1  19 

1  16 

1  13 

12 

16 

3  09 

3  04 

2  57 

2  52 

2  47 

2  42 

2  37 

2  31 

2  26 

2  21 

2  16 

2  11 

16 

20 

4  56 

4  48 

4  36 

4  28 

4  20 

4  12 

4  04 

3  56 

3  48 

3  40 

3  32 

3  24 

20 

24 

7  06 

6  55 

6  38 

6  26 

6  15 

6  03 

5  52 

5  40 

5  28 

5  17 

5  05 

4  54 

24 

28 

9  40 

9  25 

9  01 

8  45 

8  29 

8  14 

7  58 

7  43 

7  27 

7  11 

6  56 

6  40 

28 

32 

12  38 

12  17 

11  46 

11  26 

1105 

10  45 

10  24 

10  04 

9  44 

9  23 

9  03 

8  42 

32 

36 

15  59 

15  33 

14  55 

14  29 

14  03 

13  37 

13  11 

12  45 

12  18 

11  53 

11  27 

11  01 

36 

40 

19  44 

19  12 

18  24 

17  52 

17  20 

16  48 

16  16 

15  44 

15  12 

14  40 

14  08 

13  36 

40 

44 

23  52 

23  14 

22  16 

2138 

20  59 

20  20 

19  41 

19  02 

18  24 

17  45 

17  06 

16  27 

44 

48 

28  23 

27  37 

26  29 

25  43 

24  57 

24  11 

23  25 

22  39 

21  54 

21  07 

20  21 

19  35 

48 

52 

33  21 

32  27 

3105 

30  11 

29  17 

28  23 

27  29 

26  35 

25  41 

24  47 

23  53 

22  59 

52 

56 

38  40 

37  38 

36  04 

35  02 

33  59 

32  56 

31  53 

30  50 

29  48 

28  45 

27  42 

26  39 

56 

60 

44  24 

43  12 

41  24 

40  12 

39  00 

37  48 

36  36 

35  24 

34  12 

33  00 

3148 

30  36 

60 

" 

II 

II 

II 

II 

II 

" 

" 

II 

" 

II 

II 

A,h 

0.74 

0.72 

0.69 

0.67 

0.65 

0.63 

0.61 

0.59 

0.57 

0.55 

0.53 

0.51 

A,h 

Log. 

9.869 

9.857 

9.838 

9.826 

9.812 

9.799 

9.785 

9.770 

9.755 

9.740 

9.724 

9.707 

Log. 

23 

33 

85 

07 

91 

34 

33 

85 

87 

36 

28 
85 

57 

Limit 

81 

81 

81 

82 

83 

84 

84 

84 

84 

85 

86 

Min- 
utes 

Merid- 
ian 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

Alti- 
tudes 

262 


Latitude  44°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

•^"     1     ■'••'•      lAngles 

Mill. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/        n 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

91  29 

If 
2.03 

0  33 
2  13 

4  58 
8  50 
13  48 
19  52 
27  03 
35  20 
44  43 
55  12 
66  48 
79  29 
93  17 

II 
2.07 

/      // 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

95  05 

n 

2.11 

/     // 

0  35 

2  17 
5  09 
9  11 
14  20 
20  39 
28  05 
36  41 
46  27 
57  20 
69  23 
82  33 
96  53 

II 
2.15 

/     // 

0  35 
2  20 
5  15 
9  21 

14  36 
21  02 
28  37 
37  22 
•47  19 
58  24 
70  40 
84  05 
98  41 

II 
2.19 

/     // 

0  36 
2  24 
5  23 
9  33 

14  56 
21  30 
29  16 
38  14 
48  23 
59  44 
72  16 
86  01 
100  57 

2.24 

/     // 

0  36 

2  26 

5  29 

9  43 

15  12 

2153 

29  48 

38  55 

49  15 

60  48 

73  34 

87  33 

102  45 

II 
2.28 

t     II 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

2.33 

/     // 

0  38 

2  32 

5  43 

10  09 

15  52 

22  51 

3106 

40  37 

5125 

63  28 

76  48 

91  23 

107  15 

2.38 

/     // 

0  38 
2  36 
5  50 
10  22 
16  12 
23  19 
3146 
41  29 
52  29 
64  48 
78  24 
93  19 

II 
2.43 

/       // 

0  39 
2  40 
5  59 
10  37 
16  36 
23  54 
32  33 
42  30 
53  47 
66  24 
80  20 
95  37 

// 
2.49 

/     // 

0  41 
2  43 
6  07 
10  53 
17  00 
24  29 
33  19 
43  31 
55  05 
68  00 
82  17 

II 
2.55 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.307 
50 

0.315 
97 

0.324 

28 

0.332 
44 

0.340 
44 

0.350 
25 

0.357 
93 

0.367 
36 

0.376 
58 

0.385 
61 

0.396 
20 

0.406 
54 

Log. 

Limit 

46 

45 

44 

43 

43 

43 

.42 

42 

41 

41 

40 

39 

Min- 
utes 

Merid- 
ian 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

/      // 

'           H 

/     // 

/     // 

/     // 

Min. 

4 

0  42 

0  43 

0  44 

0  45 

0  46 

0  47 

0  49 

0  51 

0  52 

0  54 

0  56 

0  58 

4 

8 

2  47 

2  51 

2  56 

3  00 

3  05 

3  10 

3  16 

3  22 

3  29 

3  36 

3  44 

3  52 

8 

12 

6  15 

6  24 

6  35 

6  44 

6  56 

7  10 

7  21 

7  35 

7  50 

8  05 

8  24 

8  42 

12 

16 

1109 

1124 

11  41 

12  00 

12  20 

12  42 

13  03 

13  29 

13  54 

14  23 

14  56 

15  30 

16 

20 

17  24 

17  48 

18  16 

18  44 

19  16 

19  52 

20  24 

21  04 

2144 

22  28 

23  20 

24  12 

20 

24 

25  04 

25  38 

26  18 

26  59 

27  45 

28  36 

29  23 

30  21 

31  18 

32  21 

33  36 

34  51 

24 

28 

34  06 

34  53 

35  48 

36  43 

37  46 

38  57 

39  59 

41  17 

42  36 

44  02 

45  44 

47  26 

28 

32 

44  32 

45  34 

46  46 

47  57 

49  19 

50  52 

52  13 

53  55 

55  38 

57  31 

59  44 

61  57 

32 

36 

56  23 

57  41 

59  11 

60  42 

62  26 

64  22 

66  06 

68  16 

70  25 

72  48 

75  36 

78  25 

36 

40 

69  36 

71  12 

73  04 

74  56 

77  04 

79  28 

8136 

84  16 

86  56 

89  52 

40 

44 

84  13 

86  10 

88  24 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

n 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.61 

2.67 

2.74 

2.81 

2.89 

2.98 

3.06 

3.16 

3.26 

3.37 

3.50 

3.63 

A,h 

Log. 

0.416 

0.426 

0.437 

0.448 

0.460 

0.474 

0.485 

0.499 

0.513 

0.527 

0.544 

0.559 

Log. 

64 

51 

75 

71 

90 

22 

72 

69 

22 

63 

07 

91 

Limit 

33 

35 

37 

37 

36 

35 

34 

33 

33 

32 

31 

30 

Min- 
utes 

Merid- 
ian 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

Alti- 
tudes 

Latitude  44°  Declination  Same  Name. 


263 


Declinations. 


Hour 

Angl»8 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 
4 
9 

16 
25 
36 
49 
64 

n 

3.7 

00 

02 
03 
05 
08 
11 
16 
21 

7 

/ 

1 
4 
9 
16 
26 
37 
51 
67 

// 
3.9 

// 

03 
11 
26 
46 
12 
43 
22 
35 

1 
4 
9 

17 
27 
39 
53 
70 

II 
4.1 

// 

06 
23 
51 
33 
24 
28 
42 
38 

I 

1 
4 
10 
18 
28 
41 
56 
73 

II 
4.3 

// 

09 
35 
19 
21 
40 
17 
11 
23 

3 

/ 

1 
1 
3 
4 
5 

4 

1 
4 
0 

9 
0 
3 
9 

// 
.5 

// 

12 

49 
51 
17 
38 
24 
)i 

2 

/ 

1 
2 
3 
4 
6 

4 

1 
5 

1 
0 
1 
5 

2 

// 

.7 

16 

06 
27 
21 
48 
47 
18 

7 

1 
5 
12 
21 
33 
48 
66 

II 
5.0 

21 
24 
09 
35 
44 
35 
37 

3 

/      // 

1  26 
5  44 
12  55 
22  57 
35  52 
51  39 
70  18 

II 
5.38 

/      // 

132 

6  09 
13  50 
23  34 
38  24 
55  18 

II 
5.76 

/      // 

139 

6  38 
14  54 
26  30 
41  24 
59  27 

II 
6.21 

/     // 

148 

7  18 

16  11 

28  45 

44  56 

6.74 

/      // 

1  58 

7  54 

17  46 

31  34 

49  20 

7.40 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.576 
34 

0.594 
39 

0.613 

84 

0.633 

47 

0.655 
14 

0.678 
52 

0.704 
15 

0.730 

78 

0.760 
42 

0.793 
09 

0.828 
66 

0.869 
23 

Log. 

Limit 

29 

28 

27 

26 

25 

24 

23 

21 

20 

19 

18 

17 

Min- 
utes 

Merid- 
ian 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

2 

8 

19 

35 

54 

8.2 

// 

11 

46 
42 
32 
44 

I 

2 

9 

22 
39 

II 
9.2( 

28 
53 
14 
30 

3 

/ 

2 
11 
25 

10.6. 

51 

21 
33 

5 

/ 

3 

13 
30 

II 
12.5< 

// 

21 
26 
13 

3 

II 

// 

II 

1 

II 

// 

II 

// 

/ 

/ 

// 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.914 
34 

0.966 
61 

1.027 
35 

1.100 
03 

Log. 

Limit 

16 

14 

12 

10, 

9 

6 

4 

2 

0 

2 

4 

6 

Min- 
utes 

Merid- 
ian 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87^ 

Alti- 
tudes 

264 


Latitude  44°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min, 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

n 

// 

/ 

2 

11 
25 
45 

II 
10.6 

II 

50 
20 
30 
22 

3 

1 

2 

9 

20 

37 

II 
8.6 

n 

19 
16 
51 
35 

3 

t 

1 

7 

17 

-31 

48 

II 
7.2< 

II 

56 
i7 
30 
36 
36 

3 

/     II 

1  40 

6  40 

15  00 

26  40 

4140 

II 
6.25 

1 

5 

13  ( 
23 
36 
52 

II 
5.4 

If 

27 
19 
34 
12 
16 
13 

i 

/     // 

1  16 
5  06 
11  29 
20  23 
31  52 
45  53 

II 

4.78 

t 

1 

1 
2 

4 

5 

4 

1 
4 
0 
8 
8 
0 
5 

// 
.2 

n 

38 
32 
12 
38 
20 
18 
32 

5 

/     // 

101 
4  03 
9  07 
16  13 
25  20 
36  29 
49  39 

II 
3.80 

0  54 

3  39 

8  13 

14  35 

22  48 
32  50 
44  42 
58  22 

II 
3.42 

/     // 

0  50 
3  18 
7  25 
13  11 
20  36 
29  40 
40  23 
52  44 
66  45 

3.09 

0  45 
3  00 
6  44 
12  00 
18  44 
26  59 
36  43 
47  57 
60  42 

II 
2.81 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

1.026 
53 

0.939 
02 

0.862 
73 

0.795 
88 

0.735 
60 

0.679 
43 

0.628 
39 

0.579 
78 

0.534 
03 

0.489 
96 

0.448 
71 

Log. 

Limit 

9 

12 

14 

15 

17 

19 

21 

23 

25 

27 

29 

31 

Min- 
utes 

Merid- 
ian 

8{ 

)° 

85= 

3 

84= 

) 

83< 

3 

82° 

81 

3 

80° 

rg 

3 

78< 

3 

77 

3 

76 

3 

75° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     /' 

/      // 

/     // 

/     // 

/      // 

/      " 

/      // 

/      // 

/     // 

/     // 

/      II 

Min. 

4 

0  41 

0  38 

0  35 

0  31 

0  29 

0  27 

0  24 

0  22 

0  21 

0  19 

0  18 

0  16 

4 

8 

2  44 

2  30 

2  17 

2  06 

156 

146 

1  38 

130 

123 

1  17 

1  10 

104 

8 

12 

6  09 

5  37 

5  09 

4  44 

4  20 

3  59 

3  40 

3  23 

3  07 

2  53 

2  38 

2  24 

12 

16 

10  55 

9  59 

9  11 

8  24 

7  44 

7  05 

6  32 

6  01 

5  33 

5  07 

4  42 

4  16 

16 

20 

17  04 

15  36 

14  20 

13  08 

12  04 

1104 

10  12 

9  24 

8  40 

8  00 

7  20 

6  40 

20 

24 

24  35 

22  28 

20  39 

18  44 

17  23 

15  57 

14  41 

13  32 

12  29 

11  31 

10  34 

9  36 

24 

28 

33  27 

30  34 

28  05 

25  45 

23  39 

21  41 

20  00 

18  26 

16  59 

15  41 

14  22 

13  04 

28 

32 

43  41 

39  56 

36  41 

33  38 

30  53 

28  19 

26  07 

23  04 

22  11 

20  29 

18  46 

17  04 

32 

36 

55  18 

50  33 

46  27 

42  33 

39  06 

35  52 

33  02 

30  27 

28  05 

25  55 

23  46 

21  36 

36 

40 

68  16 

62  24 

57  20 

52  32 

48  16 

44  16 

40  48 

37  36 

34  40 

32  00 

29  20 

26  40 

40 

44 

75  30 

69  23 

63  34 

58  24 

53  34 

49  22 

45  29 

4157 

38  43 

35  30 

32  16 

44 

48 

75  39 

69  30 

63  44 

58  45 

54  09 

49  55 

46  05 

42  14 

38  24 

48 

52 

74  48 

68  57 

63  33 

58  35 

54  05 

49  34 

45  04 

52 

56 

73  41 

67  57 

62  43 

57  30 

52  16 

56 

60 

78  00 

72  00 

66  00 

60  00 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

" 

A,h 

2.56 

2.34 

2.15 

1.97 

1.81 

1.66 

1.53 

1.41 

1.30 

1.20 

1.10 

1.00 

A,h 

• 
Log. 

0.408 

0.369 

0.332 

0.294 

0.257 

0.220 

0.184 

0.149 

0.113 

0.079 

0.041 

0.00 

Log. 

24 

22 

44 

47 

68 
41 

11 

69 

22 

94 

18 

39 

Limit 

33 

35 

37 

39 

42 

44 

46 

48 

50 

53 

56 

Min- 
utes 

Merid- 
ian 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

Alti- 
tudes 

Latitude  44°  Declination  Contrary  Name* 


265 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7°   8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  II 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

9129 

2.03 

1      II 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

2.00 

/  // 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

1.96 

/  // 

0  30 

2  03 

4  38 

8  14 

12  52 

18  31 

25  14 

32  57 

41  41 

5128 

62  16 

74  07 

86  59 

100  52 

II 
1.93 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

4102 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 

II 

1.90 

/  II 

0  30 

159 

4  28 

7  56 

12  24 

17  52 

24  18 

3144 

40  11 

49  36 

60  01 

7125 

83  49 

97  13 

111  36 
II 

1.86 

/  // 

0  29 

1  57 
4  23 
7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
II 

1.83 

/  // 

0  29 

155 

4  19 

7  41 

12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

8107 

94  05 

108  00 
II 

1.80 

/  // 

0  28 
154 
4  16 
7  33 

11  48 
16  59 
23  08 
30  13 
38  14 
47  12 
57  07 
67  56 
79  46 
92  31 
106  12 

1.77 

/  // 

0  28 

152 

4  12 

7  28 

11  40 

16  48 

22  52 

29  52 

37  48 

46  40 

56  28 

67  10 

78  52 

9128 

105  00 

1.75 

/  // 

0  27 

150 

4  08 

7  20 

11  28 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 

1.72 

/   // 

0  27 

1  48 
4  03 
7  13 

11  16 
16  14 
22  05 
28  51 
36  31 
45  04 
54  32 
64  53 
76  09 
88  20 
101  24 

1.69 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.307 
50 

0.301 
03 

0.292 
26 

0.285 
56 

0.278 
75 

0.269 
51 

0.262 
45 

0.255 
27 

0.247 
97 

0.243 
04 

0.235 
53 

0.227 
89 

Log. 

Limit 

46 

46 

47 

47 

48 

48 

49 

50 

50 

51 

52 

52 

Min- 
utes 

^f/^^-  46°  !  45° 

44°  1  43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

Alti- 
tudes 

Declin.\tions. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/   // 

/  // 

/  II 

/  // 

/  // 

/  // 

/  // 

/  // 

1     II 

/  // 

1     II 

/   // 

Min. 

4 

0  27 

0  27 

0  26 

0  25 

0  25 

0  25 

0  24 

0  24 

0  23 

0  23 

0  22 

0  22 

4 

8 

147 

1  45 

143 

142 

141 

1  39 

137 

1  36 

135 

133 

1  32 

130 

8 

12 

4  00 

3  56 

3  53 

3  49 

3  46 

3  42 

3  39 

3  36 

3  34 

3  29 

3  24 

3  23 

12 

16 

7  08 

7  00 

6  55 

6  47 

6  42 

6  34 

6  29 

6  24 

6  18 

6  11 

6  06 

6  01 

16 

20 

1108 

10  56 

10  48 

10  36 

10  28 

10  16 

10  08 

10  00 

9  52 

9  40 

9  32 

9  24 

20 

24 

16  02 

15  45 

15  34 

15  16 

15  04 

14  47 

14  36 

14  24 

14  12 

13  55 

13  43 

13  32 

24 

28 

2149 

21  25 

21  10 

20  47 

20  31 

20  07 

19  52 

19  36 

19  21 

18  57 

18  42 

18  26 

28 

32 

28  30 

27  59 

27  38 

27  08 

26  48 

26  17 

25  56 

25  36 

25  16 

24  45 

24  25 

24  04 

32 

36 

36  05 

35  26 

35  00 

34  21 

33  55 

33  16 

32  50 

32  24 

3158 

31  19 

30  53 

30  27 

36 

40 

44  32 

43  44 

43  12 

42  24 

41  52 

41  04 

40  32 

40  00 

39  28 

38  40 

38  08 

37  36 

40 

44 

53  54 

52  55 

52  17 

51  18 

50  40 

49  41 

49  03 

48  24 

47  45 

46  47 

46  08 

45  29 

44 

48 

64  07 

62  58 

62  12 

61  03 

60  17 

59  08 

58  22 

57  36 

56  50 

55  41 

54  55 

54  09 

48 

52 

75  15 

73  54 

73  00 

7139 

70  45 

69  24 

68  30 

67  36 

66  42 

65  21 

64  27 

63  33 

52 

56 

87  18 

85  43 

84  41 

83  06 

82  04 

80  29 

79  27 

78  24 

77  21 

75  37 

74  44 

73  41 

56 

60 

100  12 

98  24 

97  12 
II 

95  24 

94  12 

92  24 

II 

91  12 

90  00 

II 

88  48 
II 

87  00 
II 

85  48 
II 

84  36 
II 

60 

A,h 

1.67 

1.64 

1.62 

1.59 

1.57 

1.54 

1.52 

1.50 

1.48 

1.45 

1.43 

1.41 

A,h 

Log. 

0.222 

0.214 

0.209 

0.201 

0.195 

0.187 

0.181 

0.176 

0.170 

0.161 

0.155 

0.149 

Log. 

72 

84 

52 

40 

90 

52 

84 

09 

26 

37 

34 

22 

Limit 

53 

54 

55 

56 

56 

57 

58 

59 

59 

59 

60 

61 

Min- 
utes 

Merid- 
ian 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

Alti- 
tudes 

266 


Latitude  44°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/   // 

1      II 

/  // 

/  // 

'  // 

1        n 

1     II 

/  // 

/  // 

/  // 

/  // 

1     II 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  21 

0  20 

0  20 

0  20 

0  19 

0  19 

0  19 

0  19 

4 

8 

1  29 

1  28 

126 

1  25 

1  23 

123 

1  21 

120 

1  19 

1  18 

1  16 

1  15 

8 

12 

3  20 

3  17 

3  14 

3  11 

3  08 

3  06 

3  03 

3  00 

2  57 

2  56 

2  51 

2  50 

12 

16 

5  56 

5  51 

5  46 

5  41 

5  36 

5  30 

5  25 

5  20 

5  15 

5  12 

5  05 

5  02 

16 

20 

9  16 

9  08 

9  00 

8  52 

8  44 

8  36 

8  28 

8  20 

8  12 

8  08 

7  56 

7  52 

20 

24 

13  21 

13  09 

12  58 

12  46 

12  35 

12  23 

12  11 

12  00 

11  48 

11  43 

11  26 

11  20 

24 

28 

18  10 

17  54 

17  38 

17  23 

17  07 

16  52 

16  36 

16  20 

16  05 

15  57 

15  33 

15  25 

28 

32 

23  43 

23  23 

23  02 

22  42 

22  21 

22  01 

21  41 

21  20 

21  00 

20  49 

20  18 

20  08 

32 

36 

30  02 

29  36 

29  10 

28  44 

28  18 

27  52 

27  26 

27  00 

26  34 

26  21 

25  43 

25  30 

36 

40 

37  04 

36  32 

36  00 

35  28 

34  56 

34  24 

33  52 

33  20 

32  48 

32  32 

31  44 

31  28 

40 

44 

44  51 

44  13 

43  34 

42  55 

42  16 

41  37 

40  59 

40  20 

39  41 

39  12 

38  24 

38  05 

44 

48 

53  22 

52  36 

51  50 

5104 

50  18 

49  32 

48  46 

48  00 

47  14 

46  51 

45  41 

45  18 

48 

52 

62  38 

61  44 

60  50 

59  56 

59  02 

58  08 

57  14 

56  20 

55  26 

54  59 

53  37 

53  10 

52 

56 

72  39 

7137 

70  34 

69  31 

68  28 

67  25 

66  23 

65  20 

64  17 

63  46 

62  12 

6141 

56 

60 

83  24 

82  12 

8100 

79  48 

II 

78  36 

II 

77  24 

76  12 

II 

75  00 

II 

73  48 
II 

73  12 

II 

71  24 

II 

70  48 

II 

60 

A,h 

1.39 

1.37 

1.35 

1.33 

1.31 

1.29 

1.27 

1.25 

1.23 

1.22 

1.19 

1.18 

Aih 

Log. 

0.143 

0.136 

0.130 

0.123 

0.117 

0.110 

0.103 

0.096 

0.089 

0.086 

0.075 

0.071 

Log. 

01 

72 

33 

85 

27 

59 

80 

91 

91 

36 

55 

88 

Limit 

62 

63 

64 

65 

66 

67 

68 

68 

69 

70 

71 

72 

Min- 
utes 

Merid- 
ian 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

II 

1.17 

/  // 

0  19 

1  13 

2  45 
4  55 
7  40 

11  03 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

51  49 

60  07 

69  00 
II 

1.15 

/  // 

0  18 

1  11 

2  41 

4  47 

7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

1     II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

/  // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 
65  24 

1.09 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 
II 

1.07 

1 

// 

1 

// 

// 

1 
II 

// 

1 

II 

II 

II 

II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.068 
19 

0.060 
70 

0.049 
22 

0,045 
32 

0.037 
43 

0.029 
38 

Log. 

Limit 

73 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

Alti- 
tudes 

Latitude  44°  Decimation  Contrary  Name* 

Declixations.  —  Inferior  Meridian. 


267 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aji 

/ 

// 

n 

// 

// 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

II 

0.89 

/      // 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

0.87 

/     // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

51  36 
II 

0.86 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

0  13 
0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

0.82 

1     II 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
II 

0.80 

/      // 

0  12 

0  50 

1  52 
3  19 
5  12 
7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

/     // 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  44 

45  36 
II 

0.76 

1     II 
0  12 

0  48 

1  48 
3  12 
5  00 
7  12 
9  48 

12  48 
16  12 
20  00 
24  12 
28  46 
33  48 
39  12 

45  00 

II 

0.75 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

• 

9.949 
39 

9.939 
52 

9.934 
50 

9.924 
28 

9.913 
81 

9.903 
09 

9.892 
09 

9.880 
81 

9.875 
06 

Log. 

Limit 

69 

70 

71 

72 

73 

74 

76 

78 

80 

Min- 
utes 

Merid- 
ian 

2 

o 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour  j    £.r>o 
Angles     °" 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

±lour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  12 

0  47 

1  45 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

/      // 

Oil 
0  45 
142 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  06 
42  36 

0.71 

/     // 

Oil 
0  43 

137 

2  54 

4  32 

6  32 

8  53 

1136 

14  42 

18  08 

2157 

26  06 

30  38 

35  33 

40  48 
II 

0.68 

/     // 

0  11 

0  42 

136 

2  52 

4  28 

6  26 

8  45 

11  26 

14  29 

17  52 

21  38 

25  43 

30  11 

35  02 

40  12 
II 

0.67 

0  11 

0  41 

1  33 

2  47 
4  20 
6  15 
8  29 

11  05 
14  03 
17  20 
20  59 
24  57 
29  17 
33  59 
39  00 

0.65 

0  10 

0  40 

1  30 

2  42 
4  12 
6  03 
8  14 

10  45 
13  37 
16  48 
20  20 
24  11 
28  23 
32  56 
37  48 

0.63 

0  10 
0  39 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 

36  36 

II 

0.61 

0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 

35  24 

II 

0.59 

/      // 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
21  54 
25  41 
29  48 
34  12 

0.57 

/      // 

0  09 

0  35 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

1153 
14  40 
17  45 
2107 
24  47 
28  45 
33  00 

0.55 

/     // 

0  09 

0  34 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

1127 
14  08 
17  06 
20  21 
23  53 
27  42 
3148 

0.53 

/      // 

0  08 

0  33 

1  13 

2  11 

3  24 

4  54 
6  40 
8  42 

11  01 
13  36 
16  27 
19  35 
22  59 
26  39 

30  36 

II 

0.51 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.863 
32 

9.851 
26 

9.832 
51 

9.826 
07 

9.812 
91 

9.799 
34 

9.785 
33 

9.770 
85 

9.755 

87 

9.740 
36 

9.724 

28 

85 

9.707 
57 

Log. 

Limit 

80 

80 

81 

81 

82 

82 

83 

83 

84 

85 

86 

Min- 
utes 

Merid- 
ian 

14° 

15°  i   16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

Alti- 
tudes 

268 


Latitude  45'^  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

It 
1.96 

/        n 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

ir 

2.00 

/     // 

0  32 

2  10 

4  52 

8  40 

13  32 

19  29 

26  32 

34  39 

43  51 

54  08 

65  30 

77  57 

9129 

// 
2.03 

/       n 

0  33 

2  13 

4  58 

8  50 

13  48 

19  52 

27  03 

35  20 

44  43 

55  12 

66  48 

79  29 

93  17 

// 
2.07 

1     II 

0  34 

2  15 

5  03 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

81  01 

95  05 

II 
2.11 

/      II 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

96  53 

II 
2.15 

0  35 

2  20 

5  15 

9  21 

14  36 

2102 

28  37 

37  22 

47  19 

58  24 

70  40 

84  05 

98  41 

II 
2.19 

/      // 

0  36 

2  24 

5  23 

9  33 

14  56 

21  30 

29  16 

38  14 

48  23 

59  44 

72  16 

86  01 

100  57 

2.24 

/     // 

0  36 

2  26 

5  29 

9  43 

15  12 

21  53 

29  48 

38  55 

49  15 

60  48 

73  34 

87  33 

102  45 

2.28 

/      II 

0  37 

2  29 

5  35 

9  57 

15  32 

22  22 

30  27 

39  46 

50  20 

62  08 

75  11 

89  28 

105  00 

2.33 

/     // 

0  38 

2  32 

5  43 

.10  09 

15  52 

22  51 

3106 

40  37 

51  25 

63  28 

76  48 

91  23 

107  15 

2.38 

/     II 

0  39 
2  37 
5  52 
10  24 
16  16 
23  25 
31  53 
41  39 
52  42 
65  04 
78  43 
93  42 

2.44 

Miu. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.292 
26 

0.301 
03 

0.307 
50 

0.315 
97 

0.324 
28 

0.332 
44 

0.340 
44 

0.350 
25 

0.357 
93 

0.367 
36 

0.376 
58 

0.387 
39 

Log. 

Limit 

46 

46 

45 

45 

44 

44 

43 

43 

42 

42 

41 

40 

Min- 
utes 

Merid- 
ian 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      II 

/     // 

/     // 

/     // 

/     // 

/     /' 

/     // 

/     // 

/      // 

/     // 

/      // 

/      // 

Min. 

4 

0  39 

0  41 

0  42 

0  43 

0  44 

0  45 

0  46 

0  47 

0  49 

0  51 

0  52 

0  54 

4 

8 

2  40 

2  43 

2  47 

2  51 

2  56 

3  01 

3  06 

3  11 

3  18 

3  24 

3  31 

3  39 

8 

12 

5  59 

6  07 

6  17 

6  26 

6  36 

6  47 

6  59 

7  11 

C7  35 

9  39 

)  7  54 

8  11 

12 

16 

10  37 

10  53 

11  11 

1126 

1144 

12  05 

12  25 

12  45 

13  ir 

T3  3t 

14  02 

14  33 

16 

20 

16  36 

17  00 

17  28 

17  52 

18  20 

18  52 

19  24 

19  56 

20  36 

21  16 

2156 

22  44 

20 

24 

23  54 

24  29 

25  10 

25  44 

26  24 

27  10 

27  56 

28  42 

29  40 

30  38 

31  35 

32  44 

24 

'2f8 

32  33 

33  19 

34  14 

35  01 

35  56 

36  59 

38  02 

39  05 

40  23 

4141 

43  00 

44  34 

28 

32 

42  30 

43  31 

44  42 

45  44 

46  56 

48  18 

49  40 

5102 

52  44 

54  26 

56  09 

58  12 

32 

36 

53  47 

55  05 

56  36 

57  54 

59  24 

61  08 

62  51 

64  35 

66  45 

68  55 

7104 

73  39 

36 

40 

66  24 

68  00 

69  52 

7128 

73  20 

75  28 

77  36 

79  44 

82  24 

85  04 

87  44 

90  56 

40 

44 

80  20 

82  17 

84  33 

86  29 

88  44 

44 

48 

95  37 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

" 

" 

II 

II 

II 

II 

" 

II 

A,h 

2.49 

2.55 

2.62 

2.68 

2.75 

2.83 

2.91 

2.99 

3.09 

3.19 

3.29 

3.41 

A,li 

Log. 

0.396 

0.406 

0.418 

0.428 

0.439 

0.451 

0.463 

0.475 

0.489 

0.503 

0.517 

0.532 

Log. 

20 

54 

30 

13 

33 

79 

89 

67 

96 

79 

20 

75 

Limit 

39 

38 

38 

38 

37 

36 

35 

34 

34 

33 

32 

31 

Min- 
utes 

Merid- 
ian 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

Alti- 
tudes 

Latitude  45°  Declination  Same  Name. 


269 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0. 

3 

8 

15  ( 
23 
33. 
46 
60 
76 

3.5 

// 

57 
t7 
JO 
36 
36 
59 
15 
25 
28 

i 

0 
3 

8 
15 
24 
35 

48 
62 
79 

II 
3.6 

59 
55 
50 
42 
32 
20 
05 
48 
30 

8 

1( 
4( 
9 

16- 
25. 
36' 
50  ( 
65 

II 
3.8 

II 

)2 
)5 
11 
21 
J2 
16 
33 
22 

3 

1 

1( 

4 

9 

17  ( 
26 
38 
52 
68 

n 

4.0 

// 

34 
16 
36 
34 
10 
24 
16 
16 

3 

1 

1 
4 
10 
17 
28 
40 
54 
71 

II 
4.2 

37 
29 
35 
55 
30 
19 
53 
11 

D 

1 

4' 
10 
18' 
29 
42 
57 

II 
4.4 

// 

10 
13 
35 
19 
24 
20 
38 

1 

1 

4. 
11 
19. 
31  ( 
44 
60 

II 
4.6 

15 
57 
39 
51 
30 
39 
15 

5 

1 

5 

11  ' 
20. 
32 
47 
64 

II 
4.9 

// 

18 
14 
19 
59 
18 
14 
18 

2 

1 

1 

5 

12 
22 
34 
50 
68- 

5.2 

23 
35 
33 
19 
52 
12 
21 

3 

1      II 

1  30 
5  58 
13  26 
23  54 
37  20 
53^ 

5.60 

/     // 

1  36 
6  26 
14  28 
25  44 
40  12 
57  54 

II 
6.03 

/      // 

1  45 
6  59 
15  43 
27  57 
43  40 
62  53 

II 
6.55 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.549 
00 

0.565 
85 

0.583 
20 

0.602 
06 

0.623 
25 

0.644 
44 

0.667 
45 

0.691 
97 

0.718 
50 

0.748 
19 

0.780 
32 

0.816 
24 

Log. 

Limit 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

Min- 
utes 

Merid- 
ian 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36? 

37° 

38° 

39° 

40° 

41= 

42= 

1  43= 

44° 

45"^ 

>      46° 

47° 

Hour 
Angles 

Min. 

4 

/       // 

155 

1     II 
2  07 

/      // 
2  23 

/     // 

2  45 

1     II 
3  15 

1 

//    / 

//    / 

//    1     II 

/ 

//    /     // 

/     II 

Min. 
4 

8 

7  39 

8  30 

9  34 

1100 

13  01 

8 

12 

17  14 

19  08 

2134 

24  46 

29  17 

12 

16 

30  38 

34  00 

38  18 

44  02 

16 

20 

47  52 

53  08 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

II 

II 

■,; 

',; 

II 

II 

II 

II 

II 

■//■ 

1 

II 

60 

A,h 

7.18 
0.856 
12 

7.97 

8.98 

10.32 

12.20 

A,h 

Log. 

0.901 
46 

0.953 

28 

1.013 
68 

1.086 
36 

Log. 

Limit 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

3 

6 

Min- 
utes 

Merid- 
ian 

8P 

82° 

83° 

84° 

85° 

86 

'      87 

'      88 

'      89° 

90 

=      89° 

88° 

Alti- 
tudes 

270 


Latitude  45°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51°      J 

)2° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

II 

/       w 

/     /' 

/     // 

/     /' 

/     // 

/      " 

Min. 

Min. 

4 

2  44 

2  14 

152 

136 

1  23 

1  14 

105 

0  59 

0  53 

0  48 

4 

8 

10  56 

8  54 

7  29 

6  24 

5  34 

4  54 

4  21 

3  53 

3  30 

3  09 

8 

12 

24  35 

20  02    1 

6  49 

14  24 

12  32 

11  01 

9  46 

8  44 

7  52 

7  07 

\l 

16 

43  41 

35  38    2 

9  55 

25  36 

22  16 

19  35 

17  22 

15  32 

13  57 

12  37 

16 

20 

...      4 

6  44 

40  00 

34  48 

30  36 

27  08 

24  16 

2148 

19  44 

20 

24 

50  07 

44  04 

39  04 

34  57 

3123 

28  25 

24 

28 

53  11 

47  33 

42  44 

38  41 

28 

32 

55  49 

50  31 

32 

36 

63  56 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

/ 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

10.24 

8.35      7 

.01 

6.00 

5.22 

4.59 

4.07 

3.64 

3.27 

2.96 

A,h 

1.010 

0.921    0 

.845 

0.778 

0.717 

0.661 

0.609 

0.561 

0.514 

0.471 

Log. 

Log. 

30 

69 

72 

15 

67 

81 

59 

10 

55 

29 

Limit 

8 

10 

12 

14 

16 

18 

20 

21 

23 

25 

27 

29 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85° 

84°       { 

}3° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

1  Alti- 
'  tudea 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1      II 

/      // 

/      // 

/      // 

/      // 

/      // 

1      II 

/      /' 

/      " 

/       n 

/      // 

/      '/ 

Min. 

4 

0  43 

0  39 

0  36 

0  33 

0  30 

0  27 

0  26 

0  24 

0  21 

0  19 

0  18 

0  16 

4 

8 

2  51 

2  37 

2  23 

2  11 

2  00 

150 

141 

133 

125 

1  18 

1  11 

105 

8 

12 

6  26 

5  52 

5  21 

4  54 

4  29 

4  06 

3  46 

3  29 

3  11 

2  56 

2  41 

2  27 

12 

16 

1126 

10  24 

9  32 

8  42 

7  59 

7  18 

6  42 

6  11 

5  41 

5  12 

4  47 

4  21 

16 

20 

17  52 

16  16 

14  52 

13  36 

12  28 

1124 

10  28 

9  40 

8  52 

8  08 

7  28 

6  48 

20 

24 

25  44 

23  25 

21  24 

19  35 

17  57 

16  25    15  04 

13  55 

12  46 

11  43 

10  46 

9  48 

24 

28 

35  01 

3153 

29  09 

26  39 

24  26 

22  21 

20  31 

18  57 

17  23 

15  57 

14  38 

13  20 

28 

32 

45  44 

41  39 

38  04 

34  49 

3155 

29  11 

26  48 

24  45 

22  42 

20  49 

19  06 

17  24 

32 

36 

57  54 

52  42 

48  10 

44  04 

40  24 

36  56 

33  55 

31  19 

28  44 

26  21 

24  12 

22  02 

36 

40 

65  04 

59  28 

54  24 

49  52 

45  36 

41  52 

38  40 

35  28 

32  32 

29  52 

27  12 

40 

44 

65  49 

60  21 

55  10 

50  40 

46  47 

42  55 

39  22 

36  09 

32  55 

44 

48 

7148 

65  38 

60  17 

55  41 

5104 

46  51 

43  00 

39  10 

48 

52 

70  45 

65  21 

59  56 

54  59 

50  28 

45  58 

52 

56 

75  37 

69  31 

63  46 

58  33 

53  19 

56 

60 

73  12 

67  12 

61  12 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

2.68 

2.44 

2.23 

2.04 

1.87 

1.71 

1.57 

1.45 

1.33 

1.22 

1.12 

1.02 

A,h 

Log. 

0.428 

0.387 

0.348 

0.309 

0.271 

0.233 

0.195 

0.161 

0.123 

0.086 

0.049 

0.008 

Log. 

13 

39 

30 

63 

84 

00 

90 

37 

85 

36 

22 

60 

Limit 

31 

33 

35 

37 

39 

41 

43 

45 

47 

49 

52 

55 

Min- 
utes 

Merid- 
ian 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

65° 

64° 

Alti- 
tudes 

Latitude  45°  Declination  Contrary  Name. 

Declinations. 


271 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

/  II 

/  It 

1     II 

/  // 

/  // 

/  // 

1       n 

/  // 

1     II 

/  // 

/  // 

/  II 

Min. 

4 

0  31 

0  30 

0  30 

0  30 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

0  27 

0  27 

4 

8 

2  05 

2  03 

2  01 

2  00 

158 

1  56 

154 

152 

150 

149 

147 

1  45 

8 

12 

4  43 

4  38 

4  34 

4  29 

4  25 

4  20 

4  17 

4  12 

4  08 

4  05 

4  00 

3  56 

12 

16 

8  21 

8  14 

8  06 

7  59 

7  51 

7  44 

7  35 

7  28 

7  20 

7  15 

7  08 

7  00 

16 

20 

13  04 

12  52 

12  40 

12  28 

12  16 

12  04 

11  52 

11  40 

11  28 

11  20 

1108 

10  56 

20 

24 

18  49 

18  31 

18  14 

17  57 

17  40 

17  23 

17  05 

16  48 

16  31 

16  19 

16  02 

15  45 

24 

28 

25  37 

25  14 

24  50 

24  26 

24  02 

23  39 

23  16 

22  52 

22  29 

22  13 

21  49 

21  25 

28 

32 

33  27 

32  57 

32  26 

31  55 

31  24 

30  53 

30  23 

29  52 

29  21 

29  01 

28  30 

27  59 

32 

36 

42  20 

41  41 

41  02 

40  24 

39  45 

39  06 

38  27 

37  48 

37  09 

36  43 

36  05 

35  26 

36 

40 

52  16 

51  28 

50  40 

49  52 

49  04 

48  16 

47  28 

46  40 

45  52 

45  20 

44  32 

43  44 

40 

44 

63  14 

62  16 

61  18 

60  21 

59  22 

58  24 

57  26 

56  28 

55  30 

54  51 

53  54 

52  55 

44 

48 

75  16 

74  07 

72  58 

71  48 

70  39 

69  30 

68  19 

67  10 

66  01 

65  15 

64  07 

62  58 

48 

52 

88  20 

86  59 

85  38 

84  16 

82  55 

8134 

80  13 

78  52 

77  31 

76  37 

75  15 

73  54 

52 

56 

102  26 

100  52 

99  18 

97  45 

96  10 

94  36 

93  02 

9128 

89  54 

88  51 

87  18 

85  43 

56 

60 

114  00 

112  12 

110  24 

108  36 

1/ 

106  48 

105  00 

II 

103  12 

II 

102  00 

II 

100  12 

II 

98  24 
It 

60 

A,h 

1.96 

1.93 

1.90 

1.87 

1.84 

1.81 

1.78 

1.75 

1.72 

1.70 

1.67 

1.64 

A,h 

Log. 

0.292 

0.285 

0.278 

0.271 

0.264 

0.257 

0.250 

0.243 

0.235 

0.230 

0.222 

0.214 

Log. 

26 

56 

75 

84 

82 

68 

42 

04 

53 

45 

72 

84 

Limit 

48 

47 

48 

48 

49 

50 

50 

51 

51 

52 

53 

53 

Min- 
utes 

Merid- 
ian 

45° 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1      II 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
II 

1.62 

1     II 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
5138 
61  26 
72  06 
83  38 

96  00 

II 

1.60 

1     II 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

4152 

50  40 

60  17 

70  45 

82  04 

94  12 

1.57 

1     II 

0  25 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

29  31 

69  51 

8101 

93  00 
II 

1.55 

1      II 

0  24 

1  38 
3  40 
6  32 

10  12 
14  41 
20  00 
26  07 
33  03 
40  48 
49  22 
58  45 
68  57 
79  58 

91  48 

II 

1.53 

1      II 

0  24 

1  36 
3  36 
6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 
II 

1.50 

1     II 

0  23 

1  35 
3  34 
6  18 
9  52 

14  12 
19  21 
25  16 
31  58 
39  28 
47  45 
56  50 
66  42 
77  21 
88  48 

1.48 

/   // 

0  23 

1  34 
3  31 
6  13 

9  44 
14  01 
19  05 
24  55 
31  32 
38  56 
47  06 
56  04 
65  48 
76  18 

87  36 

II 

1.46 

/   // 

0  22 

1  33 
3  28 
6  08 
9  36 

13  49 

18  49 

24  35 

31  06 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 
II 

1.44 

/   // 

0  22 

1  31 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
II 

1.42 

0  22 

1  30 
3  22 
5  58 
9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

/   // 
0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 

1.38 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.209 
52 

0.204 
12 

0.195 
90 

0.190 
33 

0.184 
69 

0.176 
09 

0.170 
26 

0.164 
35 

0.158 
36 

0.152 
29 

0.146 
13 

0.139 

88 

Log. 

Limit 

54 

55 

56 

57 

58 

58 

59 

60 

60 

60 

61 

62 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27" 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

272 


Latitude  45°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      '/ 

1     " 

/      /' 

/     // 

/     // 

/     // 

'      " 

/     // 

/      // 

/     // 

Min. 

4 

0  22 

0  22 

0  21 

0  21 

0  20 

0  20 

0  20 

0  19 

0  19 

0  19 

0  19 

0  19 

4 

8 

127 

126 

124 

123 

122 

121 

120 

1  18 

1  18 

1  16 

1  15 

1  13 

8 

12 

3  16 

3  13 

3  10 

3  07 

3  05 

3  02 

2  59 

2  56 

2  54 

2  51 

2  48 

2  45 

12 

16 

5  48 

5  43 

5  38 

5  33 

5  27 

5  22 

5  17 

5  12 

5  10 

5  05 

5  00 

4  55 

16 

20 

9  04 

8  56 

8  48 

8  40 

8  32 

8  24 

8  16 

8  08 

8  04 

7  56 

7  48 

7  40 

20 

24 

13  04 

12  52 

12  41 

12  29 

12  17 

12  06 

11  54 

11  43 

11  37 

11  26 

11  14 

10  03 

24 

28 

17  46 

17  30 

17  15 

16  59 

16  44 

16  28 

16  12 

15  57 

15  49 

15  33 

15  17 

15  01 

28 

32 

23  12 

22  52 

22  31 

22  11 

21  51 

21  30 

21  10 

20  49 

20  39 

20  18 

19  58 

19  37 

32 

36 

29  23 

28  57 

28  31 

28  05 

27  39 

27  13 

26  47 

26  21 

26  08 

25  43 

25  17 

24  51 

36 

40 

36  16 

35  44 

35  12 

34  40 

34  08 

33  36 

33  04 

32  32 

32  16 

31  44 

31  12 

30  40 

40 

44 

43  53 

43  14 

42  36 

4157 

41  18 

40  38 

40  00 

39  22 

39  02 

38  24 

37  46 

37  07 

44 

48 

52  13 

5127 

50  41 

49  55 

49  09 

48  23 

47  37 

46  51 

46  28 

45  41 

44  55 

44  09 

48 

52 

61  17 

60  23 

59  29 

58  35 

57  41 

56  47 

55  53 

54  59 

54  32 

53  37 

52  43 

51  49 

52 

56 

7105 

70  02 

69  00 

67  57 

66  54 

65  51 

64  48 

63  46 

63  14 

62  12 

61  10 

60  07 

56 

60 

8136 

80  24 

79  12 

II 

78  00 

76  48 

II 

75  36 

II 

74  24 
II 

73  12 
II 

72  36 

II 

7124 
II 

70  62 
II 

69  00 

II 

60 

Ajh 

1.36 

1.34 

1.32 

1.30 

1.28 

1.26 

1.24 

1.22 

1.205 

1.19 

1.17 

1.15 

Ajh 

Log. 

0.133 

0.127 

0.120 

0.113 

0.107 

0.100 

0.093 

0.086 

0.080 

0.075 

0.068 

0.060 

Log. 

54 

10 

57 

94 

21 

37 

42 

36 

99 

55 

19 

70 

Limit 

63 

64 

65 

66 

67 

68 

68 

69 

70 

71 

72 

73 

Min- 
utes 

Merid- 
ian 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 

12 

16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 
68  24 

1.14 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

/      // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 
66  00 

1.10 

/     // 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 
14  07 
18  26 
23  20 
28  48 
34  51 
41  28 
48  40 
56  27 

64  48 

II 

1.08 

/     // 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
4105 
48  13 
55  56 
64  12 

1.07 

/ 

// 

/ 

// 

II 

// 

/ 

// 

// 

II 

// 

/ 

// 

// 

1 

// 

// 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.056 
90 

•0.049 
22 

0.041 
39 

0.033 
42 

0.029 
38 

Log. 

Limit 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

Alti- 
tudes 

Latitude  45°  Declination  Contrary  Name 

Declinations.  —  Inferior  Meridian. 


273 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/      // 

/     ff 

/     // 

/      // 

/      // 

/     // 

/     // 

/     // 

/      // 

/     // 

/     // 

/     // 

Min. 

4 

0  14 

0  14 

0  14 

0  14 

0  14 

0  13 

0  12 

0  12 

0  12 

0  12 

4 

8 

0  57 

0  56 

0  55 

0  54 

0  53 

0  52 

0  51 

0  50 

0  49 

0  48 

8 

12 

2  10 

2  07 

2  04 

2  01 

159 

156 

154 

151 

150 

147 

12 

16 

3  50 

3  45 

3  40 

3  35 

3  33 

3  28 

3  22 

3  17 

3  14 

3  09 

16 

20 

6  00 

5  52 

5  44 

5  36 

5  32 

5  24 

5  16 

5  08 

5  04 

4  56 

20 

24 

8  38 

8  27 

8  16 

8  04 

7  58 

7  47 

7  35 

7  23 

7  18 

7  06 

24 

28 

11  46 

11  30 

11  14 

10  58 

10  51 

10  35 

10  20 

10  04 

9  56 

9  40 

28 

32 

15  22 

15  01 

14  40 

14  20 

14  10 

13  49 

13  29 

13  09 

12  58 

12  38 

32 

36 

19  26 

19  01 

18  35 

18  09 

17  56 

17  30 

17  04 

16  38 

16  25 

15  59 

36 

40 

24  00 

23  28 

22  56 

22  24 

22  08 

21  36 

21  04 

20  32 

20  16 

19  44 

40 

44 

29  02 

28  24 

27  45 

27  06 

26  47 

26  08 

25  29 

24  51 

24  31 

23  52 

44 

48 

34  34 

33  47 

33  01 

32  15 

31  52 

31  06 

30  18 

29  32 

29  09 

28  23 

48 

52 

40  34 

39  39 

38  45 

37  51 

37  24 

36  30 

35  36 

34  42 

34  15 

33  21 

52 

56 

47  02 

46  00 

44  57 

43  54 

43  23 

42  20 

41  17 

40  15 

39  44 

38  40 

56 

60 

... 

II 

54  00 

II 

52  48 

5136 

50  24 
II 

49  48 
II 

48  36 

47  24 

46  12 

45  36 

44  24 

60 

A,h 

0.90 

0.88 

0.86 

0.84 

0.83 

0.81 

0.79 

0.77 

0.76 

0.74 

A,h 

Log. 

9.954 

9.944 

9.934 

9.924 

9.919 

9.908 

9.897 

9.886 

9.880 

9.869 

Log. 

24 

48 

50 

28 

08 

49 

63 

49 

81 

23 

Limit 

68 

68 

69 

70 

71 

72 

74 

76 

78 

79 

Min- 
utes 

Merid-       oo    \      ao    \      ko 

ian     '      -^      1      *      1      '^ 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

710    1  Hour 
'■'•      [Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/     II 

Oil 
0  46 
144 

3  04 

4  48 
6  55 
9  25 

12  17 

15  33 

19  12 

23  14 

27  37 

32  27 

37  38 

43  12 
II 

0.72 

/      // 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

31  33 

36  35 

42  00 
II 

0.70 

/     // 

Oil 

0  43 

1  38 

2  54 
4  32 
6  32 
8  53 

11  36 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 
// 

0.68 

/     // 

Oil 

0  42 

1  35 

2  49 
4  24 
6  21 
8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 
II 

0.66 

/     // 

Oil 

0  41 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
II 

0.64 

/     // 

0  10 

0  39 

1  29 

2  39 

4  08 

5  58 
8  06 

10  34 

13  24 

16  32 

20  01 

23  48 

27  56 

32  25 

37  12 
II 

0.62 

1     II 

0  10 

0  38 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 
12  58 
16  00 
19  22 
23  02 
27  02 
31  22 
36  00 

0.60 

0  09 
0  37 
124 

2  28 

3  52 
5  34 
7  35 
9  54 

12  32 
15  28 
18  43 
22  16 
26  08 
30  19 
34  48 

0.58 

0  09 

0  36 

1  21 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
2130 
25  14 
29  16 

33  36 

II 

0.56 

0  09 

0  35 

1  18 

2  18 

3  36 
5  11 
7  03 
9  13 

1140 

14  24 

17  25 

20  44 

24  20 

28  13 

32  24 
II 

0.54 

/     // 

0  08 

0  33 

1  15 

2  13 

3  28 

5  00 

6  48 
8  52 

11  14 

13  52 

16  47 

19  58 

23  26 

27  11 

31  12 
II 

0.52 

/       // 

0  08 

0  32 

1  12 

2  08 

3  20 

4  48 
6  32 
8  32 

10  48 
13  20 
16  08 
19  12 
22  32 
26  08 

30  00 

// 

0.50 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Leg. 

9.857 
33 

9.845 
10 

9.832J  9.819 
51         54 

9.806 
18 

9.792 
39 

9.778 
15 

9.763 
43 

9.748 
19 

9.732 
39 

9.716 
00 

9.698 
97 

Log. 

Limit 

79 

80 

80       81 

81 

Z2 

82 

83 

83 

84 

84 

85 

Min- 
utes 

Merid- 
ian 

15° 

16° 

17°      18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

Alti- 
tudes 

274 


Latitude  46°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/       // 

/     // 

r       " 

1       n 

/     // 

/     // 

/      // 

/       n 

/     // 

/     // 

I     II 

/      // 

Min. 

4 

0  30 

0  30 

0  31 

0  32 

0  32 

0  33 

0  34 

0  35 

0  35 

0  36 

0  36 

0  37 

4 

8 

2  01 

2  03 

2  05 

2  08 

2  10 

2  13 

2  15 

2  17 

2  20 

2  24 

2  27 

2  29 

8 

12 

4  34 

4  38 

4  43 

4  48 

4  52 

4  58 

5  03 

5  09 

5  15 

5  23 

5  30 

5  35 

12 

16 

8  06 

8  14 

8  21 

8  32 

8  40 

8  50 

9  01 

9  11 

9  21 

9  33|     9  46 

9  57 

16 

20 

12  40 

12  52 

13  04 

13  20 

13  32 

13  48 

14  04 

14  20 

14  36 

14  56 

15  16 

15  32 

20 

24 

18  14 

18  31 

18  49 

19  12 

19  29 

19  52 

20  16 

20  39 

21  02 

2130 

21  59 

22  22 

24 

28 

24  50 

25  14 

25  37 

26  08 

26  32 

27  03 

27  34 

28  05 

28  37 

29  16 

29  56 

30  27 

28 

32 

32  26 

32  57 

33  27 

34  08 

34  39 

35  20 

36  00 

36  41 

37  22 

38  14 

39  05 

39  46 

32 

36 

4102 

41  41 

42  20 

43  12 

43  51 

44  43 

45  35 

46  27 

47  19 

48  23 

49  28 

50  20 

36 

40 

50  40 

5128 

52  16 

53  20 

54  08 

55  12 

56  16 

57  20 

58  24 

59  44*  61  04 

62  08 

40 

44 

61  18 

62  16 

63  14 

64  32 

65  30 

66  48 

68  05 

69  23 

70  40 

72  16|  73  53 

75  11 

44 

48 

72  58 

74  07 

75  16 

76  48 

77  57 

79  29 

81  01 

82  33 

84  05 

86  01:  87  56 

89  28 

48 

52 

85  38 

86  59 

88  20 

90  08 

91  29 

93  17 

95  05 

96  53 

98  41 

100  57 

103  12 

105  00 

52 

56 

99  18 

100  52 

102  26 

104  32 

106  06 

108  12 

56 

60 

114  00 

60 

// 

// 

" 

" 

" 

// 

II 

II 

II 

// 

II 

II 

A,h 

1.90 

1.93 

1.96 

2.00 

2.03 

2.07 

2.11 

2.15 

2.19 

2.24 

2.29 

2.33 

A,h 

iiOg. 

0.278 

0.285 

0.292 

0.301 

0.307 

0.315 

0.324 

0.332 

0.340 

0.350 

0.359 

0.367 

Log. 

75 

56 

26 

03        50 

97 

28 

44 

44 

25 

84 

36 

Limit 

47 

47 

46 

45        45 

45 

44 

44 

43 

42 

42 

41 

Min- 
utes 

Merid- 
ian 

44° 

45° 

46° 

47°      48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

Alti- 
tudes 

Declinations, 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

'       // 

/     " 

/      // 

/     // 

/      // 

/      '/ 

Min. 

Min. 

4 

0  38 

0  39 

0  40 

0  41 

0  42 

0  43 

0  44 

0  46 

0  46 

0  48 

0  50 

0  51 

4 

8 

2  33 

2  37 

2  40 

2  44 

2  47 

2  52 

2  57 

3  02 

3  06 

3  13 

3  19 

3  26 

8 

12 

5  44 

5  52 

6  00 

6  09 

6  17 

6  27 

6  38 

6  49 

7  01 

7  13 

7  27 

7  42 

12 

16 

10  12 

10  24 

10  40 

10  55 

11  11 

11  29 

11  46 

12  07 

12  27 

12  51 

13  17 

13  42 

16 

20 

15  56 

16  16 

16  40 

17  04 

17  28 

17  56 

18  24 

18  56 

19  28 

20  04 

20  44 

21  24 

20 

24 

22  57 

23  25 

24  00 

24  35 

25  10 

25  50 

26  30 

27  16 

28  02 

28  54 

29  52 

30  49 

24 

28 

31  14 

3153 

32  40 

33  27 

34  14 

35  09 

36  04 

37  06 

38  10 

39  20 

40  38 

41  57 

28 

32 

40  47 

4139 

42  40 

43  41 

44  42 

45  54 

47  06 

48  28 

49  50 

5122 

53  04 

54  47 

32 

36 

5138 

52  42 

54  00 

55  18 

56  36 

58  07 

59  37 

6121 

63  04 

65  01 

67  11 

69  20 

36 

40 

63  44 

65  04 

66  40 

68  16 

69  52 

71  44 

73  36 

75  44 

77  52 

80  16 

82  56 

85  36 

40 

44 

77  07 

78  43 

80  40 

82  36 

84  33 

86  48 

44 

48 

9146 

93  42 

96  00 

48 

52 

107  42 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

" 

II 

II 

" 

II 

II 

A,h 

2.39 

2.44 

2.50 

2.56 

2.62 

2.69 

2.76 

2.84 

2.92 

3.01 

3.11 

3.21 

A,h 

Log. 

0.378 

0.387 

0.397 

0.408 

0.418 

0.429 

0.440 

0.453 

0.465 

0  478 

0.492 

0.506 

Log. 

40 

39 

94 

24 

30 

75 

91 

32 

38 

57 

76 

51 

Limit 

40 

39 

39 

39 

38 

37 

36 

35 

35 

34 

33 

32 

Min- 
utes 

Merid- 
ian 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67°  1 

Alti- 
tudes 

Latitude  46°  Declination  Same  Name. 


275 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angies 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

0 
3 

7 
14 
22 
31 
43 
56 
71 

If 
3.3 

54 
33 
59 
13 
12 
58 
31 
30 
56 

I 

0 
3 

8 
14 
23 
33 
45 
58 
74 

II 
3.4 

// 

55 
41 
14 
43 
DO 
07 
D5 
53 
31 

5 

0 
3 

8 
15 
23 
34 
46 
61 
77 

II 
3.5J 

II 

57 
49 
36 
16 
52 
22 
i7 
06 
20 

5 

1 

3 

8 
15 
24 
35 
48 
63 

II 
3.7. 

00 
59 
57 
55 
52 
48 
45 
40 

3 

1 

4 

9 
16 
26 
37 
50 
66 

3.9( 

02 
09 
22 
38 
30 
26 
58 
34 

) 

/      // 

105 
4  21 
9  48 
17  24 
27  12 
39  10 
53  19 
69  38 

4.08 

/ 

1 

4 
10 

18 
28 
41 
56 
73 

II 
4.2 

// 

08 
35 
18 
18 
36 
11 
04 
13 

1 
1 
3 
4 
5 

4 

1 
4 
0 
9 
0 
3 
9 

// 
.5 

// 

12 
49 
51 
17 
08 
24 
04 

I 

/     // 

1  17 
5  06 
11  29 
20  23 
31  52 
45  53 
62  26 

II 
4.78 

/     // 

1  21 
5  25 
12  12 
21  40 
33  52 
48  46 
66  23 

5.08 

f     II 

127 
5  49 
14  04 
23  12 
36  16 
52  13 

5.44 
0.735 
60 

/     // 

134 
6  15 
14  04 
25  00 
39  04 
56  16 

5.86 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.522 
44 

0.537 
82 

0.553 

88 

0.571 
71 

0.591 
06 

0.610 
66 

0.632 
46 

0.655 
14 

0.679 
43 

0.705 
86 

0.767 
90 

Log. 

Limit 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

Min- 
utes 

Merid- 
ian 

68= 

69= 

70= 

71= 

72= 

73° 

74= 

7 

'5= 

) 

76= 

) 

77' 

) 

78° 

79 

> 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44°      <■ 

15° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/     // 

/     // 

/      II 

/     // 

/     // 

/      II 

/      // 

1     II    1 

" 

/     // 

/     // 

Min. 

4 

142 

151 

2  03 

2  19 

2  40 

3  09 

4 

8 

6  47 

7  25 

8  14 

9  17 

10  40 

12  35 

8 

12 

15  16 

16  43 

18  32 

20  53 

24  00 

28  19 

12 

16 

27  08 

29  41 

32  56 

37  07 

42  40 

16 

20 

42  00 

46  24 

51  28 

58  00 

20 

24 

61  04 

66  49 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

II 

II 

" 

" 

II 

II 

II 

II 

II 

II 

A,h 

6.36 

6.96 

7.72 

8.70 

10.00 

11.80 

A,h 

Log. 

0.803 
46 

0.842 
61 

0.887 
62 

0.939 
52 

1.00 

1.071 

88 

Log. 

Limit 

19 

18 

17 

15 

13 

11 

9 

7 

5 

3 

0 

3 

Min- 
utes 

Merid- 
ian 

80' 

> 

81' 

) 

82' 

J 

83 

3 

84' 

> 

i 

5° 

86' 

' 

87° 

88°      S 

9= 

s 

0° 

89° 

Alti- 
tudes 

276 


Latitude  46*  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Anglee 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

II 

// 

1 

1 

// 

1 
2 
10 
23 

II 
9.8 

38 
30 
38 

5 

2 

8 
19 
34 

II 
8.0 

38 
34 
14 
16 

3 

.  /      // 

148 

7  12 

16  11 

28  45 

44  56 

II 
6.74 

1 

1 

6 

13 

24 

38 

II 
5.7 

// 

32 
39 
50 
34 
24 

5 

/ 

1 
2 
3 
4 

5 

1 
5 
2 
1 
3 
8 

// 
.0 

20 
20 
30 
20 
20 
30 

3 

/      // 

1  10 
4  41 
10  32 
18  44 
29  16 
42  09 

II 
4.39 

/       n 

102 
4  09 
9  20 
16  36 
25  56 
37  21 
50  20 

II 
3.89 

0  55 
3  43 
8  22 
14  50 
23  12 
33  24 
45  29 
59  24 

II 
3.48 

1     II 

0  50 
3  19 
7  29 
13  19 
20  48 
29  58 
40  46 
53  14 

II 
3.12 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log, 

0.993 
44 

0.904 
72 

0.828 
66 

0.760 
42 

0.698 
97 

0.642 
46 

0.589 
95 

0.541 
58 

0.494 
15 

Log. 

Limit 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

Min- 
utes 

Merid- 
ian 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     // 

1     II 

/      // 

//      / 

/      // 

/     // 

/      '/ 

/      // 

/      // 

/     // 

/      // 

Min. 

4 

0  45 

0  41 

0  37 

0  34 

0  30 

0  28 

0  26 

0  24 

0  22 

0  20 

0  19 

0  17 

4 

8 

3  00 

2  44 

2  28 

2  15 

2  03 

154 

143 

136 

127 

120 

1  13 

107 

8 

12 

6  46 

6  09 

5  34 

5  05 

4  38 

4  15 

3  53 

3  35 

3  16 

3  00 

2  45 

2  31 

12 

16 

12  02 

10  55 

9  54 

9  03 

8  14 

7  33 

6  55 

6  21 

5  48 

5  20 

4  55 

4  29 

16 

20 

18  48 

17  04 

15  28 

14  08 

12  52 

11  48 

10  48 

9  56 

9  04 

8  20 

7  40 

7  00 

20 

24 

27  05 

24  35 

22  17 

20  22 

18  31 

16  59 

15  34 

14  18 

13  04 

12  00    1103 

10  05 

24 

28 

36  51 

33  27 

30  19 

27  42 

25  14 

23  08 

21  10 

19  29 

17  46 

16  20j   15  01 

13  43 

28 

32 

48  07 

43  41 

39  35 

36  10 

32  51 

30  13 

27  38 

25  26 

23  12 

21  20    19  37 

17  55 

32 

36 

60  55 

55  18 

50  07 

45  48 

4141 

38  14 

35  00 

32  11 

29  33 

27  00   24  51 

22  41 

36 

40 

61  52 

56  32 

51  28 

47  12 

43  12 

39  44 

36  16 

33  20    30  40 

28  00 

40 

44 

68  25 

62  16 

57  07 

52  17 

48  04 

43  53 

40  20 

37  07 

33  53 

44 

48 

67  56 

62  12 

57  13 

52  13 

48  00 

44  09 

40  19 

48 

52 

69  09 

61  17 

56  20 

5149 

47  19 

52 

56 

7105 

65  20 

60  07 

54  53 

56 

60 

75  00|  69  00 

63  00 

60 

" 

II 

II 

" 

II 

II 

II 

II 

II 

// 

II 

II 

A,li 

2.82 

2.56 

2.32 

2.12 

1.93 

1.77 

1.62 

1.49 

1.36 

1.25 

1.15 

1.05 

A,h 

Log. 

0.450 

0.408 

0.365 

0.326 

0.285 

0.247 

0.209 

0.173 

0.133 

0.096 

0.060 

0.021 

Log. 

25 

24 

49 

34 

56 

97 

52 

19 

54 

91 

70 

19 

Limit 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

51 

54 

Min- 
utes 

Merid- 
ian 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

C6° 

65° 

Alti- 
tudes 

Latitude  46"  Declination  Contrary  Name. 


277 


Dkclixations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  30 

2-m 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

4102 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 
II 

1.90 

/      // 

0  30 

159 

4  28 

7  56 

12  24 

17  52 

24  18 

3144 

40  11 

49  36 

60  01 

7125 

83  49 

97  13 

11136 
II 

1.86 

0  29 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  22 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 

1.83 

/     // 

0  29 

-155 

-4  19 

7  41 

-12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

8107 

94  05 

108  00 
II 

1.80 

/     // 

0  28 

154 

4  17 

7  35 

1152 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 
II 

1.78 

"'  0  28 
152 
4  12 

7  28 

11  40 

16  48 

22  52 

29  52 

37  48 

46  40 

56  28 

67  10 

78  52 

91  28 

105  00 
II 

1.75 

/     // 

0  27 

150 

4  08 

7  20 

1128 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 
II 

1.72 

/     // 

0  27 

149 

4  05 

7  15 

1120 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
II 

1.70 

/     // 

0  27 

147 

4  00 

7  08 

1108 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

1.67 

/     II 

0  27 

1  45 
3  56 
7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
II 

1.64 

/     // 

0  26 
143 
3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
II 

1.62 

/      II 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

51  38 

61  26 

72  06 

83  38 

96  00 
II 

1.60 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.278 
75 

0.269 
51 

0.262 
45 

0.255 
27 

0.250 
42 

0.243 
04 

0.235 
53 

0.230 
45 

0.222 
72 

0.214 
84 

0.209 
52 

0.204 
12 

Log. 

Limit 

47 

48 

49 

49 

50 

50 

51 

52 

52 

53 

54 

54 

Min- 
utes 

Merid- 
ian 

44° 

43° 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

1      II 

/      // 

Min. 

Min. 

4 

0  25 

0  25 

0  24 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

4 

8 

141 

139 

1  38 

136 

1  35 

134 

133 

131 

1  30 

128 

127 

1  26 

8 

12 

3  46 

3  43 

3  40 

3  37 

3  34 

3  31 

3  28 

3  25 

3  22 

3  19 

3  16 

3  13 

12 

16 

6  42 

6  37 

6  32 

6  27 

6  18 

6  13 

6  08 

6  03 

5  58 

5  53 

5  48 

5  43 

16 

20 

10  28 

10  20 

10  12 

10  04 

9  52 

9  44 

9  36 

9  28 

9  20 

9  12 

9  04 

8  56 

20 

24 

15  04 

14  53 

14  41 

14  30 

14  12 

14  01 

13  49 

13  38 

13  26 

13  15 

13  04 

12  52 

24 

28 

20  31 

20  15 

20  00 

19  44 

19  21 

19  05 

18  49 

18  34 

18  18 

18  02 

17  46 

17  30 

28 

32 

26  48 

26;27 

26  07 

25  46 

25  16 

24  55 

24  35 

24  14 

23  54 

23  33 

23  12 

22  52 

32 

36 

33  55 

33  29 

33  03 

32  37 

3158 

3132 

3106 

30  40 

30  14 

29  49 

29  23 

28  57 

36 

40 

4152 

4120 

40  48 

40  16 

39  28 

38  56 

38  24 

37  52 

37  20 

36  48 

36  16 

38  44 

40 

,   44 

50  40 

50  01 

49  22 

48  43 

47  45 

47  06 

46  27 

45  49 

45  10 

44  32 

43  53 

43  14 

44 

48 

60  17 

59  31 

58  45 

57  59 

56  50 

56  04 

55  18 

54  32 

53  46 

52  59 

52  13 

5127 

48 

62 

70  45 

69  51 

68  57 

68  03 

66  42 

65  48 

64  54 

64  00 

63  06 

62  11 

61  17 

60  23 

52 

56 

82  04 

8101 

79  58 

78  55 

77  21 

76  18 

75  15 

74  13 

73  10 

72  08 

7105 

70  02 

56 

60 

94  12 

93  00 

9148 

90  36 

88  48 

87  36 

86  24 

85  12 

84  00 

82  48 

8136 

80  24 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

1.57 

1.55 

1.53 

1.51 

1.48 

1.46 

1.44 

1.42 

1.40 

1.38 

1.36 

1.34 

Ajh 

Log. 

0.195 

0.190 

0.184 

0.178 

0.170 

0.164 

0.158 

0.152 

0.146 

0.139 

0.133 

0.127 

90 

33 

69 

98 

26 

35 

36 

29 

13 

88 

54 

10 

Log. 

Limit 

55 

56 

57 

58 

58 

58 

59 

60 

61 

61 

62 

63 

Min- 
utes 

Merid- 
ian 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

Alti- 
tudes 

278 


Latitude  46°  Declination  Gjntrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/  // 

0  21 

1  24 
3  10 
5  38 
8  48 

12  41 
17  15 
22  31 
28  31 
35  12 
42  36 
50  41 
59  29 
69  00 
79  12 

n 

1.32 

/  // 

0  21 

1  23 
3  07 
5  33 
8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 
II 

1.30 

/  // 

0  20 

1  23 
3  06 
5  30 
8  36 

12  23 
16  52 
22  01 
27  52 
34  24 
41  37 
49  32 
58  08 
67  25 
77  24 

1.29 

1     II 

0  20 

1  22 
3  03 
5  25 
8  28 

12  11 
16  36 
21  41 
27  26 
33  52 
40  59 
48  45 
57  14 
66  23 

76  12 

II 

1.27 

/  // 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

21  20 

.27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
II 

1.25 

0  19 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

I  II 

0  19 

1  18 

2  54 
5  10 
8  04 

II  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 
72  36 

1.21 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

1.20 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

/  // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

I  II 

0  19 

1  13 

2  45 
4  55 
7  40 

II  03 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

51  49 

60  07 

69  00 
II 

1.15 

/  // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
II 

1.13 

Min 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.120 
57 

0.113 
94 

0.110 
59 

0.103 
80 

0.096 
91 

0.089 
91 

0.082 
79 

0.079 
18 

0.071 

88 

0.068 
19 

0.060 
70 

0.053 
08 

Log. 

Limit 

64 

65 

66 

67 

68 

69 

69 

70 

71 

72 

73 

74 

Min- 
utes 

Merid- 
ian 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/   // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

II 

1.12 

/  // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

II 

1.10 

/  // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 
II 

1.08 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

II 

// 

/ 

II 

// 

II 

II 

/  // 
II 

II 

II 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.049 
22 

0.041 
39 

0.033 
42 

0.025 
31 

Log. 

Limit 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

Alti- 
tudes 

Latitude  46°  Declination  Contrary  Name. 
Declinations.  —  Inferior  Meridian. 


279 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

// 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

1/ 

0.90 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

/     II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

5136 
II 

0.86 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
II 

0.83 

/     // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

1     II 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

/     // 

0  12 

0  50 

1  53 
3  19 
5  12 
7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

0.78 

1      II 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  44 

45  36 

II 

0.76 

1     II 

0  12 
0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

II 

0.75 

/      // 

Oil 

0  47 

1  45 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
.  44 
48 
52 
56 
60 

A,h 

Log. 

9.954 
24 

9.944 

48 

9.934 
50 

9.929 
42 

9.919 
08 

9.908 
49 

9.897 
63 

9.892 
09 

9.880 
81 

9.875 
06 

9.863 
32 

Log. 

Limit 

68 

67 

67 

68 

69 

70 

71 

73 

75 

77 

78 

Min- 
utes 

Merid- 
ian 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

Alti- 
tudes 

Declinations 

.  —  Inferior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

Min. 

4 

Oil 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  08 

0  08 

4 

8 

0  46 

0  44 

0  43 

0  41 

0  41 

0  39 

0  38 

0  37 

0  36 

0  35 

0  33 

0  32 

8 

12 

142 

139 

1  36 

133 

132 

129 

126 

124 

121 

1  18 

1  15 

1  12 

12 

16 

3  02 

2  57 

2  52 

2  47 

2  44 

2  39 

2  34 

2  28 

2  23 

2  18 

2  13 

2  08 

16 

20 

4  44 

4  36 

4  28 

4  20 

4  16 

4  08 

4  00 

3  52 

3  44 

3  36 

3  28 

3  20 

20 

24 

6  49 

6  38 

6  26 

6  15 

6  09 

5  58 

5  46 

5  34 

5  23 

5  11 

5  00 

4  48 

24 

28 

9  17 

9  01 

8  45 

8  29 

8  21 

8  06 

7  50 

7  35 

7  19 

7  03 

6  48 

6  32 

28 

32 

12  07 

11  46 

11  26 

11  05 

10  55 

10  34 

10  14 

9  54 

9  33 

9  13 

8  52 

8  32 

32 

36 

15  20 

14  55 

14  29 

14  03 

13  50 

13  24 

12  58 

12  32 

12  06 

1140 

11  14 

10  48 

36 

40 

18  56 

18  24 

17  52 

17  20 

17  04 

16  32 

16  00 

15  28 

14  56 

13  24 

13  52 

13  20 

40 

44 

22  54 

22  16 

21  38 

20  59 

20  39 

20  01 

19  22 

18  43 

18  04 

17  25 

16  47 

16  08 

44 

48 

27  14 

26  29 

25  43 

24  57 

24  34 

23  48 

23  02 

22  16 

2130 

20  44 

19  58 

19  12 

48 

52 

32  00    31  05 

30  11 

29  17 

28  50 

27  56 

27  02 

26  08 

25  14 

24  20 

23  26 

22  32 

52 

56 

37  07    36  04 

35  02 

33  59 

33  27 

32  25 

31  22 

30  19 

29  16 

28  13 

27  11 

26  08 

56 

60 

42  36    41  24 

40  12 

39  00 

38  24 

37  12 

36  00 

34  48 

33  36 

32  24 

31  12 

30  00 

60 

" 

II 

// 

II 

II 

" 

II 

II 

" 

" 

II 

II 

Ajh 

0.71 

0.69 

0.67 

0.65 

0.64 

0.62 

0.60 

0.58 

0.56 

0.54 

0.52 

0.50 

Ajh 

Log. 

9.851 

9.838 

9.826 

9.812 

7.806 

9.792 

9.778 

9.763 

9.748 

9.732 

9.716 

9.698 

Log. 

26        85 

07 

91 

18 

39 

15 

43 

19 

39 

00 

97 

Limit 

78 

79 

79 

80 

81 

81 

82 

82 

83 

83 

84 

84 

Min-- 
utes 

Merid- 
ian 

16°      17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

Alti- 
tudes 

280 


Latitude  ^T  Decimation  Same  Name. 


Declinations. 


Hour 
Angle? 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

1       II 

/     // 

/      /' 

/     // 

/      // 

/      // 

/      // 

/     // 

/     // 

/     // 

/      /' 

/      " 

Min. 

4 

0  29 

0  30 

0  30 

0  30 

0  31 

0  31 

0  32 

0  33 

0  34 

0  35 

0  35 

0  36 

4 

8 

157 

159 

2  01 

2  03 

2  05 

2  07 

2  10 

2  13 

2  15 

2  17 

2  20 

2  24 

8 

12 

4  23 

4  28 

4  32 

4  38 

4  43 

4  47 

4  52 

4  58 

5  03 

5  09 

5  15 

5  23 

12 

16 

7  49 

7  56 

8  04 

8  14 

8  21 

8  29 

8  40 

8  50 

9  01 

9  11 

9  21 

9  33 

16 

20 

12  12 

12  24 

12  36 

12  52 

13  04 

13  16 

13  32 

13  48 

14  04 

14  20 

14  36 

14  56 

20 

24 

17  34 

17  52 

18  09 

18  31 

18  49 

19  06 

19  29 

19  52 

20  16 

20  39 

21  02 

21  30 

24 

28 

23  55 

24  18 

24  42 

25  14 

25  37 

26  01 

26  32 

27  03 

27  34 

28  05 

28  37 

29  16 

28 

32 

31  13 

3144 

32  15 

32  57 

33  27 

33  58 

34  39 

35  20 

36  00 

36  41 

37  22 

38  14 

32 

36 

39  32 

40  11 

40  50 

41  41 

42  20 

42  59 

43  51 

44  43 

45  35 

46  27 

47  19 

48  23 

36 

40 

48  48 

49  36 

50  24 

51  28 

52  16 

53  04 

54  08 

55  12 

56  16 

57  20 

58  24 

59  44 

40 

44 

59  03 

60  01 

60  59 

62  16 

63  14 

64  12 

65  30 

66  48 

68  05 

69  23 

70  40 

72  16 

44 

48 

70  16 

71  25 

72  34 

74  07 

75  16 

76  25 

77  57 

79  29 

8101 

82  33 

84  05 

86  01 

48 

52 

82  28 

83  49 

85  10 

86  59 

88  20 

89  41 

91  29 

93  17 

95  05 

96  53 

98  41 

100  57 

52 

56 

95  39 

97  13 

98  47 

100  52 

102  26 

104  00 

56 

60 

109  48 

11136 

113  24 

60 

II 

II 

II 

II 

II 

" 

II 

II 

II 

II 

11 

II 

A,h 

1.83 

1.86 

1.89 

1.93 

1.96 

1.99 

2.03 

2.07 

2.11 

2.15 

2.19 

2.24 

A,h 

0.262 

0.269 

0.276 

0.285 

0.292 

0.298 

0.307 

0.315 

0.324 

0.332 

0.340 

0.350 

Log. 

45 

51 

46 

56 

26 

85 

50 

97 

28 

44 

44 

25 

Limit 

48 

47 

47 

46 

46 

46 

45 

45 

44 

44 

43 

42 

Min- 
utes 

Merid- 
ian 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

/      // 

Min. 

Min. 

4 

0  36 

0  37 

0  38 

0  39 

0  40 

0  41 

0  42 

0  43 

0  44 

0  46 

0  47 

0  48 

4 

8 

2  26 

2  39 

2  33 

2  37 

2  40 

2  44 

2  48 

2  52 

2  58 

3  02 

3  08 

3  14 

8 

12 

5  29 

5  35 

5  44 

5  52 

6  00 

6  09 

6  18 

6  27 

6  39 

6  50 

7  04 

7  16 

12 

16 

9  43 

9  57 

10  12 

10  24 

10  40 

10  55 

11  14 

11  29 

11  49 

12  10 

12  32 

12  56 

16 

20 

15  12 

15  32 

15  56 

16  16 

16  40 

17  04 

17  32 

17  56 

18  28 

19  00 

19  36 

20  12 

20 

24 

2153 

22  22 

22  57 

23  25 

24  00 

24  35 

25  15 

25  50 

26  35 

27  22 

28  13 

29  05 

24 

28 

29  48 

30  27 

31  14 

3153 

32  40 

33  27 

34  22 

35  09 

36  12 

37  14 

38  25 

39  36 

28 

32 

38  55 

39  46 

40  47 

41  39 

42  40 

43  41 

44  53 

45  54 

47  17 

48  38 

50  11 

5143 

32 

36 

49  15 

50  20 

51  38 

52  42 

54  00 

55  18 

56  49 

58  07 

59  50 

6134 

63  30 

65  27 

36 

40 

60  48 

62  08 

63  44 

65  04 

66  40 

68  16 

70  08 

7144 

73  52 

76  00 

78  24 

80  48 

40 

44 

73  34 

75  11 

77  07 

78  43 

80  40 

82  36 

84  52 

86  48 

44 

48 

87  33 

89  28 

91  46 

93  42 

96  00 

48 

52 

102  45 

105  00 

107  42 

52 

56 

56 

60 

60 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

A,h 

2.28 

2.33 

2.39 

2.44 

2.50 

2.56 

2.63 

2.69 

2.77 

2.85 

2.94 

3.03 

A,h 

Log. 

0.357 

0.367 

0.378 

0.387 

0.397 

0.408 

0.419 

0.429 

0.442 

0.454 

0.468 

0.481 

Log. 

93 

36 

40 

39 

94 

24 

96 

75 

48 

84 

35 

44 

Limit 

41 

40 

40 

40 

39 

38 

37 

36 

36 

35 

34 

33 

Min- 
utes 

Merid- 
ian 

55°      56°  1   57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66" 

Alti- 
tudes 

Latitude  47°  Declination  Same  Name. 


281 


Declinations. 


Hour 

Angleti 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      II 

/     II 

/     // 

/     // 

/     // 

1     II 

/     // 

/     // 

/     // 

/     // 

1     II 

/     // 

Mm. 

4 

0  51 

0  52 

0  54 

0  55 

0  59 

100 

103 

107 

1  10 

1  15 

1  19 

1  25 

4 

8 

3  20 

3  28 

3  35 

3  44 

3  52 

4  03 

4  14 

4  28 

4  41 

4  57 

5  15 

5  38 

8 

12 

7  30 

7  48 

8  04 

8  23 

8  42 

9  06 

9  32 

9  59 

10  32 

1108 

11  50 

12  41 

12 

16 

13  22 

13  52 

14  20 

14  53 

15  30 

16  10 

16  56 

17  45 

18  44 

19  48 

2102 

22  31 

16 

20 

20  52 

21  40 

22  24 

23  16 

24  12 

25  16 

26  28 

27  44 

29  16 

30  56 

32  52 

35  12 

20 

24 

30  03 

31  12 

32  16 

33  30 

34  51 

36  23 

38  06 

39  57 

42  09 

44  33 

47  19 

50  41 

24 

28 

40  54 

42  28 

43  54 

45  37 

47  26 

49  32 

51  53 

57  22 

57  22 

60  37 

64  26 

69  00 

28 

32 

53  25 

55  28 

57  20 

59  34 

61  57 

64  41 

67  46 

74  55 

32 

36 

67  37 

70  12 

72  35 

75  23 

36 

40 

83  28 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

" 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

3.13 

3.25 

3.36 

3.49 

3.63 

3.79 

3.97 

4.16 

4.39 

4.64 

4.93 

5.28 

Ajh 

Log. 

0.495 

0.511 

0.526 

0.542 

0.559 

0.578 

0.598 

0.619 

0.642 

0.666 

0.692 

0.722 

Log. 

54 

88 

34 

83 

91 

64 

79 

09 

46 

52 

85 

63 

Limit 

32 

31 

30 

29 

28 

27 

26 

26 

25 

24 

23 

22 

Min- 
utes 

Merid- 
ian 

67° 

68° 

69° 

70° 

71= 

5 

72° 

73< 

3 

74 

i 

75 

D 

76 

} 

77 

3 

78 

3 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

f     II 

/     // 

/     // 

/      // 

/      // 

/     // 

/     II 

/     // 

/     // 

/         H 

/      // 

Min. 

4 

131 

139 

149 

159 

2  14 

2  35 

3  02 

4 

8 

6  03 

6  34 

7  12 

7  59 

8  59 

10  19 

12  11 

8 

12 

13  38 

14  47 

16  12 

17  56 

20  13 

23  12 

27  23 

12 

16 

24  14 

26  17 

28  48 

3152 

35  55 

41  16 

16 

20 

37  52 

4104 

45  00 

49  48 

56  08 

20 

24    . 

54  32 

59  09 

64  48 

24 

28 

74  13 

80  29 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

5.68 

6.16 

6.75 

7A7 

8.42 

9.67 

11.41 

Ajh 

Log. 

0.754 
35 

0.789 
58 

0.829 
30 

0.873 
32 

0.925 
31 

0.985 
43 

1.057 
29 

Log. 

Limit 

21 

20 

19 

17 

15 

13 

11 

9 

7 

5 

3 

0 

Min- 
utes 

Merid- 
ian   . 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

Alti- 
tudes 

282 


Latitude  47°  Declination  Same  Name. 


Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

// 

1 

n 

n 

1 

// 

2 
10 
22 

II 
9.4 

31 
36 
13 

5 

1 

2 

8 
18 
32 

7.7 

H 

33 
14 
30 
54 

1 

1 

1 

6 

15 

27 

43 

6.4 

// 

43 
54 
31 
33 
34 

5 

1 

1 

5 

13 

23 

36 

5.5 

n 

28 
53 
15 
33 

18 

2 

/     // 

1  16 
5  07 
11  30 
20  26 
3156 
45  59 

II 
4.79 

1     II 

107 
4  29 
10  05 
17  55 
28  00 
40  19 
54  53 

II 
4.20 

/     // 

0  59 
3  58 
8  56 
15  52 
24  48 
35  43 
48  37 

II 
3.72 

0  53 
3  32 
7  58 
14  10 
22  08 
31  53 
43  23 
56  39 

3.32 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.975 

89 

0.887 
05 

0.810 
23 

0.741 
94 

0.680 
34 

0.623 
25 

0.570 
54 

0.521 
14 

Log. 

Limit 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

Min- 
utes 

Merid- 
ian 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81= 

80° 

79° 

7QO    1  Alti- 
'°      1  tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

Min. 

4 

0  47 

0  43 

0  39 

0  35 

0  32 

0  30 

0  27 

0  25 

0  22 

0  20 

0  19 

0  17 

4 

8 

3  10 

2  51 

2  36 

2  22 

2  09 

157 

147 

1  39 

1  30 

1  22 

1  15 

1  08 

8 

12 

7  10 

6  26 

5  50 

5  18 

4  49 

4  23 

4  00 

3  42 

3  22 

3  05 

2  48 

2  33 

12 

16 

12  42 

11  26 

10  22 

9  26 

8  35 

7  49 

7  08 

6  34 

5  58 

5  27 

5  0J 

4  31 

16 

20 

19  52 

17  52 

16  12 

14  44 

13  24 

12  12 

11  OS 

10  16 

9  20 

8  32 

7  48 

7  04 

20 

24 

28  36 

25  44 

23  19 

21  13 

19  18 

17  34 

16  02 

14  47 

13  26 

12  17 

11  14 

10  11 

24 

28 

38  57 

35  01 

31  46 

28  53 

26  16 

23  55 

21  49 

20  07 

18  18 

16  44 

15  17 

13  51 

28 

32 

50  52 

45  44 

41  29 

37  43 

34  18 

31  14 

28  30 

26  17 

23  54 

2151 

19  58 

18  05 

32 

36 

64  22 

57  54 

52  29 

47  44 

43  25 

39  32 

36  05 

33  16 

30  14 

27  39 

25  17 

22  54 

36 

40 

64  48 

58  56 

53  36 

48  48 

44  32 

41  04 

37  20 

34  08 

31  12 

28  16 

40 

44 

71  18 

64  51 

59  03 

53  54 

49  41 

45  10 

41  18 

37  46 

34  12 

44 

48 

64  07 

59  08 

53  46 

49  09 

44  55 

40  42 

48 

52 

69  24 

63  06 

57  41 

52  43 

47  46 

52 

56 

66  54 

61  10 

55  24 

56 

60 

70  12 

63  36 

60 

II 

II 

" 

II 

II 

'I 

II 

II 

II 

II 

" 

II 

A,h 

2.98 
0.474 

2.68 

2.43 

2.21 

2.01 

1.83 

1.67 

1.54 

1.40 

1.28 

1.17 

1.06 

A,h 

Log. 

0.428 

0.385 

0.344 

0.303 

0.262 

0.222 

0.187 

0.146 

0.107 

0.068 

0.025 

Log. 

22 

13 

61 

39 

20 

45 

72 

52 

13 

21 

19 

31 

Limit 

29 

31 

33 

35 

37 

38 

40 

42 

45 

47 

50 

53 

Min- 
utes 

Merid- 
ian 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

66° 

Alti- 
tudes 

Latitude  47"  Declination  Contrary  Name* 


283 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  29 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 

It 

1.83 

0  29 

155 

4  19 

7  41 

12  00 

17  17 

23  31 

30  43 

38  53 

48  00 

58  05 

69  07 

8107 

94  05 

108  00 

1.80 

/     II 

0  28 
154 
4  16 
7  33 

11  48 
16  59 
23  08 
30  13 
38  14 
47  12 
57  07 
67  56 
79  46 
92  31 

106  12 

II 

1.77 

/       n 

0  28 
152 
4  12 

7  28 

11  40 

16  48 

22  52 

29  52 

37  48 

46  40 

56  28 

67  10 

78  52 

91  28 

105  00 
II 

1.75 

0  27 

150 

4  08 

7  20 

11  28 

16  31 

22  29 

29  21 

37  09 

45  32 

55  30 

66  01 

77  31 

89  54 

103  12 

1.72 

/     II 

0  27 
148 
4  03 

7  13 
11  16 
16  14 
22  05 
28  50 
36  31 
45  04 
54  32 
64  53 
76  09 
88  20 

101  24 

II 

1.69 

/     It 

0  27 
147 
4  00 

7  08 
1108 
16  02 
21  49 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 
87  18 

100  12 

II 

1.67 

/      // 

0  27 

1  45 
3  56 
7  00 

10  56 

15  45 

2125 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
II 

1.64 

1     II 

0  26 

1  43 
3  53 
6  55 

10  48 
15  34 
21  10 
27  38 
35  00 
43  12 
52  17 
62  12 
73  00 
84  41 

97  12 

II 

1.62 

/      // 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
5138 
61  26 
72  06 
83  38 

96  00 

II 

1.60 

/      // 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41  52 

50  40 

60  17 

70  45 

82  04 

94  12 

II 

1.57 

/      // 

0  25 

1  39 
3  43 
6  37 

10  20 
14  53 
20  15 
26  27 
33  29 
41  20 
50  01 
59  31 
69  51 
8101 

93  00 

II 

1.55 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.262 
45 

0.255 
27 

0.247 
97 

0.243 
04 

0.235 
53 

0.227 
89 

0.222 
72 

0.214 
84 

0.209 
52 

0.204 
12 

0.195 
90 

0.190 
33 

Log. 

Limit 

48 

49 

50 

50 

51 

51 

52 

53 

53 

54 

55 

56 

Min- 
utes 

Merid- 
ian 

43= 

42° 

41° 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18^ 

19'^ 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

1     II 

/     // 

1     II 

/      // 

/      // 

/      // 

1     II 

1     II 

1     II 

/      // 

/      // 

Min. 

4 

0  24 

0  24 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

4 

8 

138 

136 

136 

134 

133 

131 

130 

129 

128 

126 

125 

1  23 

8 

12 

3  40 

3  37 

3  35 

3  31 

3  28 

3  25 

3  22 

3  20 

3  17 

3  14 

3  11 

3  08 

12 

16 

6  32 

6  27 

6  21 

6  13 

6  08 

6  03 

5  58 

5  56 

5  51 

5  46 

5  41 

5  36 

16 

20 

10  12 

10  04 

9  56 

9  44 

9  36 

9  28 

9  20 

9  16 

9  08 

9  00 

8  52 

8  44 

20 

24 

14  41 

14  30 

14  18 

14  01 

13  49 

13  38 

13  26 

13  21 

13  09 

12  58 

12  46 

12  35 

24 

28 

20  00 

19  44 

19  29 

19  05 

18  49 

18  34 

18  18 

18  10 

17  54 

17  38 

17  23 

17  07 

28 

32 

26  07 

25  46 

25  26 

24  55 

24  35 

24  14 

23  54 

23  43 

23  23 

23  02 

22  42 

22  21 

32 

36 

33  03 

32  37 

32  11 

31  32 

31  06 

30  40 

30  14 

30  02 

29  36 

29  10 

28  44 

28  18 

36 

40 

40  48 

40  16 

39  44 

38  56 

38  24 

37  52 

37  20 

37  04 

36  32 

36  00 

35  28 

34  56 

40 

44 

49  22 

48  43 

48  04 

47  06 

46  27 

45  49 

45  10 

44  51 

44  13 

43  34 

42  55 

42  16 

44 

48 

58  45 

57  59 

57  13 

56  04 

55  18 

54  32 

53  46 

53  22 

52  36 

5150 

51  04 

50  18 

48 

52 

68  57 

68  03 

67  09 

65  48 

64  54 

64  00 

63  06 

62  38 

61  44 

60  50 

59  56 

59  02 

52 

56 

79  58 

78  55 

77  52 

76  18 

75  15 

74  13 

73  10 

72  39 

7137 

70  34 

69  31 

68  28 

56 

60 

9148 
II 

90  36 
II 

89  24 
II 

87  36 

86  24 

85  12 

II 

84  00 
II 

83  24 

82  12 

II 

81  00 

II 

79  48 

II 

78  36 

60 

A,h 

1.53 

1.51 

1.49 

1.46 

1.44 

1.42 

1.40 

1.39 

1.37 

1.35 

1.33 

1.31 

A,h 

Log. 

0.184 

0.178 

0.173 

0.164 

0.158 

0.152 

0.146 

0.143 

0.136 

0.130 

0.123 

0.117 

Log. 

69 

98 

19 

35 

36 

29 

13 

01 

72 

33 

85 

27 

Limit 

57 

58 

59 

59 

59 

60 

60 

61 

62 

62 

63 

64 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

Alti- 
tudes 

284 


Latitude  47°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26°  1  27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
•  24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/  // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

41  37 

49  32 

58  08 

67  25 

77  24 

1.29 

/  // 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  16 

66  23 

76  12 
II 

1.27 

0  20 
121 
3  02 
5  22 

8  24 
12  06 
16  28 
21  30 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 

75  36 

II 

1.26 

0  20 

120 

2  59 

5  17 

8  16 

11  54 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
II 

1.24 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 
15  57 
20  49 
26  21 
32  32 
39  12 
46  51 
54  59 
63  46 

73  12 

II 

1.22 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

II 

1.20 
0.079 
18 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
7124 

1.19 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
II 

1.17 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

II 

1.16 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
II 

1.14 

0  18 

111 

2  41 

4  47 

7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

/  // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.110 
59 

0.103 
80 

0.100 
37 

0.093 
42 

0.086 
36 

0.075 
55 

0.068 
19 

0.064 
46 

0.056 
90 

0.049 
22 

0.045 
32 

Log. 

Limit 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

Min- 
utes 

Merid- 
ian 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
II 

1.10 

/  // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 
II 

1.08 

/  // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

1 

// 

// 

/ 

// 

II 

II 

// 

II 

II 

/ 
1 

// 

/ 

// 

II 

]Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.041 
39 

0.033 
42 

0.025 
31 

Log. 

Limit 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

Alti- 
tudes 

Latitude  47**  Decimation  Contrary  Name. 
Declinations.  —  Inferior  Meridian. 


285 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

/       // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

11  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

// 

0.90 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 
52  48 

n 

0.88 

/     // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 

51  36 

If 

0.86 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 

5100 

// 

0.85 

0  13 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 
If 

0.83 

/      // 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

If 

0.82 

/     // 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 

ff 

0.80 

f     If 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

ff 

0.78 

/     // 

0  12 

0  50 

1  51 
3  17 
5  08 
7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 
ff 

0.77 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
ft 

0.75 

/     ff 

0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 

44  24 

fi 

0.74 

/     // 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 

43  12 

ff 

0.72 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.954 
24 

9.944 
48 

9.934 
50 

9.929 
42 

9.919 
08 

9.913 
81 

9.903 
09 

9.892 
09 

9.886 
49 

9.875 
06 

9.869 
23 

9.857 
33 

Log. 

Limit 

69 

67 

66 

67 

68 

69 

70 

71 

72 

74 

76 

77 

Min- 
utes 

Merid- 
ian 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

Alti- 
tudes 

Declinations 

.  —  Interior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/     // 

/     // 

/     // 

/      // 

;       '/ 

/     // 

Min. 

Min. 

4 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  08 

0  07 

4 

8 

0  45 

0  44 

0  42 

0  40 

0  40 

0  39 

0  38 

0  37 

0  35 

0  34 

0  33 

0  32 

8 

12 

141 

139 

135 

132 

1  30 

127 

125 

122 

1  19 

1  16 

1  13 

1  11 

12 

16 

2  59 

2  57 

2  49 

2  44 

2  42 

2  37 

2  31 

2  26 

2  21 

2  16 

2  11 

2  05 

16 

20 

4  40 

4  36 

4  24 

4  16 

4  12 

4  04 

3  56 

3  48 

3  40 

3  32 

3  24 

3  16 

20 

24 

6  43 

6  38 

6  21 

6  09 

6  03 

5  52 

5  40 

5  28 

5  17 

5  05 

4  54 

4  42 

24 

28 

9  09 

9  01 

8  37 

8  21 

8  14 

7  58 

7  43 

7  27 

7  11 

6  56 

6  40 

6  25 

28 

32 

1157 

1146 

11  15 

10  55 

10  45 

10  24 

10  04 

9  44 

9  23 

9  03 

8  42 

8  22 

32 

36 

15  07 

14  55 

14  16 

13  50 

13  37 

13  11 

12  45 

12  18 

1153 

11  27 

11  01 

10  35 

36 

40 

18  40 

18  24 

17  36 

17  04 

16  48 

16  16 

15  44 

15  12 

14  40 

14  08 

13  36 

13  04 

40 

44 

22  35 

22  16 

21  18 

20  39 

20  20 

19  41 

19  02 

18  24 

17  45 

17  06 

16  27 

15  48 

44 

48 

26  51 

26  29 

25  20 

24  34 

24  11 

23  25 

22  39 

2154 

21  07 

20  21 

19  35 

18  49 

48 

52 

31  33 

3105 

29  44 

28  50 

28  23 

27  29 

26  35 

25  41 

24  47 

23  53 

22  59 

22  05 

52 

56 

36  35 

36  04 

34  30 

33  27 

32  56 

31  53 

30  50 

29  48 

28  45 

27  42 

26  39 

25  36 

56 

60 

42  00 

4124 

39  36 

38  24 

37  48 

36  36 

35  24 

34  12 

33  00 

3148 

30  36 

29  24 

60 

ff 

ff 

ff 

ff 

ff 

" 

" 

ff 

" 

" 

ff 

" 

A,h 

0.70 

0.69 

0.66 

0.64 

0.63 

0.61 

0.59 

0.57 

0.55 

0.53 

0.51 

0.49 

Aih 

Log. 

9.845 

9.838 

9.819 

9.806 

9.799 

9.785 

9.770 

9.755 

9.740 

9.724 

9.707 

9.690 

10 

85 

54 

18 

34 

33 

85 

87 

36 

28 

57 

20 

Limit 

78 

78 

79 

79 

80 

81 

81 

82 

83 

83 

83 

84 

Min- 
utes 

Merid- 
ian 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

Alti- 
tudes 

286 


Latitude  48°  Declination  Same  Name. 


Declinationts. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Uour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  28 

154 

4  16 

7  33 

11  48 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 

If 

1.77 

/     // 

0  29 

1  55 
4  19 
7  41 

12  00 
17  17 
23  31 
30  43 
38  53 
48  00 
58  05 
69  07 
81  07 
94  05 
108  00 

1.80 

t      " 

0  29 

157 

4  23 

7  49 

12  12 

17  34 

23  55 

31  13 

39  32 

48  48 

59  03 

70  16 

82  28 

95  39 

109  48 
11 

1.83 

t     II 

0  30 

159 

4  28 

7  56 

12  24 

17  52 

24  18 

31  44 

40  11 

49  36 

60  01 

7125 

83  49 

97  13 

11136 

II 

1.86 

/     // 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 

II 

1.89 

/      // 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

4128 

51  12 

6157 

73  44 

86  32 

100  21 

II 
1.92 

/     // 

0  31 

2  04 

4  41 

8  19 

13  00 

18  43 

25  29 

33  17 

42  07 

52  00 

62  55 

74  53 

87  53 

101  55 

II 
1.95 

0  31 

2  07 

4  47 

8  29 

13  16 

19  06 

26  01 

33  58 

42  59 

53  04 

64  12 

76  25 

89  41 

104  00 

II 
1.99 

/     // 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

9102 

105  35 

II 
2.02 

/     // 

0  33 

2  12 

4  57 

8  47 

13  44 

19  47 

26  55 

35  09 

44  30 

54  56 

66  28 

79  06 

92  50 

II 
2.06 

0  34 

2  14 
5  02 
8  58 
14  00 
20  10 
27  26 
35  50 
45  22 
56  00 
67  46 
80  38 
94  38 

II 
2.10 

/      // 

0  35 

2  17 

5  08 

9  08 

14  16 

20  33 

27  57 

36  31 

46  14 

57  04 

69  03 

82  10 

96  26 

2.14 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.247 
97 

0.255 
27 

0.262 
45 

0.269 
51 

0.276 
46 

0.283 
30 

0.290 
03 

0.298 
85 

0.305 
35 

0.313 

87 

0.322 
22 

0.330 
41 

Log, 

Limit 

49 

49 

48 

48 

47 

47 

46 

46 

45 

45 

44 

44 

Min- 
utes 

Merid- 
ian 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

1     II 

/      // 

/      // 

/     // 

/     // 

/      // 

/      // 

/      // 

/      " 

/   •  // 

/      // 

Min. 

4 

0  35 

0  35 

0  36 

0  37 

0  38 

0  39 

0  40 

0  41 

0  42 

0  43 

0  44 

0  46 

4 

8 

2  20 

2  23 

2  26 

2  29 

2  32 

2  37 

2  40 

2  44 

2  48 

2  53 

2  58 

3  03 

8 

12 

5  15 

5  21      5  29 

5  35 

5  43 

5  52 

6  00 

6  09 

6  18 

6  29 

6  41 

6  52 

12 

16 

9  21 

9  31 

9  43 

9  57 

10  09 

10  24 

10  40 

10  55 

11  14 

11  31 

11  51 

12  12 

16 

20 

14  36 

14  52 

15  12 

15  32 

15  52 

16  16 

16  40 

17  04 

17  32 

18  00 

18  32 

19  04 

20 

24 

2102 

21  24 

21  53 

22  22 

22  51 

23  25 

24  00 

24  35 

25  15 

25  55 

26  41 

27  28 

24 

28 

28  37 

29  09 

29  48 

30  27 

3106 

31  53 

32  40 

33  27 

34  22 

35  17    36  20 

37  22 

28 

32 

37  22 

38  04 

38  55 

39  46 

40  37 

4139 

42  40 

43  41 

44  53 

46  05 

47  27 

48  48 

32 

36 

47  19 

48  10 

49  15 

50  20 

51  25 

52  42 

54  00 

55  18 

56  49 

58  19 

60  03 

61  47 

36 

40 

58  24 

59  28 

60  48 

62  08 

63  28 

65  04 

66  40 

68  16 

70  08 

72  00 

74  08 

76  16 

40 

44 

70  40 

71  57 

73  34 

75  11 

76  48 

78  43 

80  40 

82  36 

84  52 

87  07 

44 

48 

84  05 

85  38 

87  33 

89  28 

91  23 

93  42 

96  00 

48 

52 
56 

98  41 

100  30 

102  45 

105  00 

107  15 

52 
56 

60 

II 

// 

II 

'// ' 

II 

II 

II 

II 

II 

II 

II 

II 

60 

Ajh 

2.19 

2.23 

2.28 

2.33 

2.38 

2.44 

2.50 

2.56 

2.63 

2.70 

2.78 

2.86 

A,h 

0.340 

0.348 

0.357 

0.367 

0.376 

0.387 

0.397 

0.408 

0.419 

0.431 

0.444 

0.456 

Log. 

Log. 

44 

30 

93 

36 

58 

39 

94 

24 

96 

36 

04 

37 

Limit 

43 

43 

42 

41 

41 

40 

39 

38 

37 

36 

35 

34 

Min- 
utes 

Merid- 
ian 

54° 

55°  1   56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

Alti- 
tudes 

Latitude  48"  Declination  Same  Name. 


287 


Declinations. 


Hoar 
Angltsti 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

1     II 

/     // 

/     // 

t'      " 

/     // 

/      // 

/     // 

/     II 

/      // 

/      // 

Min. 

4 

0  47 

0  49 

0  51 

0  52 

0  54 

0  56 

0  59 

102 

105 

107 

1  12 

1  17 

4 

8 

3  08 

3  15 

3  21 

3  30 

3  38 

3  46 

3  55 

4  06 

4  19 

4  33 

4  48 

5  06 

8 

12 

7  05 

7  19 

7  33 

7  51 

8  08 

8  28 

8  50 

9  14 

9  42 

10  14 

10  48 

11  29 

12 

16 

12  35    13  01 

13  27 

13  57 

14  28 

15  04 

15  42 

16  26 

17  14 

18  10 

19  12 

20  23 

16 

20 

19  40    20  20 

2100 

2148 

22  36 

23  32 

24  32 

25  40 

26  56 

28  24 

30  00    31  52 

20 

24 

28  19j  29  17 

30  15 

3123 

32  32 

33  53 

35  20 

36  58 

38  47 

40  54 

43  12    45  53 

24 

28 

38  33!  39  51 

41  09 

42  44 

44  18 

46  08 

48  05 

50  18 

52  47 

55  40 

58  48 

62  26 

28 

32 

50  2l|  52  03 

53  45 

55  49 

57  51 

60  15 

62  48 

65  42 

68  57 

32 

36 

63  43    65  53 

68  03 

70  38 

73  14 

76  15 

36 

40 

78  40    81  20 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

// 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

A,h 

2.95      3.05 

3.15 

3.27 

3.39 

3.53 

3.68 

3.85 

4.04 

4.26 

4.50 

4.78 

A,h 

liOg. 

0.469    0.484 

0.498 

0.514 

0.530 

0.547 

0.565 

0.585 

0.606 

0.629 

0.653 

0.679 

82 

30 

31 

55 

20 

77 

85 

46 

38 

41 

21 

43 

Log. 

Limit 

33 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

Min- 
utes 

Merid- 
ian 

66°  i    67° 

68° 

69° 

70* 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36°       37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46°      47° 

Hour 
Angles 

Min. 

'      " 

/     // 

/     '/ 

1       n 

/     // 

/     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

122 

128 

135 

144 

155 

2  10 

2  29 

2  56 

4 

8 

5  26 

5  52 

6  21 

6  57 

7  43 

8  41 

9  58 

11  45 

8 

12 

12  15    13  12 

14  19 

15  39 

17  21 

19  32 

22  25 

26  27 

12 

16 

21  49    23  28 

25  25 

27  49 

30  51 

34  44 

39  51 

16 

20 

34  04    36  40 

39  44 

43  28 

48  12 

54  16 

20 

24 

49  04    52  48 

57  13 

62  36 

24 

28 

66  46 

7152 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

" 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

5.11 

5.50 

5.96 

6.52 

7.23 

8.14 

9.34 

11.02 

Ajh 

Log. 

0.708,  0.740 

0.775 

0.814 

0.859 

0.910 

0.970 

1.042 

42        36 

25 

25 

14 

62 

35 

18 

Log. 

Limit 

23        22 

21 

19 

17 

16 

14 

12 

10 

8 

5 

3 

Min- 
utes 

Merid- 
ian 

78' 

' 

^ 

'9= 

80 

3 

81° 

82 

3 

83< 

9 

84° 

85< 

} 

86° 

I 

r 

' 

88° 

89' 

Alti- 
tudee 

288 


Latitude  48°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Honr 

Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

II 

/ 

// 

// 

/ 

// 
II 

1 
II 

// 

II 

// 

2; 

9' 
21' 
38' 

II 
9.0 

25 
11 
16 
12 

r 

1 

1 
7 

17 
31 
49 

II 
7.3 

J8 
53 
14 
32 
16 

1     It 

139 

6  35 

14  50 

26  22 

41  12 

II 
6.18 

/      // 

124 
5  38 
12  41 
22  31 
35  12 
50  41 

II 
5.28 

1  13 
4  53 
10  58 
19  30 
30  28 
43  52 

II 
4.57 

/     // 

104 
4  17 
9  37 
17  07 
26  44 
38  30 
52  24 

II 
4.01 

/     // 

0  57 
3  47 
8  31 
15  09 
23  40 
34  05 
46  23 
60  35 

II 
3.55 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.957 
61 

0.868 
64 

0.790 
99 

0.722 
63 

0.659 
92 

0.603 
14 

0.550 
23 

Log. 

Limit 

0 

3 

5 

8 

11 

13 

15 

17 

19 

21 

23 

25 

Min- 
utes 

Merid- 
ian 

9C 

1° 

8 

9= 

fi 

8° 

87= 

8e 

>° 

85= 

84' 

) 

83° 

82 

> 

81° 

80 

> 

79° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 

0  51 

1     II 
0  46 

0  41 

0  37 

0  34 

/      // 
0  30 

1     II 
0  27 

0  26 

0  23 

1     It 
0  21 

0  19 

0  17 

Min. 
4 

8 

3  21 

3  01 

2  43 

2  27 

2  14 

2  01 

151 

142 

133 

123 

1  17 

1  10 

8 

12 

7  35 

6  47 

6  07 

5  31 

5  01 

4  34 

4  09 

3  48 

3  28 

3  08 

2  53 

2  37 

12 

16 

13  29 

12  05 

10  53 

9  49 

8  36 

8  06 

7  23 

6  44 

6  08 

5  36 

5  07 

4  39 

16 

20 

2104 

18  52 

17  00 

15  20 

13  56 

12  40 

11  32 

10  32 

9  36 

8  44 

8  00 

7  16 

20 

24 

30  21 

27  10 

24  29 

22  05 

20  04 

18  14 

16  36 

15  10 

13  49 

12  35 

1131 

10  28 

24 

28 

41  17 

36  59 

33  19 

30  03 

27  19 

24  50 

22  37 

20  39 

18  49 

17  07 

15  41 

14  15 

28 

32 

53  55 

48  18 

43  31 

39  15 

35  40 

32  26 

29  32 

26  58 

24  35 

22  21 

20  29 

18  36 

32 

36 

6108 

55  05 

49  41 

45  09 

4102 

37  22 

34  08 

3106 

28  18 

25  55 

23  33 

36 

40 

6120 

55  44 

50  40 

46  08 

42  08 

38  24 

34  56 

32  00 

29  04 

40 

44 

61  18 

55  49 

50  59 

46  27 

42  16 

38  43 

35  10 

44 

48 

66  24 

60  40 

55  18 

50  18 

46  05 

4151 

48 

52 

71  12 

64  54 

59  02 

54  05 

49  07 

52 

56 

68  28 

62  43 

56  58 

56 

60 

',; 

II 

'//' ' 

'// ' 

II 

II 

II 

II 

II 

II 

72  00 

65  24 

II 

60 

Aih 

3.16 

2.83 

2.55 

2.30 

2.09 

1.90 

1.73 

1.58 

1.44 

1.31 

1.20 

1.09 

A,h 

Log. 

0.499 
69 

0.451 

79 

0.406 
54 

0.361 
73 

0.320 
15 

0.278 
75 

0.238 
05 

0.198 
66 

0.158 
36 

0.117 
27 

0.079 
18 

0.037 
43 

Log. 

Limit 

27 

29 

31 

33 

35 

37 

39 

41 

43 

45 

48 

51 

Min- 
utes 

Merid- 
ian 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

67° 

Alti- 
tudes 

Latitude  48°  Declination  Contrary  Name* 


289 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/     // 

Min. 

Min. 

4 

0  28 

0  28 

0  27 

0  27 

0  27 

0  27 

0  26 

0  25 

0  25 

0  25 

0  24 

0  24 

4 

8 

1  54 

1  52 

150 

148 

146 

145 

143 

1  42 

141 

1  39 

138 

136 

8 

12 

4  16 

411 

4  06 

4  03 

3  59 

3  56 

3  53 

3  49 

3  46 

3  43 

3  40 

3  36 

12 

16 

7  33 

7  25 

7  18 

7  13 

7  05 

7  00 

6  55 

6  47 

6  42 

6  37 

6  32 

6  24 

16 

20 

11  48 

11  36 

1124 

11  16 

1104 

10  56 

10  48 

10  36 

10  28 

10  20 

10  12 

10  00 

20 

24 

16  59 

16  42 

16  25 

16  14 

15  57 

15  45 

15  34 

15  16 

15  04 

14  53 

14  41 

14  24 

24 

28 

23  08 

22  44 

22  21 

22  05 

2141 

2125 

21  10 

20  47 

20  31 

20  15 

20  00 

19  36 

28 

32 

30  13 

29  42 

29  11 

28  50 

28  19 

27  59 

27  38 

27  08 

26  48 

26  27 

26  07 

25  36 

32 

36 

38  14 

37  35 

36  56 

36  31 

35  52 

35  26 

35  00 

34  21 

33  55 

33  29 

33  03 

32  24 

36 

40 

47  12 

46  24 

45  36 

45  04 

44  16 

43  44 

43  12 

42  24 

41  52 

41  20 

40  48 

40  00 

40 

44 

57  07 

56  08 

55  10 

54  32 

53  34 

52  55 

52  17 

51  18 

50  40 

50  01 

49  22 

48  24 

44 

48 

67  56 

66  47 

65  38 

64  53 

63  44 

62  58 

62  12 

6103 

60  17 

59  31 

58  45 

57  36 

48 

52 

79  46 

78  25 

77  04 

76  09 

74  48 

73  54 

73  00 

7139 

70  45 

69  51 

68  57 

67  36 

52 

56 

92  31 

90  56 

89  22 

88  20 

86  46 

85  43 

84  41 

83  06 

82  04 

8101 

79  58 

78  24 

56 

60 

106  12 

104  24 

102  36 

101  24 

99  36 

98  24 

97  12 

95  24 

94  12 

93  00 

9148 

90  00 

60 

II 

II 

" 

" 

" 

" 

II 

II 

II 

II 

II 

It 

A,h 

1.77 

1.74 

1.71 

1.69 

1.66 

1.64 

1.62 

1.59 

1.57 

1.55 

1.53 

1.50 

Ajh 

Log. 

0.247 

0.240 

0.233 

0.227 

0.220 

0.214 

0.209 

0.201 

0.195 

0.190 

0.184 

0.176 

Log. 

97 

55 

00 

89 

11 

84 

52 

40 

90 

33 

69 

09 

Limit 

49 

49 

50 

51 

52 

53 

53 

54 

55 

56 

56 

56 

Min- 
utes 

Merid- 
ian 

42° 

41° 

40°      39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

/     // 

1     II 

/      // 

/      // 

/      // 

/      // 

/     // 

/      // 

/      // 

/     // 

/      // 

Min. 

4 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

021 

0  21 

0  20 

4 

8 

1  35 

134 

133 

1  31 

130 

129 

128 

126 

125 

1  23 

123 

122 

8 

12 

3  34 

3  31 

3  28 

3  25 

3  23 

3  20 

3  17 

3  14 

3  11 

3  08 

3  07 

3  05 

12 

16 

6  18 

6  13 

6  08 

6  03 

6  01 

5  56 

5  51 

5  46 

5  41 

5  36 

5  33 

5  27 

16 

20 

9  52 

9  44 

9  36 

9  28 

9  24 

9  16 

9  08 

9  00 

8  52 

8  44 

8  40 

8  32 

20 

24 

14  12 

14  01 

13  49 

13  38 

13  32 

13  21 

13  09 

12  58 

12  46 

12  35 

12  29 

12  17 

24 

28 

19  21 

19  05 

18  49 

18  34 

18  26 

18  10 

17  54 

17  38 

17  23 

17  07 

16  59 

16  44 

28 

32 

25  16 

24  55 

24  35 

24  14 

24  04 

23  43 

23  23 

23  02 

22  42 

22  21 

22  11 

21  51 

32 

36 

3158 

31  32 

3106 

30  40 

30  27 

30  02 

29  36 

29  10 

28  44 

28  18 

28  05 

27  39 

36 

40 

39  28 

38  56 

38  24 

37  52 

37  36 

37  04 

36  32 

36  00 

35  28 

34  56 

34  40 

34  08 

40 

44 

47  45 

47  06 

46  27 

45  49 

45  29 

44  51 

44  13 

43  34 

42  55 

42  16 

4157 

41  18 

44 

48 

56  50 

56  04 

55  18 

54  32 

54  09 

53  22 

52  36 

51  50 

51  04 

50  18 

49  55 

49  09 

48 

52 

66  42 

65  48 

64  54 

64  00 

63  33 

62  38 

61  44 

60  50 

59  56 

59  02 

58  35 

57  41 

52 

56 

77  21 

76  18 

75  15 

74  13 

73  41 

72  39 

71  37 

70  34 

69  31 

68  28 

67  57 

66  54 

56 

60 

88  48 

87  36 

86  24 

85  12 

84  36 

83  24 

82  12 

8100 

79  48 

78  36 

78  00 

76  48 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

A,h 

1.48 

1.46 

1.44 

1.42 

1.41 

1.39 

1.37 

1.35 

1.33 

1.31 

1.30 

1.28 

Aih 

Log. 

0.170 

0.164 

0.158 

0.152 

0.149 

0.143 

0.136 

0.130 

0.123 

0.117 

0.113 

0.107 

Log. 

26 

35 

36 

29 

22 

01 

72 

33 

85 

27 

94 
64 

21 
65 

Limit 

57 

58 

59 

60 

60 

61 

61 

62 

63 

63 

Min- 
utes 

Merid- 
ian 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

Alti- 
tudes 

290 


Latitude  48°  Declination  Gwitfafy  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

2130 

27  13 

33  36 

40  38 

48  23 

56  47 

65  51 

75  36 

1.26 

/      // 

0  20 

120 

2  59 

5  17 

8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 

1.24 

0  20 

1  19 

2  57 
5  15 
8  12 

1148 
16  05 
2100 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 

73  48 

// 

1.23 

/      // 

0  19 

1  18 

2  54 
5  10 
8  04 

1137 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
If 

1.21 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
II 

1.20 

/      // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 
69  36 

1.16 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
II 

1.14 

/      // 

0  19 

112 

2  42 

4  50 

7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 

1.13 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

II 

1.12 

/     // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  50 

II 

1.10 

0  17 

109 

2  35 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 

II 

1.08 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.100 
37 

0.093 
42 

0.089 
91 

0.082 
79 

0.079 

18 

0.071 

88 

0.064 
46 

0.056 
90 

0.053 
08 

0.049 
22 

0.041 
39 

0.033 
42 

Log. 

Limit 

66 

67 

67 

68 

69 

70 

71 

73 

74 

75 

76 

77 

Min- 
utes 

Merid- 
ian 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37°      38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  17 

1  09 

2  34 
4  34 
7  08 

10  16 
13  59 
18  16 
23  07 
28  32 
34  32 
41  05 
48  13 
55  56 

64  12 

II 

1.07 

1     II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  50 

63  00 

II 

1.05 

1 
II 

// 

II 

// 

II 

II 

// 

II 

// 

II 

// 

II 

// 

/ 

// 

// 

I  II 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

II  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

0.90 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.029 
38 

0.021 
19 

'•-;  .0. 

Limit 

78 

79 

gq        Min- 
^^     1  utes 

Merid- 
ian 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

40     [     50     ,  Alti- 
*      1     ^       'tudes 

Latitude  48°  Declination  Contrary  Name. 
Declinations.  —  Inferior  Meridian. 


291 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 

52  48 

If 

0.88 

/  // 

0  14 
0  56 

2  05 

3  43 

5  48 
8  21 
1122 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

n 

0.87 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 
5100 

0.85 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

1     II 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

II 

0.82 

1     II 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

31  06 

36  30 

42  20 

48  36 

II 

0.81 

/  // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

/  // 

0  12 
0  50 
151 
3  17 

5  08 
7  23 
10  04 
13  09 
16  38 
20  32 
24  51 
29  32 
34  42 
40  15 

46  12 

II 

0.77 

0  12 
0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

0.75 

/  // 

0  12 

0  48 

1  47 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 

44  24 

II 

0.74 

/  // 

0  12 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 

15  46 

19  28 

23  33 

28  00 

32  54 

38  09 

43  48 
II 

0.73 

/  // 

Oil 
0  46 
142 

3  02 

4  44 
6  49 
9  17 

12  07 

15  20 

18  56 

22  54 

27  14 

32  00 

37  07 

42  36 
II 

0.71 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.944 

48 

9.939 
52 

9.929 
42 

9.924 
28 

9.913 
81 

9.908 
49 

9.897 
63 

9.886 
49 

9.875 
06 

9.869 
23 

9.863 
32 

9.851 
26 

Log. 

Limit 

68 

67 

66 

67 

68 

68 

69 

70 

71 

73 

75 

76 

Min- 
utes 

Merid- 
ian 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

Alti- 
tudes 

Declinations. 


Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/  // 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

11  57 
15  07 
18  40 
22  35 
26  51 
31  33 
36  35 

42  00 

II 

0.70 

/  // 

Oil 
0  43 

138 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

21  57 

26  08 

30  38 

35  33 

40  48 
II 

0.68 

/  // 

Oil 

0  41 

133 

2  47 

4  20 

6  15 

8  29 

1105 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 
// 

0.65 

/  II 

Oil 

0  40 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
II 

0.63 

/  // 

0  10 
0  39 
129 
2  39 

4  08 

5  58 
8  06 

10  34 

13  24 

16  32 

20  01 

23  48 

27  56 

32  25 

37  12 
II 

0.62 

/  // 

0  10 
0  38 
126 
2  34 

4  00 

5  46 
7  50 

10  14 

12  58 

16  00 

19  22 

23  02 

27  02 

31  22 

36  00 
II 

0.60 

/  // 

0  09 
0  37 
124 

2  28 

3  52 
5  34 
7  35 
9  54 

12  32 

15  28 

18  43 

22  16 

26  08 

30  19 

34  48 
II 

0.58 

1     II 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  19 

15  12 

18  24 

21  52 

25  41 

29  48 

34  12 
II 

0.57 

/  // 

0  09 

0  35 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

1153 
14  40 
17  45 
21  07 
24  47 
28  45 

33  00 

II 

0.55 

I  II 

0  09 

0  34 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

II  27 
14  08 
17  06 
20  21 
23  53 
27  42 

31  48 

II 

0.53 

/  // 

0  08 

0  33 

1  13 

2  11 

3  24 

4  54 
6  40 
8  42 

1101 
13  36 
16  27 
19  35 
22  59 
26  39 

30  36 

II 

0.51 

1     II 

0  07 

0  32 

1  11 

2  05 

3  16 

4  42 
6  25 
8  22 

10  35 

13  04 

15  48 

18  49 

22  05 

25  36 

29  24 
II 

0.49 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

Log. 

9.845 
10 

9.832 
51 

9.812 
91 

9.799 
34 

9.792 
39 

9.778 
15 

9.763 
43 

9.755 

87 

9.740 
36 

9.724 

28 

9.707 
57 

9.690 
20 

Log. 

Limit 

76 

77 

78 

79 

79 

80 

80 

81 

82 

83 

83 

24 

Min- 
utes 

Merid- 
ian 

18° 

19° 

20°   21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

Alti- 
tudes 

292 


Latitude  49^  Decimation  Same  Name. 


Declination.s. 


Hour  1     no 
Angles'     ^ 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8°    1    9° 

10°      11° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

/       1/ 

0  27 

150 

4  06 

7  18 

1124 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 

II 

1.71 

/     // 

0  27 

1  51 
4  09 
7  23 

1132 

16  36 

22  37 

29  32 

37  22 

46  08 

55  49 

66  24 

77  58 

90  25 

103  48 
II 

1.73 

/       n 

0  28 

153 

4  14 

7  30 

1144 

16  54 

23  00 

30  02 

38  01 

46  56 

56  47 

67  33 

79  19 

9159 

105  36 

II 

1.76 

/      // 

0  28 

155 

4  18 

7  38 

1156 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 
II 

1.79 

/      // 

0  29 

156 

4  22 

7  46 

12  08 

17  29 

23  47 

3103 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 
II 

1.82 

/      // 

0  30 

158 

4  26 

7  54 

12  20 

17  46 

24  10 

31  34 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 
II 

1.85 

/      //    /      // 

0  30     0  30 

2  00     2  02 

4  31      4  35 

8  01      8  09 

12  32    12  44 

18  03    18  20 

24  34    24  58 

32  05    32  36 

40  37    41  15 

50  08    50  56 

60  40    61  37 

72  11    73  21 

84  43j  86  05 

98  15    99  49 

112  48  114  36 
//          // 

1.88      1.91 

/     // 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

41  54 

51  44 

62  35 

74  30 

87  26 

101  23 

II 
1.94 

/     // 

0  31 

2  06 

4  46 

8  26 

13  12 

19  00 

25  53 

33  48 

42  46 

52  48 

63  53 

76  02 

89  14 

103  29 

II 
1.98 

/      // 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

9102 

105  35 

II 
2.02 

0  33 

2  11 

4  55 

8  45 

13  40 

19  41 

26  47 

34  59 

44  17 

54  40 

66  09 

78  43 

92  23 

107  08 

II 
2.05 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Log. 

0.233 
00 

0.238 
05 

0.245 
51 

0.252 
85 

0.260 
07 

0.267 
17 

0.274 
16 

0.281 
03 

0.287 
80 

0.296 
67 

0.305 
35 

0.311 
75 

Log. 

Limit 

50 

50 

49 

49 

48 

48 

47 

47 

46 

46 

45 

4K     1    Min- 
*^     1    utes 

Merid- 
ian 

41° 

42° 

43°      44°      45° 

46° 

47°  i   48° 

49° 

50° 

51° 

COO       Alti- 
^^        tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

1     II 

/     // 

/     // 

/      // 

/      // 

1     II 

/     // 

/     It 

/     // 

/     // 

Min. 

Min. 

4 

0  33 

0  34 

0  35 

0  35 

0  36 

0  37 

0  38 

0  39 

0  40     0  41 

0  42 

0  43 

4 

8 

2  14 

2  16 

2  19 

2  23 

2  26 

2  28 

2  32 

2  37 

2  40 

2  44 

2  48 

2  53 

8 

12 

5  01 

5  06 

5  14 

5  21 

5  27 

5  34     5  43 

5  52 

6  00 

6  09 

6  18 

6  29 

12 

16 

8  55 

9  06 

9  18 

9  31 

9  41 

9  54 

10  09 

10  24 

10  40 

10  55 

11  14 

11  31 

16 

20 

13  56 

14  12 

14  32 

14  52 

15  08 

15  28 

15  52 

16  16 

16  40 

17  04 

17  32 

18  00 

20 

24 

20  04 

20  27 

20  56 

21  24 

2147 

22  17 

22  51 

23  25 

24  00 

24  35 

25  15 

25  55 

24 

28 

27  19 

27  50 

28  29    29  09 

29  40 

30  19 

3106 

3153 

32  40 

33  27 

34  22 

35  17 

28 

32 

35  40 

36  21 

37  12,  38  04 

38  45 

39  35    40  37 

4139 

42  40    43  41 

44  53 

46  05 

32 

36 

45  09 

46  01 

47  06 

48  10 

49  02 

50  07 

5125 

52  42 

54  oo'  55  18 

56  49 

58  19 

36 

40 

55  44 

56  48 

58  08 

59  28 

60  32 

61  52 

63  28 

65  04 

66  40    68  16 

70  08 

72  00 

40 

44 

67  26 

68  44 

70  21 

7157 

73  15 

74  52 

76  48 

78  43 

80  40 

82  36 

84  52 

87  07 

44 

48 

80  15 

8146 

83  42    85  38 

87  10 

89  05 

9123 

93  42 

96  00 

48 

52 

94  11 

95  59 

98  14,100  30 

102  18 

104  33 

107  15 

52 

56 

... 

56 

60 

60 

II 

" 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

A,h 

2.09 

2.13 

2.18 

2.23 

2.27 

2.32 

2.38 

2.44 

2.50 

2.56 

2.63 

2.70 

Ajh 

Log. 

0.320 

0.328 

0.338 

0.348 

0.356 

0.365   0.376 

0.387 

0.397 

0.408 

0.419 

0.431 

Log. 

15 

38 

46 

30 

03 

49,        58 

39 

94 

24 

96 

36 

Limit 

44 

44 

43 

42 

42 

41 

41 

40 

39 

38 

37 

36 

Min- 
utes 

Merid- 
ian 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

Alti- 
tudes 

Latitude  49°  Declination  Same  Name. 


293 


Declinations.  ' 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      /' 

/     // 

1     II 

/     // 

/      II 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  44 

0  46 

0  47 

0  49 

0  50 

0  52 

0  54 

0  57 

100 

102 

106 

1  10 

4 

8 

2  58 

3  04 

3  10 

3  16 

3  23 

3  31 

3  40 

3  49 

4  00 

4  10 

4  23 

4  39 

8 

12 

6  41 

6  55 

7  08 

7  21 

7  36 

7  54 

8  14 

8  34 

8  59 

.9  25 

9  53 

10  28 

12 

16 

11  51 

12  17 

12  40 

13  03 

13  32 

14  02 

14  38 

15  14 

15  57 

16  43 

17  35 

18  36 

16 

20 

18  32 

19  12 

19  48 

20  24 

2108 

21  56 

22  52 

23  48 

24  56 

26  08 

27  28 

29  04 

20 

24 

26  41 

27  39 

28  30 

29  23 

30  26 

31  35 

32  55 

34  16 

35  54 

37  38 

39  34 

4152 

24 

28 

36  20 

37  38 

38  49 

39  59 

4125 

43  00 

44  50 

46  39 

48  52 

51  14 

53  50 

56  58 

28 

32 

47  27 

49  09 

50  42 

52  13 

54  06 

56  09 

58  33 

60  56 

63  50 

66  54 

32 

36 

60  03 

62  13 

64  09 

66  06 

68  29 

7104 

74  05 

36 

40 

74  08 

76  48 

79  12 

8136 

40 

44 

44 

48 

. . . 

48 

52 

52 

56 

56 

60 

60 

n 

II 

II 

II 

II 

" 

II 

II 

II 

II 

II 

II 

Ajh 

2.78 

2.88 

2.97 

3.06 

3.17 

3.29 

3.43 

3.57 

3.74 

3.92 

4.12 

4.36 

Ajh 

Log. 

0.444 

0.459 

0.472 

0.485 

0.501 

0.517 

0.535 

0.552 

0.572 

0.593 

0.614 

0.639 

Log. 

04 

39 

76 

72 

06 

20 

29 

67 

87 

29 

90 

49 

Limit 

35 

34 

33 

82 

31 

30 

29 

28 

27 

26 

25 

25 

Min- 
utes 

Merid- 
ian 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

.74° 

75° 

76° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/      // 

/     // 

/      // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

1  14 

1  19 

125 

1  32 

1  41 

151 

2  06 

2  24 

2  50 

4 

8 

4  56 

5  16 

5  40 

6  09 

6  44 

7  26 

8  22 

9  37 

1120 

8 

12 

11  06 

1153 

12  44 

13  50 

15  08 

16  46 

18  50 

21  37 

25  30 

12 

16 

19  46 

2107 

22  40 

24  34 

26  56 

29  46 

33  30 

38  27 

45  22 

16 

20 

30  52 

33  00 

35  24 

38  24 

42  04 

46  32 

52  20 

20 

24 

44  27 

47  31 

50  59 

55  18 

60  35 

24 

28 

60  30 

64  41 

69  23 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

" 

n 

II 

II 

II 

II 

II 

II 

// 

A,h 

4.63 

4.95 

5.31 

5.76 

6.31 

6.98 

7.85 

9.01 

10.63 

Ajh 

Log. 

0.665 

0.694 

0.725 

0.760 

0.800 

0.843 

0.894 

0.954 

1.026 

58 

61 

09 

42 

03 

86 

87 

72 

53 

Limit 

24 

23 

22 

21 

19 

18 

16 

14 

12 

10 

8 

6 

Min- 
utes 

Merid- 
ian 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

Alti- 
tudes 

294 


Latitude  49°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49 

'      50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/       n 

1 

II    1     II 

/     // 

/     // 

/     // 

/      // 

1     II 

1      n 

1     II 

1      II 

1      II 

Min. 

4 

2  19 

153 

134 

1  21 

1  10 

101 

4 

8 

9  16 

7  33 

6  18 

5  23 

4  39 

4  05 

8 

12 

20  51 

16  58 

14  11 

12  06 

10  28 

9  10 

12 

16 

37  05 

30  10 

25  13 

21  30 

18  36 

16  18 

16 

20 

39  24 

33  36 

29  04 

25  18 

20 

24 

48  23 

41  52 

36  41 

24 

28 

49  55 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

ir 

" 

II 

// 

II 

" 

" 

II 

II 

II 

II 

II 

Ajh 

8.69 

7.07 

5.91 

5.04 

4.36 

3.82 

A,h 

0.939 

0.849 

0.771 

0.702 

0.639 

0.582 

■Log. 

02 

42 

59 

43 

49 

06 

Log. 

Limit 

3 

0 

3 

5 

7 

9 

12 

14 

17 

19 

21 

23 

Min- 
utes 

Merid- 
ian 

89° 

90^ 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

Alti- 
tudes 

Decx,inations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

//      / 

/     // 

/      // 

/     '/ 

/     // 

Min. 

Min. 

4 

0  54 

0  48 

0  43 

0  38 

0  35 

0  32 

0  28 

0  26 

0  23 

0  22 

0  19 

0  18 

4 

8 

3  36 

3  12 

2  52 

2  35 

2  19 

2  05 

1  55 

144 

1  35 

1  26 

1  19 

1  11 

8 

12 

8  07 

7  12 

6  27     5  49 

5  14 

4  44 

4  18 

3  54 

3  34 

3  14 

2  57 

2  39 

12 

16 

14  25 

12  48 

11  29    10  19 

9  18 

8  24 

7  38 

6  58 

6  18 

5  46 

5  15 

4  45 

16 

20 

22  27 

20  00 

17  56 

16  08 

14  32 

13  08 

1156 

10  52 

9  52 

9  00 

8  12 

7  24 

20 

24 

32  27 

28  48 

25  50 

23  14 

20  56 

18  44 

17  11 

15  39 

14  12 

12  58 

11  48 

10  40 

24 

28 

44  10 

39  12 

35  09 

3138 

28  29 

25  45 

22  24 

21  18 

19  21 

17  38 

16  05 

14  30 

28 

32 

57  41 

51  12 

45  54 

41  18 

37  12 

33  48 

30  33 

27  49 

25  16 

23  02 

21  00 

18  56 

32 

36 

58  07 

52  16 

47  06 

42  33 

38  40 

35  13 

31  58 

29  10 

26  34 

23  59 

36 

40 

58  08 

52  32 

47  44 

43  28 

39  28 

36  00 

32  48 

29  36 

40 

44 

63  34 

57  45 

52  36 

47  45 

43  34 

39  41 

35  49 

44 

48 

62  35 

56  50 

51  50 

47  14 

42  37 

48 

52 

60  50 

55  26 

50  01 

52 

56 

64  17 

58  01 

56 

60 

66  36 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

Ajh 

3.38 

3.00 

2.69 

2.42 

2.18 

1.97 

1.79 

1.63 

1.48 

1.35 

1.23 

1.11 

A,h 

Log. 

0.528 

0.477 

0.429 

0.383 

0.338 

0.294 

0.252 

0.212 

0.170 

0.130 

0.089 

0.045 

Log. 

92 

12 

75        82 

46 

47 

85 

19 

26 

33 

91 

32 

Limit 

26 

28 

30 

32 

34 

36 

38 

40 

42 

45 

47 

48 

Min- 
utes 

Merid- 
ian 

79° 

78° 

770 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

69° 

68° 

Alti- 
tudes 

Latitude  49°  Declination  Contrary  Name. 


295 


Declinations. 


Hour 
Angles 

0° 

1° 

2°    1      3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  27 

150 

4  06 

7  18 

1124 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 

It 

1.71 

0  27 

147 
4  02 
7  10 
11  12 
16  08 
21  57 
28  40 
36  18 
44  48 
54  13 
64  30 
75  42 
87  49 

100  48 

It 

1.68 

0  27 

1  46 
3  59 
7  05 

11  04 
15  57 
21  41 
28  19 
35  52 
44  16 
53  34 
63  44 
74  48 
86  46 

99  36 

II 

1.66 

/      // 

0  26 

144 

3  54 

6  58 

10  52 

15  39 

21  18 

27  49 

35  13 

43  28 

52  36 

62  35 

73  27 

85  12 

97  48 

II 

1.63 

/  ■    // 

0  26 

142 

3  51 

6  53 

10  44 

15  28 

21  02 

27  28 

34  47 

42  56 

51  57 

61  49 

72  33 

84  09 

96  36 

It 

1.61 

1     It 

0  25 

1  42 
3  49 
6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

61  03 

71  39 

83  06 

95  24 
II 

1.59 

0  25 

140 
3  45 
6  39 
10  24 
14  59 
20  23 
26  37 
33  42 
41  36 
50  20 
59  54 
70  18 
81  32 
93  36 

1.56 

/      // 

0  25 
139 

3  42 
6  34 
10  16 
14  47 
20  07 
26  17 
33  16 
41  04 
49  41 
59  08 
69  24 
80  29 

92  24 

II 

1.54 

/      // 

0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 

It 

L52 

/     // 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 

It 

1.50 

/      // 

0  23 

135 

3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

3158 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
It 

1.48 

/      // 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
It 

1.46 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.233 
00 

0.225 
31 

0.220 
11 

0.212 
19 

0.206 
83 

0.201 
40 

0.193 
12 

0.187 
52 

0.181 
84 

0.176 
09 

0.170 
26 

0.164 
•       35 

Log. 

Limit 

50 

50 

51 

52 

53 

54 

54 

54 

55 

56 

57 

57 

Min- 
utes 

Merid- 
ian 

41= 

40° 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

1      It 

/      // 

1     It 

/      // 

t     It 

1      It 

1      It 

/      // 

/      // 

/      // 

1      It 

1     It 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

0  21 

0  20 

0  20 

0  20 

4 

8 

133 

1  31 

1  30 

1  28 

128 

1  26 

1  25 

123 

1  23 

122 

1  21 

1  20 

8 

12 

3  28 

3  25 

3  22 

3  19 

3  17 

3  14 

3  11 

3  08 

3  07 

3  05 

3  02 

3  00 

12 

16 

6  08 

6  03 

5  58 

5  53 

5  51 

5  46 

5  41 

5  36 

5  33 

5  27 

5  22 

5  20 

16 

20 

9  36 

9  28 

9  20 

9  12 

9  08 

9  00 

8  52 

8  44 

8  40 

8  32 

8  24 

8  20 

20 

24 

13  49 

13  38 

13  26 

13  15 

13  09 

12  58 

12  46 

12  35 

12  29 

12  17 

12  06 

12  00 

24 

28 

18  49 

18  34 

18  18 

18  02 

17  54 

17  38 

17  23 

17  07 

16  59 

16  44 

16  28 

16  20 

28 

32 

24  35 

24  14 

23  54 

23  33 

23  23 

23  02 

22  42 

22  21 

22  11 

2151 

21  30 

21  20 

32 

36 

3106 

30  40 

30  14 

29  49 

29  36 

29  10 

28  44 

28  18 

28  05 

27  39 

27  13 

27  00 

36 

40 

38  24 

37  52 

37  20 

36  48 

36  32 

36  00 

35  28 

34  56 

34  40 

34  08 

33  36 

33  20 

40 

44 

46  27 

45  49 

45  10 

44  32 

44  13 

43  34 

42  55 

42  16 

41  57 

41  18 

40  39 

40  20 

44 

48 

55  18 

54  32 

53  46 

52  59 

52  36 

5150 

51  04 

50  18 

49  55 

49  09 

48  23 

48  00 

48 

52 

64  54 

64  00 

63  06 

62  11 

6144 

60  50 

59  56 

59  02 

58  35 

57  41 

56  47 

56  20 

52 

56 

75  15 

7-413 

73  10 

72  08 

71  37 

70  34 

69  31 

68  28 

67  57 

66  54 

65  51 

65  20 

56 

60 

86  24 

II 

85  12 

84  00 
It 

82  48 
It 

82  12 
It 

8100 
It 

79  48 

78  36 

It 

78  00 

It 

76  48 
It 

75  36 

It 

75  00 
11 

60 

Aih 

1.44 

1.42 

1.40 

1.38 

.1.37 

1.35 

1.33 

1.31 

1.30 

1.28 

1.26 

1.25 

Ajh 

0.158 

0.152 

0.146 

0.139 

0.136 

0.130 

0.123 

0.117 

0.113 

0.107 

0.100 

0.096 

Log. 

36 

29 

13 

88 

72 

33 

85 

27 

94 

21 

37 

91 

Limit 

58 

59 

60 

61 

61 

61 

62 

63 

64 

64 

65 

66 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

20G 


Latitude  49°  Declination  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

«ro   I  Hour 
"^^      [Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/     // 

0  20 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
II 

1.23 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 

15  49 

20  39 

26  08 

33  16 

39  02 

46  28 

54  32 

63  14 

72  36 
II 

1.21 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

II 

1.20 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 

70  48 

II 

1.18 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

1.17 

/     // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 

69  00 

II 

1.15 
0.060 
70 

/     // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 

67  48 

II 

1.13 

/     // 

0  18 

1  11 

2  41 

4  47 

7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
II 

1.12 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

II 

1.11 

/     // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 

65  24 

II 

1.09 

/      // 

0  17 
109 
2  36 
4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 
II 

1.08 

0  17 

1  08 

2  33 
4  31 
7  04 

10  11 
13  51 
18  05 
22  54 
28  16 
34  12 
40  42 
47  46 
55  24 
63  36 

1.06 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.089 
91 

0.082 
79 

0.079 

18 

0.071 

88 

0.068 
19 

0.053 
08 

0.049 
22 

0.045 
32 

0.037 
43 

0.033 
42 

0.025 
31 

Log. 

Limit 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

Alti- 
tudes 

Declinations.  - 

-Inferior  I 

Me 

RII 

)IAN 

Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 
II 

1.05 

1 

// 

II 

II 

// 

/     // 
II 

II 

// 

1 

II 

II 

II 

// 

1 

// 

// 

II 

// 

/     // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

II 

0.90 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 

52  48 

II 

0.88 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.021 
19 

9.954 
24 

9.944 
48 

Log. 

Limit 

79 

69 

68 

•  Min- 
utes 

Merid- 
ian 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

Alti- 
tudes 

Latitude  49*^  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


297 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55°      56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
?S 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  14 
0  55 

2  05 

3  43 

5  48 
8  21 
11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

0.87 

/        n 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 
5136 

n 

0.86 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
It 

0.84 

1        n 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 
13  59 
17  43 
21  52 
26  28 
31  29 
36  57 
42  52 
49  12 

0.82 

/      II 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 

0.80 

/     // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
// 

0.79 

/     // 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
II 

1     II 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
II 

0.75 

0  12 
0  47 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 

0.74 

/     // 

0  12 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 
15  46 
19  28 
23  33 
28  00 
32  54 
38  09 

43  48 

II 

0.73 

1     II 

Oil 
0  46 

144 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 
43  12 

0.72 

/      // 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

11  57 

15  07 

18  40 

22  35 

26  51 

31  33 

36  35 

42  00 
II 

0.70 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.939 
52 

9.934 
50 

9.924 

28 

9.913 
81 

9.903 
09 

9.897 
63 

9.886 
49 

9.875 
06 

9.869 
23 

9.863 
32 

9.857 
33 

9.845 
10 

Log. 

Limit 

67 

67 

67 

67 

67 

67 

68 

69 

71 

72 

74 

75 

Min- 
utes 

Merid- 
ian 

7° 

8° 

9° 

10° 

11° 

12°  1    13° 

14° 

15° 

16° 

17° 

18° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

/     // 

/     // 

Min. 

4 

Oil 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

4 

8 

0  44 

0  42 

0  40 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  33 

0  32 

0  31 

8 

12 

1  39 

136 

1  32 

130 

127 

125 

122 

121 

1  18 

1  15 

1  12 

1  09 

12 

16 

2  57 

2  52 

2  44 

2  42 

2  37 

2  31 

2  26 

2  23 

2  18 

2  13 

2  08 

2  02 

16 

20 

4  36 

4  28 

4  16 

4  12 

4  04 

3  56 

3  48 

3  44 

3  36 

3  28 

3  20 

3  12 

20 

24 

6  38 

6  26 

6  09 

6  03 

5  52 

5  40 

5  28 

5  23 

5  11 

5  00 

4  48 

4  36 

24 

28 

9  01 

8  45 

8  21 

8  14 

7  58 

7  43 

7  27 

7  19 

7  03 

6  48 

6  32 

6  17 

28 

32 

11  46 

1126 

10  55 

10  45 

10  24 

10  04 

9  44 

9  33 

9  13 

8  52 

8  32 

8  12 

32 

36 

14  55 

14  29 

13  50 

13  37 

13  11 

12  45 

12  18 

12  06 

1140 

11  14 

10  48 

10  22 

36 

40 

18  24 

17  52 

17  04 

16  48 

16  16 

15  44 

15  12 

14  56 

14  24 

13  52 

13  20 

12  48 

40 

44 

22  16 

21  38 

20  39 

20  20 

19  41 

19  02 

18  24 

18  04 

17  25 

16  47 

16  08 

15  29 

44 

48 

26  29 

25  43 

24  34 

24  11 

23  25 

22  39 

2154 

2130 

20  44 

19  58 

19  12 

18  26 

48 

52 

31  05 

30  11 

28  50 

28  23 

27  29 

26  35 

25  41 

25  14 

24  20 

23  26 

22  32 

21  38 

52 

56 

36  04 

35  02 

33  27 

32  56 

3153 

30  50 

29  48 

29  16 

28  13 

27  11 

26  08 

25  05 

56 

60 

41  24 

II 

40  12 

38  24 
II 

37  48 
II 

36  36 

II 

35  24 
II 

34  12 
II 

33  36 
II 

32  24 
II 

31  12 

30  00 
II 

28  48 
II 

60 

A,h 

0.69 

0.67 

0.65 

0.63 

0.61 

0.59 

0.57 

0.56 

0.54 

0.52 

0.50 

0.48 

A,h 

Log. 

9.838 

9.826 

9.812 

9.799 

9.785 

9.770 

9.755 

9.748 

9.732 

9.716 

9.698 

9.681 

Log, 

85 

07 

91 

34 

33 

85 

87 

19 

39 

00 

97 

24 

Limit 

76 

76 

77 

78 

79 

80 

80 

81 

81 

82 

83 

83 

Min- 
utes 

Merid- 
ian 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

Alti- 
tudes 

298 


Latitude  50°  Declination  Same  Name. 


Declinations. 


Hour 
Lngles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10°   11° 

Hour 
Angles 

Min.  - 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/   // 

0  27 

1  45 
3  57 
7  03 

11  00 
15  51 
21  33 
28  09 
35  39 
44  00 
53  15 
63  21 
74  21 
86  15 
99  00 

1.65 

/  // 

0  27 

147 

4  00 

7  08 

11  08 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

II 

1.67 

1     1' 

0  27 

1  49 
4  05 
7  15 

1120 
16  19 
22  13 
29  01 
36  43 
45  20 
54  51 
65  15 
76  37 
88  51 

102  00 

II 

1.70 

I  II 

0  27 

1  50 
4  08 
7  20 

II  28 
16  31 
22  29 
29  21 
37  09 
45  52 
55  30 
66  01 
77  31 
89  54 

103  12 

II 

1.72 

/  // 

0  28 

1  52 

4  12 
7  28 
11  40 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 
91  28 

105  00 

II 

1.75 

/  // 

0  28 

154 

4  17 

7  35 

1152 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 
II 

1.78 

/  // 

0  29 

156 

4  20 

7  44 

12  04 

17  23 

23  39 

30  53 

39  06 

48  16 

58  24 

69  30 

81  34 

94  36 

108  36 

II 

1.81 

/  // 

0  30 

1  58 
4  25 
7  51 

12  16 
17  40 
24  02 
31  24 
39  45 
49  04 
59  22 
70  39 
82  55 
96  10 

110  24 

II 

1.84 

/  // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

31  55 

40  24 

49  52 

60  21 

7148 

84  16 

97  45 

112  12 

II 

1.87 

/  // 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

41  02 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 

II 

1.90 

/  // 

0  30 

2  03 

4  38 

8  14 

12  52 

18  31 

25  14 

32  57 

41  41 

51  28 

62  16 

74  07 

86  59 

100  52 

1.93 

/  // 

0  31 

2  05 

4  44 

8  24 

13  08 

18  54 

25  45 

33  38 

42  33 

52  32 

63  34 

75  39 

88  47 

102  57 

1.97 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.217 
48 

0.222 

72 

0.230 
45 

0.235 
53 

0.243 
04 

0.250 
42 

0.257 
68 

0.264 
82 

0.271 
84 

0.278 
75 

0.285 
56 

0.294 

47 

Log. 

Limit 

51 

51 

50 

50 

49 

49 

48 

47 

47 

46 

46 

45 

Min- 
utes 

Merid- 
ian 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 
/  // 

Hour 
Angles 

Min. 

1      II 

/  // 

t      II 

/  /' 

/  //  /  /' 

/  // 

/  // 

/  // 

/  // 

1      II 

Min. 

4 

0  32 

0  33 

0  33 

0  34 

0  35  0  35 

0  36 

0  37 

0  38 

0  38 

0  39 

0  41 

4 

8 

2  09 

2  11 

2  13 

2  16 

2  19 

2  22 

2  26 

2  28 

2  32 

2  36 

2  40 

2  44 

8 

12 

4  49 

4  54 

5  00 

5  06 

5  12 

5  20 

5  27 

5  34 

5  41 

5  50 

5  59 

6  09 

12 

16 

8  35 

8  42 

8  52 

9  06 

9  16 

9  28 

9  41 

9  54 

10  07 

10  22 

10  37 

10  55 

16 

20 

13  24 

13  36 

13  52 

14  12 

14  28 

14  48 

15  08 

15  28 

15  48 

16  12 

16  36 

17  04 

20 

24 

19  18 

19  35 

19  58 

20  27 

20  50 

21  19 

2147 

22  17 

22  45 

23  19 

23  54 

24  35 

24 

28 

26  16 

26  39 

27  11 

27  50 

28  21 

29  01 

29  40 

30  19 

30  58 

3146 

32  33 

33  27 

28 

32 

34  18 

34  49 

35  30 

36  21 

37  02 

37  53 

38  45 

39  35 

40  27 

41  29 

42  30 

43  41 

32 

36 

43  25 

44  04 

44  56 

46  01 

46  53 

47  57 

49  02 

50  07 

51  12 

52  29 

53  47 

55  18 

36 

40 

53  36 

54  24 

55  28 

56  48 

57  52 

59  12 

60  32 

6152 

63  12 

64  48 

66  24 

68  16 

40 

44 

64  51 

65  49 

67  07 

68  44 

70  02 

7138 

73  15 

74  52 

76  39 

78  24 

80  20 

82  36 

44 

48 

77  11 

78  20 

79  52 

8146 

83  19 

85  15 

87  10 

89  05 

91  00 

93  19 

95  37 

48 

52 

90  35 

91  56 

93  44 

95  59 

97  47 

100  03 

102  18 

104  33 

106  48 

52 

56 

105  03 

106  37 

108  43 

56 

60 

60 

II 

II 

II 

" 

// 

II 

II 

II 

II 

II 

II 

II 

A,h 

2.01 

2.04 

2.08 

2.13 

2.17 

2.22 

1.21 

2.32 

2.37 

2.43 

2.49 

2.56 

A,h 

Log. 

0.303 

0.309 

0.318 

0.328 

0.336 

0.346 

0.356 

0.365 

0.374 

0.385 

0.396 

0.408 

Log. 

20 

63 

06 

38 

46 

35 

03 

49 

75 

61 

20 

24 
37 

Limit 

44 

44 

43 

43 

42 

41 

41 

40 

40 

39 

38 

Min- 
utes 

Merid- 
ian 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

Alti- 
tude! 

Latitude  50°  Declination  Same  Name. 


299 


Declinations. 


Hour 
Angled 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

/      /' 

Min. 

Min. 

4 

0  42 

0  43 

0  44 

0  46 

0  47 

0  49 

0  51 

0  53 

0  55 

0  58 

101 

1  03 

4 

8 

2  48 

2  54 

2  59 

3  04 

3  10 

3  17 

3  25 

3  32 

3  42 

3  51 

4  03 

4  15 

8 

12 

6  18 

6  30 

6  42 

6  55 

7  08 

7  24 

7  41 

7  58 

8  19 

8  41 

9  07 

9  35 

12 

16 

11  14 

11  34 

1154 

12  17 

12  40 

13  08 

13  39 

14  10 

14  45 

15  27 

16  13 

17  01 

16 

20 

17  32 

18  04 

18  36 

19  12 

19  48 

20  32 

21  20 

22  08 

23  04 

24  08 

25  20 

26  36 

20 

24 

25  15 

26  01 

26  47 

27  39 

28  30 

29  34 

30  43 

3153 

33  13 

34  46 

36  29 

38  18 

24 

28 

34  22 

35  25 

36  28 

37  38 

38  49 

40  15 

4149 

43  23 

45  13 

47  18 

49  39 

52  09 

28 

32 

44  53 

46  15 

47  37 

49  09 

50  42 

52  34 

54  37 

56  39 

59  03 

6146 

64  51 

68  06 

32 

36 

56  49 

58  32 

60  16 

62  13 

64  09 

66  32 

69  07 

7143 

36 

40 

70  08 

72  16 

74  24 

76  48 

40 

44 

84  52 

87  26 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

A,h 

2.63 

2.71 

2.79 

2.88 

2.97 

3.08 

3.20 

3.32 

3.46 

3.62 

3.80 

3.99 

z.,h 

Log. 

0.419 

0.432 

0.445 

0.459 

0.472 

0.488 

0.505 

0.521 

0.539 

0.558 

0.579 

0.600 

96 

97 

60 

39 

76 

55 

15 

14 

08 

71 

78 

97 

Log. 

Limit 

36 

35 

34 

33 

32 

31 

30 

29 

28 

28 

27 

26 

Min- 
utes 

Merid- 
ian 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/     // 

/     '/ 

/     // 

/     // 

/     II 

/     // 

/     // 

/     // 

/     // 

/     '/ 

/      II 

Min. 

4 

107 

1  12 

1  17 

123 

1  29 

137 

1  48 

2  01 

2  19 

2  44 

4 

8 

4  30 

4  47 

5  06 

5  29 

5  57 

6  30 

7  12 

8  05 

9  16 

10  56 

8 

12 

10  08 

10  46 

11  29 

12  20 

13  22 

14  37 

16  11 

18  10 

20  51 

24  35 

12 

16 

18  00 

19  06 

20  23 

2156 

23  46 

25  59 

28  45 

32  18 

37  05 

43  41 

16 

20 

28  08 

29  52 

31  52 

34  16 

37  08 

40  36 

44  56 

50  28 

20 

24 

40  31 

42  59 

45  53 

49  21 

53  28 

58  28 

24 

28 

55  09 

58  33 

62  26 

67  09 

28 

32 

72  01 

76  28 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

Ajh 

4.22 

4.48 

4.78 

5.14 

5.57 

6.09 

6.74 

7.57 

8.69 

10.24 

A,h 

0.625 

0.651 

0.679 

0.710 

0.745 

0.784 

0.828 

0.879 

0.939 

1.010 

Log. 

Log. 

31 

28 

43 

96 

86 

62 

66 

10 

02 

30 

Limit 

26 

25 

24 

22 

21 

20 

18 

16 

14 

13 

10 

7 

Min- 
utes 

Merid- 
ian 

76= 

77' 

78= 

3 

79' 

3 

80° 

81° 

82 

3 

83 

3 

84 

3 

85 

0 

86 

3 

37 

3 

Alti- 
tudes 

300 


Latitude  50°  Declination  Same  Name. 
Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

If 

/ 

// 

1 

■ 

// 

/ 

// 

n 

// 

1 

1 
3 

8 

2 
8 
9 
5 

// 
.3 

// 

13 
52 
56 

28 

I 

/     // 

149 

7  12 
16  12 

28  48 

II 
6.75 

1     II 

1  31 

6  01 

13  32 

24  04 

37  36 

II 
5.64 

/     II 

1  17 
5  08 
1132 
20  32 
32  04 
46  11 

II 
4.81 

/      // 

107 
4  26 

9  59 
17  4.^ 
27  4' 
39  5: 

II 
4.16 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

Log. 

0.919 
60 

0.829 
30 

0.751 

28 

0.682 
15 

0.619 
09 

Log. 

Limit 

5 

3 

0 

3 

6 

8 

10 

12 

14 

16 

18 

21 

Min- 
utes 

Merid- 
ian 

8{ 

1° 

89' 

> 

9( 

)° 

8S 

)° 

8i 

5° 

8' 

7° 

8( 

5° 

{ 

15' 

84 

3 

83 

3 

82 

3 

81 

} 

Alti- 
tudes 

Declinations, 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     // 

/      " 

/     // 

/      // 

/      /' 

/     // 

/     // 

/     // 

/     II 

/      // 

/     // 

Min. 

4 

0  58 

0  51 

0  46 

0  41 

0  36 

0  33 

0  30 

0  27 

0  24 

0  22 

0  20 

0  18 

4 

8 

3  52 

3-26 

3  02 

2  43 

2  27 

2  12 

159 

148 

138 

129 

121 

1  12 

8 

12 

8  42 

7  42 

6  50 

6  07 

5  30 

4  57 

4  28 

4  03 

3  40 

3  20 

3  02 

2  42 

12 

16 

15  30 

13  42 

12  10 

10  53 

9  46 

8  47 

7  56 

7  13 

6  32 

5  56 

5  22 

4  50 

16 

20 

24  12 

21  24 

19  00 

17  00 

15  16 

13  44 

12  24 

11  16 

10  12 

9  16 

8  24 

7  32 

20 

24 

34  51 

30  49 

27  22 

24  29 

2159 

19  47 

17  52 

16  14 

14  41 

13  21 

12  06 

10  51 

24 

28 

47  26 

4157 

37  14 

33  19 

29  56 

26  55 

24  18 

22  05 

20  00 

18  10 

16  28 

14  46 

28 

32 

54  47 

48  38 

43  31 

39  05 

35  09 

3144 

28  50 

26  07 

23  43 

21  30 

19  17 

32 

36 

55  05 

49  28 

44  30 

40  11 

36  31 

33  03 

30  02 

27  13 

24  25 

36 

40 

54  56 

49  36 

45  04 

40  48 

37  04 

33  36 

30  08 

40 

44 

54  32 

49  22 

44  51 

40  39 

36  28 

44 

48 

64  53 

58  45 

53  22 

48  23 

43  23 

48 

52 

62  38 

56  47 

50  55 

52 

56 

65  51 

59  04 

56 

60 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

" 

A,h 

3.63 

3.21 

2.85 

2.55 

2.29 

2.06 

1.86 

1.69 

1.53 

1.39 

1.26 

1.13 

A,h 

Log. 

0.559 

0.506 

0.454 

0.406 

0.359 

0.313 

0.269 

0.227 

0.184 

0.143 

0.100 

0.053 

Log. 

91 

51 

84 

54 

84        87 

51 

89 

69 

01 

37 

08 

Limit 

24 

26 

28 

30 

32 

34 

36 

38 

41 

43 

46 

48 

Min- 
utes 

Merid- 
ian 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70» 

69° 

Alti- 
tudes 

Latitude  50°  Declination  Contrary  Name. 


301 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Mil). 

4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

1       n 

0  27 

145 

3  57 

7  03 

1100 

15  51 

21  33 

28  09 

35  39 

44  00 

53  15 

63  21 

74  21 

86  15 

99  00 

1.65 

/      If 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 

n 

1.62 

0  26 

142 

3  50 

6  50 

10  40 

15  22 

20  54 

27  18 

34  34 

42  40 

5138 

61  26 

72  06 

83  38 

96  00 

II 

1.60 

/      // 

0  25 

1  41 

3  48 

6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/       n 

0  25 

140 

3  45 

6  39 

10  24 

14  59 

20  23 

26  37 

33  42 

4136 

50  20 

59  54 

70  18 

81  32 

93  36 

II 

1.56 

/      // 

0  24 

1  38 
3  40 
6  32 

10  12 

14  41 

20  00 

26  07 

33  03 

40  48 

49  22 

58  45 

68  57 

79  58 

9148 
II 

1.53 

0  24 

1  36 
3  37 
6  27 

10  04 
14  30 
19  44 
25  46 
32  37 
40  16 
48  43 
57  59 
68  03 
78  55 

90  36 

II 

1.51 

/     II 

0  23 

1  36 
3  35 
6  21 
9  56 

14  18 

19  29 

25  26 

32  11 

39  44 

48  04 

57  13 

67  09 

77  52 

89  24 
II 

1.49 

0  23 

134 

3  32 

6  16 

9  48 

14  06 

19  13 

25  06 

3145 

39  12 

47  26 

56  27 

66  15 

76  50 

88  12 
II 

1.47 

/     II 

0  23 

1  33 
3  29 
6  11 
9  40 

13  55 

18  57 

24  45 

31  19 

38  40 

46  47 

55  41 

65  21 

75  37 

87  00 
II 

1.45 

1      II 

0  22 

1  33 
3  28 
6  08 
9  36 

13  49 

18  49 

24  35 

31  06 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 
II 

1.44 

/      // 

0  22 

1  31 
3  25 
6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
II 

1.42 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.217 
48 

0.209 
52 

0.204 
12 

52 

0.198 
66 

0.193 
12 

0.184 
69 

0.178 
98 

0.173 
19 

0.167 
32 

0.161 
37 

0.158 
36 

0.152 
29 

Log. 

Limit 

51 

51 

53 

54 

55 

55 

55 

56 

57 

58 

58 

Min- 
utes 

Merid-j     ino        oqo 
ian     1    *"      '    ^^ 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/     // 

/      // 

/      II 

/      // 

/      // 

/     // 

/     // 

/     // 

/           // 

/      // 

/      // 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

0  20 

0  20 

0  20 

0  19 

0  19 

4 

8 

1  30 

1  28 

127 

126 

125 

123 

1  23 

122 

121 

1  20 

1  19 

1  17 

8 

12 

3  22 

3  19 

3  16 

3  14 

3  11 

3  08 

3  06 

3  05 

3  02 

3  00 

2  57 

2  54 

12 

16 

5  58 

5  53 

5  48 

5  46 

5  41 

5  36 

5  30 

5  27 

5  22 

5  20 

5  15 

5  10 

16 

20 

9  20 

9  12 

9  04 

9  00 

8  52 

8  44 

8  36 

8  32 

8  24 

8  20 

8  12 

8  04 

20 

24 

13  26 

13  15 

13  04 

12  58 

12  46 

12  35 

12  23 

12  17 

12  06 

12  00 

11  48 

11  37 

24 

28 

18  18 

18  02 

17  46 

17  38 

17  23 

17  07 

16  52 

16  44 

16  28 

16  20 

16  05 

15  49 

28 

32 

23  54 

23  33 

23  12 

23  02 

22  42 

22  21 

22  01 

2151 

21  30 

21  20 

2100 

20  39 

32 

36 

30  14 

29  49 

29  23 

29  10 

28  44 

28  18 

27  52 

27  39 

27  13 

27  00 

26  34 

26  08 

36 

40 

37  20 

36  48 

36  16 

36  00 

35  28 

34  56 

34  24 

34  08 

33  36 

33  20 

32  48 

32  16 

40 

44 

45  10 

44  32 

43  53 

43  34 

42  55    42  16 

41  37 

41  18 

40  39 

40  20 

39  41 

39  02 

44 

48 

53  46 

52  59 

52  13 

51  50 

51  04    50  18 

49  32 

49  09 

48  23 

48  00 

47  14 

46  28 

48 

52 

63  06 

62  11 

61  17 

60  50 

59  56    59  02 

58  08 

57  41 

56  47 

56  20 

55  26 

54  32 

52 

56 

73  10 

72  08 

7105 

70  34 

69  31,  68  28 

67  25 

66  54 

65  5*1 

65  20 

64  17 

63  14     56 

60 

84  00 

II 

82  48 
II 

81  36 

81  00 

79  48    78  36 

77  24 

II 

76  48 
II 

75  36 
II 

75  00 

73  48 

72  36      60 

A,h 

1.40 

1.38 

1.36 

1.35 

1.33      1.31 

1.29 

1.28 

1.26 

1.25 

1.23 

1.21 

A,h 

Log. 

0.146 

0.139 

0.133 

0.130 

0.123    0.117J  0.110 

0.107 

0.100 

0.096 

0.089 

0.082 

13 

88 

54 

33 

85|        27|        59 

21 

37 

91 

91 

79 

Log. 

Limit 

59 

60 

61 

62 

62 

62 

63 

64 

65 

65 

66 

67 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

■loo       Alti- 
■^'         tudes 

302 


Latitude  50°  Declination  Gsntrary  Name. 
Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Aih 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 

72  00 

// 

1.20 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 
70  48 

•1.18 

/     II 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 

15  09 

19  47 

25  04 

30  56 

37  26 

44  52 

52  16 

60  38 

69  36 
■II 

1.16 

/      // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 

69  00 

II 

1.15 

/       n 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
5122 
59  35 
68  24 

1.14 

/       n 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

II 

1.12 

1     II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 

14  30 

18  56 

23  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 
II 

1.11 

/     II 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 
65  24 
"    4 

1.09 

/      /' 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 
// 

1.08 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

II 

1.06 

/      // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/     If 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

II 

1.04 

Min. 

4 

8 
12 
16 

20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.079 

18 

0.071 

88 

0.064 
46 

0.060 
70 

0.056 
90 

0.049 
22 

0.045 
32 

0.037 
43 

0.033 
42 

0.025 
31 

0.021 
19 

0.017 
03 

Log. 

Limit 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

80 

Min- 
utes 

Merid- 
ian 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7°    1     6° 

5° 

Alti- 
!  tudes 

Declinations. — Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39°  1 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

II 

'/ 

/      '/ 

II 

n 

II 

II 

II 

/ 

// 

// 

II 

// 

II 

// 

/      // 

0  14 

0  57 

2  10 

3  50 
6  00 
8  38 

11  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

II 

0.90 

/     // 

0  14 

0  56 

2  07 

3  45 
5  52 

8  27 
1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 
52  48 

0.88 

/      // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 
5136 

0.86 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.954 
24 

9.944 

48 

9.934   ^ 
50   ^°«- 

Limit 

70 

69 

68      S'teY 

Merid- 
ian 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

170     1  Alti- 
'        1  tudes 

Latitude  50°  Declination  Contrary  Name 
Declinations.  —  Inferior  Meridian. 


303 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/      // 

/      // 

/     // 

/      // 

/          N 

/     // 

/     // 

/          // 

Min. 

Min. 

4 

0  14 

0  13 

0  13 

0  13 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

4 

8 

0  54 

0  54 

0  52 

0  51 

0  51 

0  50 

0  49 

0  47 

0  47 

0  46 

0  45 

0  44 

8 

12 

2  02 

2  01 

158 

155 

154 

152 

150 

147 

1  45 

1  44 

142 

139 

12 

16 

3  38 

3  35 

3  30 

3  25 

3  22 

3  19 

3  14 

3  09 

3  07 

3  04 

3  02 

2  57 

16 

20 

5  40 

5  36 

5  28 

5  20 

5  16 

5  12 

5  04 

4  56 

4  52 

4  48 

4  44 

4  36 

20 

24 

8  10 

8  04 

7  53 

7  41 

7  35 

7  29 

7  18 

7  06 

7  00 

6  55 

6  49 

6  38 

24 

28 

1106 

10  58 

10  43 

10  27 

10  20 

10  12 

9  56 

9  40 

9  33 

9  25 

9  17 

9  01 

28 

32 

14  30 

14  20 

13  59 

13  39 

13  29 

13  19 

12  58 

12  38 

12  28 

12  17 

12  07 

11  46 

32 

36 

18  22 

18  09 

17  43 

17  17 

17  04 

16  51 

16  25 

15  59 

15  46 

15  33 

15  20 

14  55 

36 

40 

22  40 

22  24 

2152 

2120 

2104 

20  48 

20  16 

19  44 

19  28 

19  12 

18  56 

18  24 

40 

44 

27  26 

27  06 

26  28 

25  49 

25  29 

25  10 

24  31 

23  52 

23  33 

23  14 

22  54 

22  16 

44 

48 

32  38 

32  15 

31  29 

30  43 

30  18 

29  55 

29  09 

28  23 

28  00 

27  37 

27  14 

26  29 

48 

52 

38  18 

37  51 

36  57 

36  03 

35  36 

35  09 

34  15 

33  21 

32  54 

32  27 

32  00 

3105 

52 

56 

44  26 

43  54 

42  52 

4149 

41  17 

40  46 

39  43 

38  40 

38  09 

37  38 

37  06 

36  04 

56 

60 

5100 

50  24 

49  12 

48  00 

47  24 

46  48 

45  36 

44  24 

43  48 

43  12 

42  36 

4124 

60 

w 

n 

n 

n 

// 

It 

II 

II 

II 

II 

II 

II 

Ajh 

0.85 

0.84 

0.82 

0.80 

0.79 

0.78 

0.76 

0.74 

0.73 

0.72 

0.71 

0.69 

A,h 

Log. 

9.929 

9.924 

9.913 

9.903 

9.897 

9.892 

9.880 

9.869 

9.863 

9.857 

9.851 

9.838 

Log. 

42 

28 

81 

09 

63 

09 

81 

23 

32 

33 

26 

85 

Limit 

67 

67 

67 

67 

67 

68 

68 

69 

70 

71 

72 

73 

Min- 
utes 

Merid- 
ian 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70°      71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

Oil 

0  43 

137 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 

II 

0.68 

/     // 

Oil 

0  42 

1  35 

2  49 
4  24 
6  21 
8  37 

11  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 
39  36 

0.66 

/      // 

Oil 

0  40 

132 

2  44 

4  16 

6  09 

8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 

II 

0.64 

/      // 

0  10 
0  39 
129 
2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

0.62 

/     // 

0  10 
0  39 

127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
31  53 
36  36 

0.61 

/      // 

0  09 
0  38 
125 

2  31 

3  56 
5  40 
7  43 

10  04 

12  45 

15  44 

19  02 

22  39 

26  35 

30  50 

35  24 
II 

0.59 

/     // 

0  09 
0  37 
122 

2  26 

3  48 
5  28 
7  27 
9  44 

12  18 
15  12 
18  24 
2154 
25  41 
29  48 

34  12 

II 

0.57 

/      // 

0  09 
0  36 
121 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
21  30 
25  14 
29  16 

33  36 

II 

0.56 

/      // 

0  09 

0  35 

1  18 

2  18 

3  36 
5  11 
7  03 
9  13 

1140 
14  24 
17  25 
20  44 
24  20 
28  13 

32  24 

II 

0.54 

/     // 

0  08 
0  33 
115 

2  13 

3  28 

5  00 

6  48 
8  52 

11  14 
13  52 
16  47 
19  58 
23  26 
27  11 

31  12 

II 

0.52 

/      // 

0  08 

0  32 

1  12 

2  08 

3  20 

4  48 
6  32 
8  32 

10  48 
13  20 
16  08 
19  12 
22  32 
26  08 

30  00 

II 

0.50 

/     // 

0  07 
0  31 
109 

2  02 

3  12 

4  36 
6  17 
8  12 

10  22 

12  48 

15  29 

18  26 

2138 

25  05 

28  48 
II 

0.48 

Min, 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

Log. 

9.832 
51 

9.819 
54 

9.806 
18 

9.792 
39 

9.785 
33 

9.770 
85 

9.755 

87 

9.748 
19 

9.732 
39 

9.716 
00 

9.698 
97 

9.681 
24 

Log. 

Limit 

74 

75 

76 

77 

78 

79 

80 

81 

81 

82 

82 

82 

Min- 
utes 

Merid- 
ian 

20° 

21° 

22° 

23° 

24° 

25°- 

26° 

27° 

28° 

29° 

30° 

31° 

Alti- 
tudes 

304 


Latitude  5J^  Decimation  Same  Name. 


Declinations. 


Hour 
AnglfiS 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

61  03 

71  39 

83  06 

95  24 

1.59 

/      // 

0  26 
142 
3  51 
6  53 

10  44 

15  28 

2102 

27  28 

34  47 

42  56 

5157 

61  49 

72  33 

84  09 

96  36 
It 

1.61 

/     // 

0  27 

1  45 
3  56 
7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
If 

1.64 

/     // 

0  27 

146 

3  59 

7  05 

1104 

15  57 

21  41 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

86  46 

99  36 

If 

1.66 

0  27 

148 

4  03 

7  13 

11  16 

16  14 

22  05 

28  50 

36  31 

45  04 

54  32 

64  53 

76  09 

88  20 

101  24 
II 

1.69 

/     // 

0  27 

1  50 
4  06 
7  18 

11  24 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 
II 

1.71 

/     // 

0  28 

152 

411 

7  25 

1136 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

104  24 
II 

1.74 

/     // 

0  28 

154 

4  16 

7  33 

1148 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 
II 

1.77 

/     // 

0  28 
155 

4  18 

7  38 

1156 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 
II 

1.79 

/     // 

0  29 

156 

4  22 

7  46 

12  08 

17  29 

23  47 

3103 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 

1.82 

/     // 

0  30 

158 

4  26 

7  54 

12  20 

17  46 

24  10 

3134 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 
II 

1.85 

/     // 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

98  47 

113  24 
II 

1.89 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.201 
40 

0.206 

83 

0.214 

84 

0.220 
11 

0.227 

89 

0.233 
00 

0.240 
55 

0.247 
97 

0.252 

85 

0.260 
07 

0.267 
17 

0.276 
46 

Log. 

Limit 

53 

52 

51 

51 

50 

50 

49 

48 

48        47 

47 

46 

Min- 
utes 

Merid- 
ian 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47°  1   48° 

49° 

50° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16°  ]    17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     /' 

/     // 

/      // 

/      // 

/      // 

/     // 

Min. 

Min. 

4 

0  30 

0  31 

0  31 

0  32 

0  33 

0  34 

0  35 

0  35 

0  36 

0  37 

0  38 

0  38 

4 

8 

2  02 

2  05 

2  07 

2  10 

2  13 

2  15 

2  18 

2  21 

2  24 

2  28 

2  31 

2  35 

8 

12 

4  37 

4  43 

4  47 

4  52 

4  58 

5  03 

5  11 

5  17 

5  24 

5  32 

5  40 

5  49 

12 

16 

8  11 

8  21 

8  29 

8  40 

8  50 

9  01 

9  13 

9  23 

9  36 

9  52 

10  04 

10  19 

16 

20 

12  48 

13  04 

13  16 

13  32 

13  48 

14  04 

14  24 

14  40 

15  00 

15  24 

15  44 

16  08 

20 

24 

18  26 

18  49 

19  06 

19  29 

19  52 

20  16 

20  45 

2107 

21  36 

22  11 

22  40 

23  14 

24 

28 

25  06 

25  37 

26  01 

26  32 

27  03 

27  34 

28  13 

28  45 

.29  24 

30  11 

30  50 

3138 

28 

32 

32  46 

33  27 

33  58 

34  39 

35  20 

36  00 

36  51 

37  33 

38  24 

39  25 

40  16 

41  18 

32 

36 

41  28 

42  20 

42  59 

43  51 

44  43 

45  35 

46  40 

47  31 

48  36 

49  54 

50  59 

52  16 

36 

40 

51  12 

52  16 

53  04 

54  08 

55  12 

56  16 

57  36 

58  40 

60  00 

61  36 

62  56 

64  32 

40 

44 

61  57 

63  14 

64  12 

65  30 

66  48 

68  05 

69  42 

70  59 

72  36 

74  32 

76  09 

78  05 

44 

48 

73  44 

75  16 

76  25 

77  57 

79  29 

81  01 

82  56 

84  29 

86  24 

88  42 

90  37 

92  56 

48 

52 

86  32 

88  20 

89  41 

91  29 

93  17 

95  05 

97  20 

99  09 

101  24 

104  06 

106  21 

52 

56 

.  i 

56 

60 

60 

II 

II 

II 

II 

// 

II 

II 

II 

II 

" 

II 

II 

A,h 

1.92 

1.96 

1.99 

2.03 

2.07 

2.11 

2.16 

2.20 

2.25 

2.31 

2.36 

2.42 

Aji 

Log. 

0.283 

X).292 

0.298 

0.307 

0.315 

0.324 

0.334 

0.342 

0.352 

0.363 

0.372 

0.383 

Log. 

30 

26 

85 

50 

97 

28 

45 

42 

18 

61 

91 

82 

Limit 

46 

45 

45 

44 

44 

43 

42 

42 

41 

40 

39 

38 

Min- 
utes 

Merid- 
ian 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61» 

62° 

Alti- 
tudes 

Latitude  5J°  Declination  Same  Name. 


J05 


Declination's. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
,44 
48 
52 
56 
60 

A,h 

0  40 
2  40 
5  59 
10  37 
16  36 
23  54 
32  33 
42  30 
53  47 
66  24 
80  20 

// 
2.49 

0  41 
2  44 
6  09 
10  55 
17  04 
24  35 
33  27 
43  41 
55  18 
68  16 
82  56 

It 
2.56 

/     // 

0  42 
2  48 
6  18 
11  14 
17  32 
46  15 
34  22 
44  53 
56  49 
70  08 
84  52 

II 
2.63 

/ 

0 
2 
6 

11 

18 
26 
35 
46 
58 
72 

II 
2.7 

13 

54 
30 
34 
34 
31 
25 
15 
32 
16 

I 

1 

0 
2 
6 
H 
18 
26 
36 
47 
60 
74 

If 
2.7 

// 

i4 
59 
12 
54 
36 
47 
28 
37 
16 
24 

3 

0 
3 
6 

12 
19 
27 
37 
49 
62 
77 

II 

2.8 

i6 
35 
56 
20 
16 
i5 
16 
19 
26 
34 

3 

0 
3 

7 

12 
19 
28 
39 
51 
64 
79 

II 
2.9 

47 
11 
11 
45 
56 
42 
35 
32 
35 
44 

3 

0 
3 

7 
13 
20 
29 
40 
52 
66 

3.1 

50 

18 
26 
14 
40 
46 
30 
54 
58 

3 

0  51 
3  26 
7  44 
13  44 
21  28 
30  55 
42  05 
54  57 
69  33 

II 
3.22 

0  54 
3  34 

8  02 
14  18 
22  20 
32  10 
43  46 
57  10 
72  22 

II 
3.35 

/      // 

0  56 
3  44 

8  24 
14  56 
23  20 
33  36 
45  44 
59  44 

II 
3.50 

0  59 
3  55 

8  48 
15  40 
24  28 
35  14 
47  57 
62  38 

II 
3.67 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.396 
20 

0.408 
24 

0.419 
96 

0.432 
97 

0.445 
60 

0.460 
90 

0.475 
67 

0.491 
36 

0.507 
86 

0.525 
04 

0.544 
07 

0.564 
67 

Log. 

Limit 

37 

36 

35 

34 

33 

33 

32 

31 

30 

29 

28 

28 

Min- 
utes 

Merid- 
ian 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/      // 

/      // 

Min, 

Min. 

4 

102 

105 

109 

1  14 

1  19 

126 

134 

143 

156 

2  14 

2  38 

4 

8 

4  07 

4  21 

4  37 

4  55 

5  17 

5  44 

6  16 

6  56 

7  47 

8  54 

10  30 

8 

12 

9  16 

9  48 

10  23 

1105 

1155 

12  53 

14  05 

15  35 

17  30 

20  02 

23  38 

12 

16 

16  28 

17  24 

18  29 

19  43 

2109 

22  55 

25  03 

27  41 

31  06 

35  38 

42  02 

16 

20 

25  44 

27  12 

28  52 

30  48 

33  04 

35  48 

39  08 

43  16 

48  36 

20 

24 

37  04 

39  10 

41  34 

44  22 

47  37 

5133 

56  21 

24 

28 

50  26 

53  19 

56  35 

60  22 

64  49 

28 

32 

65  52 

69  38 

73  53 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

II 

II 

II 

II 

II 

II 

II 

II 

II 

" 

II 

II 

A,h 

3.86 

4.08 

4.33 

4.62 

4.96 

5.37 

5.87 

6.49 

7.29 

8.35 

9.85 

A,h 

Log. 

0.586 

0.610 

0.636 

0.664 

0.695 

0.729 

0.768 

0.812 

0.862 

0.921 

0.993 

Log. 

59 

66 

49 

64 

48 

97 

64 

24 

73 

69 

44 

Limit 

27 

26 

25 

24 

22 

21 

19 

17 

15 

14 

13 

11 

Min- 
utes 

Merid- 
ian 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

Alti- 
tudes 

30G 


Latitude  5i°  Declination  Same  Name. 
Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

1 

1 

n 

1 

H 

n 

II 

n 

/ 

// 

1 

// 

1 

/ 

1 

// 

/      // 

2  06 

8  27 

19  02 

33  50 

n 

7.93 

/     // 

1  43 
6  53 

15  28 
27  28 

ir 

6.44 

1  26 

5  44 

12  53 

22  15 

35  48 

11 
5.37 

/     // 

1  13 
4  53 
10  58 
19  30 
30  28 
43  52 

n 

4.57 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.899 
27 

0.808 
89 

0.729 
97 

0.659 
92 

Log. 

Limit 

9 

6 

3 

0 

3 

6 

8 

10 

12 

14 

16 

19 

Min- 
utes 

Merid- 
ian 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/       // 

/     // 

/      // 

/     // 

/     // 

/     // 

/      // 

/     // 

/      II 

/     // 

/     II 

/     // 

Min. 

4 

103 

0  55 

0  49 

0  43 

0  38 

0  35 

0  31 

0  28 

0  26 

0  23 

0  21 

0  19 

4 

8 

4  13 

3  41 

3  15 

2  53 

2  35 

2  18 

2  04 

152 

141 

132 

123 

1  15 

8 

12 

9  31 

8  17 

7  18 

6  29 

5  47 

5  11 

4  40 

4  12 

3  48 

3  24 

3  07 

2  48 

12 

16 

16  53 

14  43 

12  58 

11  31 

10  17 

9  13 

8  16 

7  28 

6  44 

6  06 

5  33 

5  00 

16 

20 

26  24 

23  00 

20  16 

18  00 

16  04 

14  24 

12  56 

11  40 

10  32 

9  32 

8  40 

7  48 

20 

24 

38  01 

33  07 

29  11 

25  55 

23  08 

20  45 

18  37 

16  48 

15  10 

13  43 

12  29 

11  14 

24 

28 

45  05 

39  43 

35  17 

3130 

28  13 

25  21 

22  52 

20  39 

18  42 

16  59 

15  17 

28 

32 

46  05 

4108 

36  51 

33  07 

29  52 

26  58 

24  25 

22  11 

19  58 

32 

36 

52  03 

46  40 

41  54 

37  48 

34  08 

30  53 

28  05 

25  17 

36 

40 

57  36 

51  44 

46  40 

42  08 

38  08 

34  40 

31  12 

40 

44 

56  28 

50  59 

46  08 

41  57 

37  46 

44 

48 

60  40 

54  55 

49  55 

44  55 

48 

52 

64  27 

58  35 

52  43 

52 

56 

67  57 

61  10 

56 

60 

70  12 

60 

II 

II 

II 

II 

II 

" 

// 

II 

II 

II 

II 

II 

A,h 

3.96 

3.45 

3.04 

2.70 

2.41 

2.16 

1.94 

1.75 

1.58 

1.43 

1.30 

1.17 

A,h 

Log. 

0.597 

0.537 

0.482 

0.431 

0.382 

0.334 

0.287 

0.243 

0.198 

0.155 

0.113 

0.068 

Log. 

70 

82 

87 

36 

02 

45 

80 

04 

66 

34 

94 

19 

Limit 

22 

24 

26 

28 

30 

33 

35 

38 

41 

43 

45 

47 

Min- 
utes 

Merid- 
ian 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

70° 

Alti- 
tudes 

Latitude  51®  Declination  Contrary  Name. 


307 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

/   " 

/  // 

/   /' 

/  // 

1     II 

1     II 

/  n 

/  II 

/  // 

/   // 

1     II 

/  // 

Min. 

4 

0  25 

0  25 

0  25 

0  24 

0  24 

0  23 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

4 

8 

142 

141 

139 

1  38 

1  36 

135 

134 

133 

132 

130 

129 

128 

8 

12 

3  49 

3  46 

3  43 

3  40 

3  36 

3  34 

3  32 

3  29 

3  24 

3  23 

3  20 

3  17 

12 

16 

6  47 

6  42 

6  37 

6  32 

6  24 

6  18 

6  16 

6  11 

6  06 

6  01 

5  56 

5  51 

16 

20 

10  36 

10  28 

10  20 

10  12 

10  00 

9  52 

9  48 

9  40 

9  32 

9  24 

9  16 

9  08 

20 

24 

15  16 

15  04 

14  53 

14  41 

14  24 

14  12 

14  06 

13  55 

13  43 

13  32 

13  21 

13  09 

24 

28 

20  47 

20  31 

20  15 

20  00 

19  36 

19  21 

19  13 

18  57 

18  42 

18  26 

18  10 

17  54 

28 

32 

27  08 

26  48 

26  27 

26  07 

25  36 

25  16 

25  06 

24  45 

24  25 

24  04 

23  43 

23  23 

32 

36 

34  21 

33  55 

33  29 

33  03 

32  24 

3158 

3145 

31  19 

30  53 

30  27 

30  02 

29  36 

36 

40 

42  24 

41  52 

41  20 

40  48 

40  00 

39  28 

39  12 

38  40 

38  08 

37  36 

37  04 

36  32 

40 

44 

51  18 

50  40 

50  01 

49  22 

48  24 

47  45 

47  26 

46  47 

46  08 

45  29 

44  51 

44  13 

44 

48 

6103 

60  17 

59  31 

58  45 

57  36 

56  50 

56  27 

55  41 

54  55 

54  09 

53  22 

52  36 

48 

52 

7139 

70  45 

69  51 

68  57 

67  36 

66  42 

66  15 

65  21 

64  27 

63  33 

62  38 

6144 

52 

56 

83  06 

82  04 

8101 

79  58 

78  24 

77  21 

76  50 

75  37 

74  44 

73  41 

72  39 

7137 

56 

60 

95  24 

94  12 

93  00 

9148 

90  00 

88  48 

88  12 

87  00 

85  48 

84  36 

83  24 

82  12 

60 

II 

II 

It 

II 

II 

" 

II 

It 

It 

It 

It 

/' 

A,h 

1.59 

1.57 

1.55 

1.53 

1.50 

1.48 

1.47 

1.45 

1.43 

1.41 

1.39 

1.37 

A,h 

liOg. 

0.201 

0.195 

0.190 

0.184 

0.176 

0.170 

0.167 

0.161 

0.155 

0.149 

0.143 

0.136 

Log. 

40 

90 

33 

69 

09 

26 

32 

37 

34 

22 

01 

72 

Limit 

53 

53 

54 

54 

55 

56 

56 

56 

57 

58 

59 

59 

Min- 
utes 

Merid- 
ian 

39= 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Anglos 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

71  05 

81  36 
II 

1.36 

0  22 

126 

3  13 

5  43 

8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

51  27 

60  23 

70  02 

80  24 
II 

1.34 

/  // 

0  21 

124 

3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
II 

1.32 

/  // 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 
It 

1.31 

1      It 

0  20 

1  23 
3  06 
5  30 
8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

4137 

49  32 

58  08 

67  25 

77  24 
It 

1.29 

1      It 

0  20 

121 

3  03 

5  25 

8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
II 

1.27 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
It 

1.26 

1       n 

0  20 

120 

2  59 

5  17 

8  16 

11  54 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
It 

1.24 

/  It 

0  19 

119 

2  57 

5  15 

8  12 

11  48 

16  05 

2100 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
It 

1.23 

t     II 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
It 

1.21 

/  // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
It 

1.20 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

6141 

70  48 
II 

1.18 

Min. 

8 

12 
16 
20 
•24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.133 
54 

0.127 
10 

0.120 
57 

0.117 
27 

0.110 
59 

0.103 
80 

0.100 
37 

0.093 
42 

0.089 
91 

0.082 
79 

0.079 
18 

0.071 

88 

Log, 

Limit 

60 

61 

62 

63 

63 

63 

64 

65 

66 

67 

68 

69 

Min- 
utes 

Merid- 
ian 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

Altl. 
tudes 

308 


Latitude  5i°  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/       n 

/  // 

/   n 

/  I' 

/  // 

/  " 

/  // 

/   // 

/   n 

/  '/ 

/  II 

f     II 

Min. 

4 

0  19 

0  19 

0  19 

0  18 

0  18 

0  18 

0  17 

0  17 

0  17 

0  17 

0  16 

4 

8 

1  15 

1  13 

1  12 

1  11 

1  11 

1  10 

109 

108 

1  07 

107 

1  06 

8 

12 

2  48 

2  45 

2  42 

2  41 

2  39 

2  38 

2  36 

2  33 

2  31 

2  30 

2  28 

12 

16 

5  00 

4  55 

4  50 

4  47 

4  45 

4  42 

4  36 

4  31 

4  29 

4  26 

4  24 

16 

20 

7  48 

7  40 

7  32 

7  28 

7  24 

7  20 

7  12 

7  04 

7  00 

6  56 

6  52 

20 

24 

11  14 

1103 

10  51 

10  46 

10  40 

10  34 

10  22 

10  11 

10  05 

9  59 

9  53 

24 

28 

15  17 

15  01 

14  46 

14  38 

14  30 

14  22 

14  07 

13  51 

13  43 

13  35 

13  28 

28 

32 

19  58 

19  37 

19  17 

19  06 

18  56 

18  46 

18  26 

18  05 

17  55 

17  45 

17  35 

32 

36 

25  17 

24  51 

24  25 

24  12 

23  59 

23  46 

23  20 

22  54 

22  41 

22  28 

22  15 

36 

40 

31  12 

30  40 

30  08 

29  52 

29  36 

29  20 

28  48 

28  16 

28  00 

27  44 

27  28 

40 

44 

37  46 

37  07 

36  28 

36  09 

35  49 

35  30 

34  51 

34  12 

33  53 

33  33 

33  14 

44 

48 

44  55 

44  09 

43  23 

43  00 

42  37 

42  14 

41  28 

40  42 

40  19 

39  56 

39  33 

48 

52 

52  43 

51  49 

50  55 

50  28 

50  01 

49  34 

48  40 

47  46 

47  19 

46  52 

46  25 

52 

56 

61  10 

60  07 

59  04 

58  33 

58  01 

57  30 

56  27 

55  24 

54  53 

54  21 

53  50 

56 

60 

70  12 

69  00 

67  48 

67  12 

66  36 

66  00 

64  48 

63  36 

63  00 

62  24 

61  48 

60 

* 

It 

H 

n 

n 

n 

n 

It 

It 

' 

It 

It 

A,h 

1.17 

1.15 

1.13 

1.12 

1.11 

1.10 

1.08 

1.06 

1.05 

1.04 

1.03 

A,h 

Log. 

0.068 

0.060 

0.053 

0.049 

0.045 

0.041 

0.033 

0.025 

0.021 

0.017 

0.012 

Log. 

19 

70 

08 

22 

32 

39 

42 

31 

19 

03 

84 

Limit 

70 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

70 

6° 

5° 

4° 

Alti- 
tudes 

Declinations. — Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

r 

It 

// 

r 

/ 

r 

It 

// 

1 

/ 

// 

It 

/ 

II 
It 

/  // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
It 

0.89 

/  // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
If 

0.88 

/   // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

51  36 
It 

0.86 

/  // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

51  00 
It 

0.85 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.949 
39 

9.944 

48 

9.934 
50 

9.929 
42 

Log, 

Limit 

72 

72 

72 

72 

Min- 
utes 

Merid- 
ian 

3° 

2° 

1° 

0° 

1° 

2° 

3°   4° 

5° 

.6° 

7° 

8° 

Alti- 
tudes 

Latitude  51°  Declination  Contrary  Name* 

Declinations.  —  Inferior  Meridian. 


309 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/   n 

/  // 

/   // 

1      II 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/    // 

Min. 

4 

0  14 

0  13 

0  13 

0  12 

0  12 

0  12 

0  12 

0  12 

0  11 

0  11 

Oil 

Oil 

4 

8 

0  54 

0  52 

0  51 

0  51 

0  50 

0  49 

0  48 

0  47 

0  46 

0  46 

0  45 

0  43 

8 

12 

2  01 

1  58 

155 

154 

153 

1  50 

148 

145 

144 

1  42 

141 

138 

12 

16 

3  35 

3  30 

3  25 

3  22 

3  19 

3  14 

3  12 

3  07 

3  04 

3  02 

2  59 

2  54 

16 

20 

5  36 

5  28 

5  20 

5  16 

5  12 

5  04 

5  00 

4  52 

4  48 

4  44 

4  40 

4  32 

20 

24 

8  04 

7  53 

7  41 

7  35 

7  29 

7  18 

7  12 

7  00 

6  55 

6  49 

6  43 

6  32 

24 

28 

10  58 

10  43 

10  27 

10  20 

10  12 

9  56 

9  48 

9  33 

9  25 

9  17 

9  09 

8  53 

28 

32 

14  20 

13  59 

13  39 

13  29 

13  19 

12  58 

12  48 

12  28 

12  17 

12  07 

11  57 

11  36 

32 

36 

18  09 

17  43 

17  17 

17  04 

16  51 

16  25 

16  12 

15  46 

15  33 

15  20 

15  07 

14  42 

36 

40 

22  24 

21  52 

2120 

21  04 

20  48 

20  16 

20  00 

19  28 

19  12 

18  56 

18  40 

18  08 

40 

44 

27  06 

26  28 

25  49 

25  29 

25  10 

24  31 

24  12 

23  33 

23  14 

22  54 

22  35 

2157 

44 

48 

32  15 

31  29 

30  43 

30  18 

29  55 

29  09 

28  46 

28  00 

27  37 

27  14 

26  51 

26  06 

48 

52 

37  51 

36  57 

36  03 

35  36 

35  09 

34  15 

33  48 

32  54 

32  27 

32  00 

31  33 

30  38 

52 

56 

43  54 

42  52 

41  49 

41  17 

40  46 

39  44 

39  12 

38  09 

37  38 

37  06 

36  35 

35  33 

56 

60 

50  24 

49  12 

48  00 

47  24 

46  48 

45  36 

45  00 

43  48 

43  12 

42  36 

42  00 

40  48 

60 

It 

It 

It 

" 

It 

It 

t 

" 

It 

It 

It 

It 

A,h 

0.84 

0.82 

0.80 

0.79 

0.78 

0.76 

0.75 

0.73 

0.72 

0.71 

0.70 

0.68 

A,h 

liOg. 

9.924 

9.913 

9.903 

9.897 

9.892 

9.880 

9.875 

9.863 

9.857 

9.851 

9.845 

9.832 

Log. 

28 

81 

09 

63 

09 

81 

06 

32 

33 

26 

10 

51 

Limit 

72 

72 

72 

72 

72 

72 

72 

72 

72 

72 

72 

72 

Min- 
utes 

Merid- 
ian 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/  // 

/  // 

1     It 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

Min. 

4 

Oil 

Oil 

0  10 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

4 

8 

0  42 

0  41 

0  40 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  34 

0  32 

0  30 

8 

12 

1  36 

1  33 

1  30 

127 

126 

1  24 

121 

1  19 

1  16 

1  13 

1  11 

1  08 

12 

16 

2  52 

2  47 

2  42 

2  37 

2  34 

2  28 

2  23 

2  21 

2  16 

2  11 

2  05 

2  00 

16 

20 

4  28 

4  20 

4  12 

4  04 

4  00 

3  52 

3  44 

3  40 

3  32 

3  24 

3  16 

3  08 

20 

24 

6  26 

6  15 

6  03 

5  52 

5  46 

5  34 

5  23 

5  17 

5  05 

4  54 

4  42 

4  30 

24 

28 

8  45 

8  29 

8  14 

7  58 

7  50 

7  35 

7  19 

7  11 

6  56 

6  40 

6  25 

6  09 

28 

32 

11  26 

11  05 

10  45 

10  24 

10  14 

9  54 

9  33 

9  23 

9  03 

8  42 

8  22 

8  02 

32 

36 

14  29 

14  03 

13  37 

13  11 

12  58 

12  32 

12  06 

1153 

1127 

11  01 

10  35 

10  09 

36 

40 

17  52 

17  20 

16  48 

16  16 

16  00 

15  28 

14  56 

14  40 

14  08 

13  36 

13  04 

12  32 

40 

44 

2138 

20  59 

20  20 

19  41 

19  22 

18  43 

18  04 

17  45 

17  06 

16  27 

15  48 

15  10 

44 

48 

25  43 

24  57 

24  11 

23  25 

23  02 

22  16 

21  30 

2107 

20  21 

19  35 

18  49 

18  03 

48 

52 

30  11 

29  17 

28  23 

27  29 

27  02 

26  08 

25  14 

24  47 

23  53 

22  59 

22  05 

21  11 

52 

56 

35  02 

33  59 

32  56 

3153 

31  22 

30  19 

29  16 

28  45 

27  42 

26  39 

25  36 

24  34 

56 

60 

40  12 

39  00 

37  48 

36  36 

36  00 

34  48 

33  36 

33  00 

3148 

30  36 

29  24 

28  12 

60 

It 

It 

It 

It 

It 

If 

It 

It 

It 

It 

It 

It 

A,h 

0.67 

0.65 

0.63 

0.61 

0.60 

0.58 

0.56 

0.55 

0.53 

0.51 

0.49 

0.47 

A,h 

Log. 

9.826 

9.812 

9.799 

9.785 

9.778 

9.763 

9.748 

9.740 

9.724 

9.707 

9.690 

9.672 

Log. 

07 

91 

34 

33 

15 

43 

19 

36 

28 

57 

20 

10 

Limit 

73 

74. 

75 

76 

77 

78 

79 

80 

81 

82 

82 

82 

Min- 
utes 

Merid- 
ian 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

Alti- 
tudes 

310 


Latitude  52"  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8°        9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  24 

1  38 
3  40 
6  32 

10  12 
14  41 
20  00 
26  07 
33  03 
40  48 
49  22 
58  45 
68  57 
79  58 
9148 

n 

1.53 

/       n 

0  25 

1  40 
3  45 
6  39 

10  24 
14  59 
20  23 
26  37 
33  42 
41  36 
50  20 
59  54 
70  18 
81  32 
93  36 

n 

1.56 

/        n 

0  25 

141 

3  48 

6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
It 

r.58 

/       n 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
51  38 
61  26 
72  06 
83  38 

96  00 

It 

1.60 

/     // 

0  26 

1  43 
3  53 
6  55 

10  48 
15  34 
21  10 
27  38 
35  00 
43  12 
52  17 
62  12 
73  00 
84  41 
97  12 

n 

1.62 

/     // 

0  27 

1  45 
3  57 
7  03 

11  00 
15  51 
21  33 
28  09 
35  39 
44  00 
53  15 
63  21 
74  21 
86  15 
99  00 

n 

1.65 

/     // 

0  27 

147 

4  00 

7  08 

1108 

16  02 

2149 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

n 

1.67 

0  27 

149 

4  05 

7  15 

11  20 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 
It 

1.70 

/     // 

0  27 

150 

4  08 

7  20 

11  28 

16  31 

22  29 

29  21 

37  09 

45  52 

55  30 

66  01 

77  31 

89  54 

103  12 

It 

1.72 

0  28 

1  52 
4  12 
7  28 

11  40 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 
91  28 

105  00 

It 

1.75 

/     // 

0  28 

154 

4  17 

7  35 

11  52 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 
It 

1.78 

/      // 

0  29 

156 

4  20 

7  44 

12  04 

'  17  23 

23  39 

30  53 

39  06 

48  16 

58  24 

69  30 

81  34 

94  36 

108  36 

It 

1.81 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.184 
69 

0.193 
12 

0.198 
66 

0.204 
12 

0.209 
52 

0.217 
48 

0.222 
72 

0.230 
45 

0.235 
53 

0.243 
04 

0.250 
42 

0.257 
68 

Log. 

Limit 

54 

53 

52 

52 

51 

51 

50 

50 

49 

49 

48 

48 

Min- 
utes 

Merid- 
ian 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

Alti- 
tudea 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/      // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

/      // 

/      // 

1      II 

1     II 

Min. 

4 

0  30 

t)30 

0  30 

0  31 

0  31 

0  32 

0  33 

0  34 

0  35 

0  35 

0  36 

0  37 

4 

8 

1  58 

2  00 

2  02 

2  04 

2  06 

2  09 

2  12 

2  14 

2  17 

2  20 

2  24 

2  27 

8 

12 

4  25 

4  29 

4  35 

4  40 

4  46 

4  51 

4  57 

5  02 

5  08 

5  15 

5  23 

5  31 

12 

16 

7  51 

7  59 

8  09 

8  16 

8  26 

8  37 

8  47 

8  58 

9  08 

9  21 

9  33 

9  49 

16 

20 

12  16 

12  28 

12  44 

12  56 

13  12 

13  28 

13  44 

14  00 

14  16 

14  36 

14  56 

15  20 

20 

24 

17  40 

17  57 

18  20 

18  37 

19  00 

19  24 

19  47 

20  10 

20  33 

2102 

21  30 

30  03 

24 

28 

24  02 

24  26 

24  58 

25  21 

25  53 

26  24 

26  55 

27  26 

27  57 

28  37 

29  16 

39  15 

28 

32 

3124 

3155 

32  36 

33  07 

33  48 

34  28 

35  09 

35  50 

36  31 

37  22 

38  14 

49  41 

32 

36 

39  45 

40  24 

41  15 

4154 

42  46 

43  38 

44  30 

45  22 

46  14 

47  19 

48  23 

6120 

36 

40 

49  04 

49  52 

50  56 

5144 

52  48 

53  52 

54  56 

56  00 

57  04 

58  24 

59  44 

74  13 

40 

44 

59  22 

60  21 

61  37 

62  35 

63  53 

65  11 

66  28 

67  46 

69  03 

70  40 

72  16 

88  19 

44 

48 

70  39 

7148 

73  21 

74  30 

76  02 

77  34 

79  06 

80  38 

82  10 

84  05 

86  01 

103  39 

48 

52 

82  55 

84  16 

86  05 

87  26 

89  14 

91  02 

92  50 

94  38 

96  26 

98  41 

100  57 

52 

56 

96  10 

97  45 

99  49 

10123 

103  29 

105  34 

56 

60 

110  24 

112  12 

114  36 

60 

* 

It 

" 

It 

If 

It 

It 

It 

It 

It 

It 

It 

Aih 

1.84 

1.87 

1.91 

1.94 

1.98 

2.02 

2.06 

2.10 

2.14 

2.19 

2.24 

2.30 

A,h 

Log. 

0.264    0.271 

0.281 

0.287 

0.296 

0.305 

0.313 

0.322 

0.330 

0.340 

0.350 

0.361 

Log. 

82        84 

03 

80 

67 

35 

87 

22 

41 

44 

25 

73 

Limit 

47        47 

46 

46 

45 

44 

43 

43 

42 

41 

40 

39 

Min- 
utes 

Merid- 
ian 

50°      51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

Alti- 
tudes 

Latitude  52^  Declination  Same  Name. 


311 


DlOCLINATIOXS. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30°      31° 

32 

0 

33° 

34° 

qco      Hour 
^^      Angles 

Min. 

4 

8 

12 

16 

20 

0  38 
2  30 
5  38 
10  02 
15  40 
22  34 
30  42 
40  06 
50  46 
62  40 
75  50 

n 

2.35 

1     " 

0  38 
2  35 
5  47 
10  17 
16  04 
23  08 
3130 
4108 
52  03 
64  16 
77  45 

It 
2.41 

/      // 

0  39 
2  39 
5  58 
10  34 
16  32 
23  48 
32  25 
42  20 
53  34 
66  08 
80  01 

n 

2.48 

0  41 

2  43 
6  07 
10  53 
17  00 
24  29 
33  19 
43  31 
55  05 
68  00 
82  17 

n 

2.55 

/      // 

0  42 

2  47 

6  17 

11  11 

17  28 

/      // 

0  43 

2  54 

6  30 

11  34 

18  04 

/      // 

0  44 

2  59 

6  42 

11  54 

18  36 

/      // 

0  46 

3  05 

6  56 

12  20 

19  16 

/      // 

0  48 
3  12 

7  12 
12  48 
20  00 

0  50 

3  19 

7  27 

13  17 

20  44 

/      // 

0  52 

3  28 

7  47 

13  49 

21  36 

0  54 
3  37 

8  08 
14  28 
22  36 

Min. 

4 

8 
12 
16 
20 

24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

4 

A 
i 

2 

'5 
4 
4 
6 
9 

n 

.6 

10 
14 
42 
36 
52 

2 

2 

JbOl 
5  25 
16  15 
8  32 
2  16 

n 

.71 

26  " 
36 
47 
60 

74 

It 
1.1 

5/ 
28 
37 
16 
24 

9 

27  45 
37  46 
49  19 
62  26 
77  04 

It 
2.89 

28  48 
39  12 
51  12 
64  48 
80  00 

It 
3.00 

29  52 
40  38 
53  04 
67  11 

It 
3.11 

31  06 
42  20 
55  18 
69  59 

It 
3.24 

32  33 
44  18 
57  51 
73  14 

II 
3.39 

24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.371 
07 

0.382 
02 

0.394 
45 

0.406 
54 

0.418 
30 

0.432 
97 

0.445 
60 

0.460 
90 

0.477 
12 

0.492 
76 

0.510 
55 

0.530 
20 

Log. 

Limit 

38 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

29 

Min- 
utes 

Merid- 
ian 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

ff 

/     // 

/      // 

/     // 

/      // 

/      // 

/     // 

Min. 

Min. 

4 

0  57 

0  59 

103 

107 

1  11 

116 

1  23 

131 

1  40 

152 

2  08 

2  31 

4 

8 

3  47 

4  00 

4  12 

4  27 

4  45 

5  06 

5  31 

6  01 

6  40 

7  29 

8  34 

10  06 

8 

12 

8  31 

8  57 

9  28 

10  02 

10  41 

11  29 

12  24 

13  33 

15  00 

16  49 

19  14 

22  43 

12 

16        1 

5  09 

15  55 

16  48 

17  50 

18  59 

20  23 

22  04 

24  07 

26  40 

29  55 

34  16 

40  21 

16 

20       1 

3  40 

24  52 

26  16 

27  52 

29  40 

3152 

34  28 

37  40 

41  40 

46  44 

53  32 

20 

24       3 

4  05 

35  48 

37  49 

40  08 

42  43 

45  53 

49  38 

54  15 

60  00 

24 

28       4 

6  23 

48  45 

51  29 

54  37 

58  09 

62  26 

67  33 

28 

32       € 

0  35 

63  40 

67  15 

7120 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

It 

It 

II 

It 

It 

It 

» 

It 

It 

It 

" 

Ajh      S 

.55 

3.73 

3.94 

4.18 

4.45 

4.78 

5.17 

5.65 

6.25 

7.01 

8.03 

9.46 

A,h 

T                   t 

.550 

0.571 

0.595 

0.621 

0.648 

0.679 

0.713 

0.752 

0.795 

0.845 

0.904 

0.975 

Log. 

23 

71 

50 

18 

36 

43 

49 

05 

88 

72 

72 

89 

Limit 

28 

27 

26 

25 

24 

23 

22 

20 

18 

16 

14 

12 

Min- 
utes 

Merid- 
ian 

74 

0 

75 

0 

76 

0 

77 

° 

78 

o 

79° 

80 

0 

81 

= 

82 

0 

83 

o 

34 

0 

85 

o 

Alti- 
tudes 

312 


Latitude  52*  Declination  Same  Name. 

Declinations. 


Hiiui- 
A  nglos 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 
4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

i> 

/ 

If 

I 

1 

r 

It 

It 

/ 

// 

1 

n 

/      // 

It 

1 

1 

t 

1 

II 

1     II 

2  01 

8  03 

18  07 

32  13 

It 
7.55 

/     II 

1  38 

6  32 

14  42 

26  10 

40  52 

It 
6.13 

/       n 

1  22 

5  27 

12  15 

21  49 

34  04 

It 
5.11 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.877 
95 

0.787 
46 

0.708 
42 

Log. 

Limit 

10 

8 

5 

3 

0 

3 

6 

8 

11 

13 

16 

18 

Min- 
utes 

Merid- 
ian 

8 

S° 

57° 

8 

8° 

89° 

9 

0° 

8 

9° 

88° 

8 

7° 

8 

6° 

85 

0 

84 

o 

83 

o 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     /' 

/      // 

/      // 

/     // 

/     // 

1     II 

/     '/ 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

1  10 

100 

0  52 

0  46 

0  41 

0  36 

0  32 

0  29 

0  27 

0  23 

0  22 

0  19 

4 

8 

4  38 

4  00 

3  30 

3  04 

2  43 

2  25 

2  10 

156 

145 

135 

126 

117 

8 

12 

10  25 

9  00 

7  51 

6  55 

6  07 

5  26 

4  52 

4  22 

3  56 

3  34 

3  13 

2  53 

12 

16 

18  31 

16  00 

13  57 

12  17 

10  53 

9  38 

8  40 

7  46 

7  00 

6  18 

5  43 

5  07 

16 

20 

28  56 

25  00 

21  48 

19  12 

17  00 

15  04 

13  32 

12  08 

10  56 

9  52 

8  56 

8  00 

20 

24 

4140 

36  00 

31  23 

27  39 

24  29 

21  42 

19  29 

17  29 

15  45 

14  12 

12  52 

1131 

24 

28 

42  44 

37  38 

33  19 

29  32 

26  32 

23  47 

2125 

19  21 

17  30 

15  41 

28 

32 

49  09 

43  31 

38  24 

34  39 

31  03 

27  59 

25  16 

22  52 

20  29 

32 

36 

48  49 

43  51 

39  19 

35  26 

3158 

28  57 

25  55 

36 

40 

54  08 

48  32 

43  44 

39  28 

35  44 

32  00 

40 

44 

58  44 

52  55 

47  45 

43  14 

38  43 

44 

48 

62  58 

56  50 

5127 

46  05 

48 

52 

60  23 

54  05 

52 

56 

62  43 

56 

60 

60 

* 

It 

It 

It 

" 

It 

It 

It 

It 

It 

It 

It 

A,h 

4.34 

3.75 

3.27 

2.88 

2.55 

2.26 

2.03 

1.82 

1.64 

1.48 

1.34 

1.20 

A,h 

Log. 

0.637 

0.574 

0.514 

0.459 

0.406 

0.354 

0.307 

0.260 

0.214 

0.170 

0.127 

0.079 

Log. 

49 

03 

55 

39 

54 

11 

50 

07 

84 

26 

10 

18 

Limit 

20 

22 

24 

27 

29 

31 

34 

36 

39 

41 

44 

47 

Min- 
utes 

Merid- 
ian 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

71° 

Alti- 
tudes 

Latitude  52°  Declination  Contrary  Name. 


313 


Declinations. 


Hour 
Angles 

o» 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

/       // 

/     // 

/     // 

/     // 

/     // 

/      // 

/     // 

/      It 

/     // 

/     // 

/      // 

/      // 

Min. 

4 

0  24 

0  24 

0  23 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

4 

8 

1  38 

1  36 

1  36 

1  34 

1  33 

1  33 

1  31 

1  30 

1  28 

128 

126 

125 

8 

12 

3  40 

3  37 

3  35 

3  32 

3  29 

3  28 

3  25 

3  22 

3  19 

3  17 

3  14 

3  11 

12 

16 

6  32 

6  27 

6  21 

6  16 

6  11 

6  08 

6  03 

5  58 

5  53 

5  51 

5  46 

5  41 

16 

20 

10  12 

10  04 

9  56 

9  48 

9  40 

9  36 

9  28 

9  20 

9  12 

9  08 

9  00 

8  52 

20 

24 

14  41 

14  30 

14  18 

14  06 

13  55 

13  49 

13  38 

13  26 

13  15 

13  09 

12  58 

12  46 

24 

28 

20  00 

19  44 

19  29 

19  13 

18  57 

18  49 

18  34 

18  18 

18  02 

17  54 

17  38 

17  23 

28 

32 

26  07 

25  46 

25  26 

25  06 

24  45 

24  35 

24  14 

23  54 

23  33 

23  23 

23  02 

22  42 

32 

36 

33  03 

32  37 

32  11 

3145 

31  19 

31  06 

30  40 

30  14 

29  49 

29  36 

29  10 

28  44 

36 

40 

40  48 

40  16 

39  44 

39  12 

38  40 

38  24 

37  52 

37  20 

36  48 

36  32 

36  00 

35  28 

40 

44 

49  22 

48  43 

48  04 

47  26 

46  47 

46  27 

45  49 

45  10 

44  32 

44  13 

43  34 

42  55 

44 

48 

58  45 

57  59 

57  13 

56  27 

55  41 

55  18 

54  32 

53  46 

52  59 

52  36 

5150 

5104 

48 

52 

68  57 

68  03 

67  09 

66  15 

65  21 

64  54 

64  00 

63  06 

62  11 

6144 

60  50 

59  56 

52 

56 

79  58 

78  55 

77  52 

76  50 

75  37 

75  15 

74  13 

73  10 

72  08 

71  37 

70  34 

69  31 

56 

60 

9148 

90  36 

89  24 

88  12 

87  00 

86  24 

85  12 

84  00 

82  48 

82  12 

81  00 

79  48 

60 

n 

" 

It 

n 

n 

n 

It 

It 

It 

It 

It 

It 

A,h 

1.53 

1.51 

1.49 

1.47 

1.45 

1.44 

1.42 

1.40 

1.38 

1.37 

1.35 

1.33 

Ajh 

Log. 

0.184 

0.178 

0.173 

0.167 

0.161 

0.158 

0.152 

0.1*46 

0.139 

0.136 

0.130 

0.123 

Log. 

69 

98 

19 

32 

37 

36 

29 

13 

88 

72 

33 

85 

Limit 

53 

54 

55 

55 

56 

57 

57 

58 

59 

60 

61 

61 

Min- 
utes 

Merid- 
ian 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour  " 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1     It 

0  21 

124 

3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 
It 

1.32 

/      // 

0  21 

123 

3  07 

5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

4157 

49  55 

58  35 

67  57 

78  00 
It 

1.32 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
It 

L28 

/        n 

0  20 

1  21 
3  03 
5  25 
8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
It 

1.27 

/      // 

0  20 

120 

3  00 

5  20 

8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 

It 

1.25 

/      // 

0  20 

1  20 

2  59 
5  17 
8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
It 

1.24 

/     // 

0  19 

1  18 

2  56 
5  12 
8  08 

1143 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

It 

1.22 

/     // 

0  19 

1  17 

2  54 
5  10 
8  04 

1137 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

It 

1.21 

1     II 

0  19 

1  16 

2  51 
5  05 
7  56 

1126 
15  33 
20  18 
25  43 
31  44 
38  24 
45  41 
53  37 
62  12 
71  24 

n 

1.19 

/      // 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

31  28 

38  05 

45  18 

53  10 

61  41 

70  48 
It 

1.18 

/     // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

1.17 

r       It 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
51  49 
60  07 

69  00 

It 

1.15 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.120 
57 

0.113 
94 

0.107 
21 

0.103 
80 

0.096 
91 

0.093 
42 

0.086 
36 

0.082 
79 

0.075 
55 

0  071 

88 

0.068 
19 

0.060 
70 

Log. 

Limit 

62 

63 

64 

64 

64 

64 

65 

66 

67 

68 

69 

70 

Min- 
utes 

Merid- 
ian 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

Alti- 
tudes 

314 


Latitude  52°  Declination  Contrary  Name. 
Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34°      35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

5122 

59  35 

68  24 
It 

1.14 

/     // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

n 

1.12 

/      // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 
66  00 

n 

1.10 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

n 

1.09 

0  17 

109 

2  35 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 

n 

1.08 

0  17 

109 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

n 

1.07 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

n 

1.05 

/     // 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

n 

1.04 

/     // 

0  17 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
It 

1.03 

/     // 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

1.02 

/ 

T 

/ 
• 

1 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.056 
90 

0.049 
22 

0.041 
39 

0.037 
43 

0.033 
42 

0.029 
38 

0.021 
19 

0.017 
03 

0.012 
84 

0.008 
60 

Log. 

Limit 

71 

71 

72 

73 

74 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

Alti- 
tudes 

Declinations.  - 

—  Inferior  Me 

RIDIA^ 

. 

Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43°      44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

/ 

// 

1 

/ 

// 

1 

// 

/ 

■ 
• 

1 

/ 

II 

t 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

■19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
It 

0.88 

/       // 

0  14 
0  56 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

It 

0.87 

/     // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 
51  36 

0.86 

/      // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 

5100 

It 

0.85 

0  14 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 
It 

0.83 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.944 
48 

9.939 
52 

9.934 
50 

9.929 
42 

9.919 
08 

Log. 

Limit 

74 

74 

74 

74 

74 

Min- 
utes 

Merid- 
ian 

}° 

1 

o 

( 

)° 

] 

L° 

J 

>o 

a 

° 

i 

1° 

5° 

6° 

7° 

8° 

9° 

Alti- 
tudes 

Latitude  52*^  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


315 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

MiD. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

2152 

26  28 

3129 

36  57 

42  52 

49  12 

0.82 

/   n 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
It 

0.80 

1      II 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 

0.79 

/  II 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
It 

0.78 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

0.77 

/  // 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

It 

0.75 

/  // 

0  12 
0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 

44  24 

It 

0.74 

1     II 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 

43  12 

It 

0.72 

/  // 

Oil 
0  46 
142 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  07 

42  36 

It 

0.71 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

11  57 

15  07 

18  40 

22  35 

26  51 

31  33 

36  35 

42  00 

It 

0.70 

/   // 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

1146 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

4124 

It 

0.69 

/  // 

Oil 

0  43 

1  36 

2  52 

4  28 
6  26 
8  45 
11  26 
14  29 
17  52 
21  38 
25  43 
30  11 
35  02 

40  12 

It 

0.67 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Log. 

9.913 
81 

9.903 
09 

9.897 
63 

9.892 
09 

9.886 
49 

9.875 
06 

9.869 
23 

9.857 
33 

9.851 
26 

9.845 
10 

9.838 
85 

9.826 
07 

Log. 

Limit 

74 

74 

74 

74 

74 

74 

74 

74 

74 

74 

74 

74 

Min- 
utes 

Merid- 
ian 

10° 

IP 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

Alti- 
tudes 

D 

ECI.INATIONS 

.  —  Inferior  Meridian 

• 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/  '/ 

/   // 

/  // 

/  // 

/  /' 

1     II 

/  // 

/   // 

/  // 

/  /' 

/  // 

/  // 

Min, 

4 

Oil 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

4 

8 

0  42 

0  40 

0  40 

0  38 

0  38 

0  37 

0  36 

0  35 

0  33 

0  32 

0  32 

0  30 

8 

12 

1  35 

1  32 

1  29 

126 

1  25 

1  22 

121 

1  18 

1  15 

1  13 

1  11 

108 

12 

16 

2  49 

2  44 

2  39 

2  34 

2  31 

2  26 

2  23 

2  18 

2  13 

2  11 

2  05 

2  00 

16 

20 

4  24 

4  16 

4  08 

4  00 

3  56 

3  48 

3  44 

3  36 

3  28 

3  24 

3  16 

3  08 

20 

24 

6  21 

6  09 

5  58 

5  46 

5  40 

5  28 

5  23 

5  11 

5  00 

4  54 

4  42 

4  30 

24 

28 

8  37 

8  21 

8  06 

7  50 

7  43 

7  27 

7  19 

7  03 

6  48 

6  40 

6  25 

6  09 

28 

32 

11  15 

10  55 

10  34 

10  14 

10  04 

9  44 

9  33 

9  13 

8  52 

8  42 

8  22 

8  02 

32 

36 

14  16 

13  50 

13  24 

12  58 

12  45 

12  19 

12  06 

1140 

11  14 

11  01 

10  35 

10  09 

36 

40 

17  36 

17  04 

16  32 

16  00 

15  44 

15  12 

14  56 

14  24 

13  52 

13  36 

13  04 

12  32 

40 

44 

21  18 

20  39 

20  01 

19  22 

19  02 

18  24 

18  04 

17  25 

16  47 

16  27 

15  48 

15  10 

44 

48 

25  20 

24  34 

23  48 

23  02 

22  39 

2153 

21  30 

20  44 

19  58 

19  35 

18  49 

18  03 

48 

52 

29  44 

28  50 

27  56 

27  02 

26  35 

25  41 

25  14 

24  20 

23  26 

22  59 

22  05 

21  11 

52 

56 

34  30 

33  27 

32  25 

31  22 

30  50 

29  48 

29  16 

28  13 

27  11 

26  39 

25  36 

24  34 

56 

60 

39  36 

38  24 

37  12 

36  00 

35  24 

34  12 

33  36 

32  24 

31  12 

30  36 

29  24 

28  12 

60 

It 

It 

II 

" 

" 

It 

It 

» 

It 

It 

It 

It 

A,h 

0.66 

0.64 

0.62 

0.60 

0.59 

0.57 

0.56 

0.54 

0.52 

0.51 

0.49 

0.47 

A,h 

Log. 

9.819 

9.806 

9.792 

9.778 

7.770 

9.755 

9.748 

9.732 

9.716 

9.707 

9.690 

9.672 

Log. 

54 

18 

39 

15 

85 

87 

19 

39 

00 

57 

20 

10 

Limit 

74 

74 

74 

74 

76 

77 

78 

79 

80 

81 

81 

81 

Min- 
utes 

Merid- 
ian 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

Alti- 
tudes 

316 


Latitude  53"  Decimation  Same  Name 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  23 
135 
3  34 

6  18 

9  52 

14  12 

19  21 

25  16 

31  58 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
It 

1.48 

/  // 

0  24 

1  36 
3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 
» 

1.50 

/  // 

.  0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 
// 

1.52 

/  // 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

41  04 

49  41 

59  08 

69  24 

80  29 

92  24 

n 

1.54 

/  II 

0  25 

140 

3  45 

6  39 

10  24 

14  59 

20  23 

26  37 

33  42 

41  36 

50  20 

59  54 

70  18 

81  32 

93  36 
It 

1.56 

/  // 

0  25 

1  41 
3  48 
6  44 

10  32 

15  10 

20  39 

26  58 

34  08 

42  08 

50  59 

60  40 

71  12 

82  35 

94  48 
II 

1.58 

/  // 

0  26 

1  42 
3  51 
6  53 

10  44 
15  28 
21  02 
27  28 
34  47 
42  56 
5157 
61  49 
72  33 
84  09 
96  36 

n 

1.61 

/  // 

0  26 

1  44 
3  54 
6  58 

10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 
97  48 

n 

1.63 

/  // 

0  27 

1  45 
3  57 
7  03 

11  00 
15  51 
21  33 
28  09 
35  39 
44  00 
53  15 
63  21 
74  21 
86  15 
99  00 

n 

1.65 

/  // 

0  27 

1  47 
4  02 
7  10 

11  12 
16  08 
21  57 
28  40 
36  18 
44  48 
54  13 
64  30 
75  42 
87  49 
100  48 

n 

1.68 

/  // 

0  27 
150 
4  06 

7  18 
11  24 
16  25 
22  21 
29  11 
36  56 
45  36 
55  10 
65  38 
77  04 
89  22 
102  36 

n 

1.71 

/  II 

0  27 

151 

4  09 

7  23 

11  32 

16  36 

22  37 

29  32 

37  22 

46  08 

55  49 

66  24 

77  58 

90  2S 

103  48 

n 

1.73 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.170 
26 

0.176 
09 

0.181 

84 

0.187 
52 

0.193 
12 

0.198 
66 

0.206 
83 

0.212 
19 

0.217 

48 

0.225 
31 

0.233 
00 

0.238 
05 

Log. 

Limit 

55 

55 

54 

54 

53 

52 

52 

51 

51 

50 

49 

49 

Min- 
utes 

Merid- 
ian 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/   // 

/  // 

/  /' 

/  // 

/  // 

/  // 

/  // 

1     II 

Min. 

Min. 

4 

0  28 

0  28 

0  29 

0  30 

0  30 

0  30 

0  31 

0  32 

0  33 

0  33 

0  34 

0  35 

4 

8 

1  53 

1  55 

1  56 

158 

2  01 

2  02 

2  05 

2  08 

2  11 

2  13 

2  16 

2  19 

8 

12 

414 

4  18 

4  22 

4  26 

4  32 

4  37 

4  43 

4  48 

4  54 

5  00 

5  06 

5  14 

12 

16 

7  30 

7  38 

7  46 

7  54 

8  04 

8  11 

8  21 

8  32 

8  42 

8  52 

9  06 

9  18 

16 

20 

11  44 

1156 

12  08 

12  20 

12  36 

12  48 

13  04 

13  20 

13  36 

13  52 

14  12 

14  32 

20 

24 

16  54 

17  11 

17  29 

17  46 

18  09 

18  26 

18  49 

19  12 

19  35 

19  58 

20  27 

20  56 

24 

28 

23  00 

23  24 

23  47 

24  10 

24  42 

25  06 

25  37 

26  08 

26  39 

27  11 

27  50 

28  29 

28 

32 

30  02 

30  33 

31  03 

3134 

32  15 

32  46 

33  27 

34  08 

34  49 

35  30 

36  21 

37  12 

32 

36 

38  01 

38  40 

39  19 

39  58 

40  50 

41  28 

42  20 

43  12 

44  04 

44  56 

46  01 

47  06 

36 

40 

46  56 

47  44 

48  32 

49  20 

50  24 

51  12 

52  16 

53  20 

54  24 

55  28 

56  48 

58  08 

40 

44 

56  47 

57  45 

58  44 

59  42 

60  59 

6157 

63  14 

64  32 

65  49 

67  07 

68  44 

70  21 

44 

48 

67  33 

68  42 

69  53 

71  02 

72  34 

73  44 

75  16 

76  48 

78  20 

79  52 

81  46 

83  42 

48 

52 

79  19 

80  40 

82  01 

83  22 

85  10 

86  32 

88  20 

90  08 

9156 

93  44 

95  59 

98  14 

52 

56 

91  59 

93  33 

95  08 

96  42 

98  47 

100  21 

102  26 

104  32 

106  37 

56 

60 

105  36 

107  24 

109  12 

111  00 

113  24 

60 

n 

" 

n 

n 

n 

n 

II 

n 

II 

* 

n 

n 

A,h 

1.76 

1.79 

1.82 

1.85 

1.89 

1.92 

1.96 

2.00 

2.04 

2.08 

2.13 

2.18 

A,h 

Log. 

0.245 

0.252 

0.260 

0.267 

0.276 

0.283 

0.292 

0.301 

0.309 

0.318 

0.328 

0.338 

Log. 

51 

85 

07 

17 

46 

30 

26 

03 

63 

06 

38 

46 

Limit 

48 

47 

46 

46 

45 

44 

44 

43 

43 

42 

41 

40 

Min- 
utes 

ISrerid- 
ian 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60^ 

Alti- 
t\i<les 

Latitude  53"  Declination  Same  Name. 


317 


Declinations. 

Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       n 

0  35 

2  23 
5  21 
9  31 
14  52 
21  24 
29  09 
38  03 
48  10 
59  28 
7157 
85  38 

2.23 

/      // 

0  36 

2  25 

5  27 

9  40 

15  08 

21  47 

29  40 

38  45 

49  02 

60  32 

73  15 

87  10 

It 
2.27 

0  38 
2  30 
5  37 
10  00 
15  36 
22  27 
30  33 
39  56 
50  33 
62  24 
75  30 
89  51 

It 
2.34 

/     // 

0  39 

2  33 
5  45 
10  15 
16  00 
23  03 
3121 
40  57 
51  50 
64  00 
77  26 

It 
2.40 

/     // 

0  39 

2  38 
5  57 
10  31 
16  28 
23  42 
32  17 
42  10 
53  21 
65  52 
79  42 

It 
2.47 

/     // 

0  41 
2  42 
6  06 
10  51 
16  56 
24  24 
33  11 
43  20 
54  52 
67  44 
81  57 

It 
2.54 

1 

0 
2 
6 
11 
17 
25 
34 
44 
56 
69 

n 

2.6 

43 
49 
18 
10 
28 
10 
15 
42 
36 
52 

2 

/ 

] 
1 

A 

c 

1 

2 

0 
2 
6 

1 
8 
5 
5 
6 
8 
2 

It 
.7 

// 

44 
54 
30 
30 
00 
55 
18 
05 
19 
00 

0 

/      // 

0  45 
2  59 
6  43 
1157 
18  39 
26  52 
36  35 
47  47 
60  29 
74  40 

It 
2.80 

/     If 

0  47 
3  06 
6  57 
12  22 
19  19 
27  49 
37  54 
49  30 
62  38 
77  20 

2.90 

/     // 

0  48 
3  12 

7  12 
12  48 
19  59 
28  48 
39  12 
51  12 
64  48 

It 
3.00 

f     II 

0  50 
3  21 
7  33 
13  27 
21  00 
30  15 
41  09 
53  45 
68  03 

It 
3.13 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.348 
30 

0.356 
03 

0.369 
22 

0.380 
21 

0.392 
70 

0.404 
83 

0.418 
30 

0.431 
36 

0.447 
16 

0.462 
40 

0.47.7 
12 

0.495 
54 

Log. 

Limit 

40 

39 

38 

37 

36 

35 

34 

34 

33 

32 

31 

30 

Min- 
utes 

Merid- 
ian 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/     // 

/     // 

/      // 

/     // 

/     // 

/     '/ 

/     // 

t     II 

Min. 

Min. 

4 

0  52 

0  55 

0  58 

101 

104 

108 

1  14 

1  20 

127 

1  36 

148 

2  03 

4 

8 

3  29 

3  38 

3  50 

4  03 

4  17 

4  35|     4  55 

5  19 

5  48 

6  24 

7  12 

8  13 

8 

12 

7  50 

8  12 

8  38 

9  07 

9  39 

10  19 

1103 

11  56 

13  03 

14  24 

16  11 

18  30 

12 

16 

13  56 

14  35 

15  22 

16  13 

17  09 

18  18 

19  38 

21  12 

23  11 

25  36 

28  44 

32  54 

16 

20 

2148 

22  48 

24  00 

25  19 

26  48 

28  36 

30  40 

33  08 

36  16 

40  00 

44  56 

20 

24 

3123 

32  50 

34  34 

36  28 

38  36 

41  11 

44  10 

47  42 

52  13 

57  36 

24 

28 

42  44 

44  41 

47  02 

49  39 

52  32 

56  04 

60  06 

64  57 

28 

32 

55  49 

58  22 

6126 

64  51 

68  36 

32 

36 

70  38 

73  52 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

•    60 

60 

" 

" 

It 

It 

It 

It 

It 

It 

It 

It 

It 

f 

Ajh 

3.27 

3.42 

3.60 

3.80 

4.02 

4.29 

4.60 

4.97 

5.44 

6.00 

6.74 

7.71 

A,h 

Log. 

0.514 

0.534 

0.556 

0.579 

0.604 

0.632 

0.662 

0.696 

0.735 

0.778 

0.828 

0.887 

55 

03 

30 

78 

23 

46 

76 

36 

60 

15 

66 

05 

Log. 

Limit 

30 

29 

28 

26 

25 

25 

23 

22 

20 

18 

17 

15 

Min- 
utes 

Merid- 
ian 

73° 

74° 

75° 

76° 

77° 

78^ 

79° 

80° 

81° 

82° 

83^ 

84° 

Alti- 
tudes 

;i8 


Latitude  53°  Declination  Same  Name. 

Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

2 

9 

21 

38 

n 

9.0 

// 

25 
41 
46 
42 

7 

/ 

/ 

II 
If 

1 

It 

// 

1 

// 

1 

// 

1 

7 

/ 

1 

/ 

r 

/ 

r 

/     II 

155 

7  41 

17  15 

30  41 

47  56 

n 

7.19 

/     // 

134 
6  16 
14  06 
25  04 
39  12 
56  27 

n 

5.88 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.957 
61 

0.856 
73 

0.769 
38 

Log. 

Limit 

13 

11 

8 

6 

3 

0 

3 

5 

8 

11 

14 

16 

Min- 
utes 

Merid- 
ian 

.85 

3 

8 

B° 

37° 

88 

0 

89 

0 

9 

3° 

8 

9° 

8 

8° 

8 

7° 

8 

6° 

85 

o 

84 

0 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/      // 

Min. 

Min. 

4 

1  18 

1  06 

0  57 

0  49 

0  44 

0  39 

0  35 

0  30 

0  27 

0  25 

0  22 

0  19 

4 

8 

5  11 

4  23 

3  47 

3  18 

2  54 

2  33 

2  17 

2  02 

1  50 

1  39 

128 

1  18 

8 

12        ] 

139 

9  52 

8  30 

7  25 

6  31 

5  45 

5  08 

4  35 

4  06 

3  42 

3  19 

2  56 

12 

16       2 

0  41 

17  34 

15  09 

13  10 

11  37 

10  15 

9  08 

8  09 

7  18 

6  34 

5  53 

5  12 

16 

20       5 

2  20 

27  28 

23  40 

20  36 

18  07 

16  00 

14  16 

12  44 

11  24 

10  16 

9  12 

8  08 

20 

24       4 

6  34 

39  34 

34  05 

29  40 

26  07 

23  03 

20  33 

18  20 

16  25 

14  47 

13  15 

1143 

24 

28 

53  50 

46  16 

40  23 

35  33 

31  21 

27  57 

24  58 

22  21 

20  07 

18  02 

15  57 

28 

32 

52  44 

46  24 

40  57 

36  31 

32  36 

29  11 

26  17 

23  33 

20  49 

32 

36 

5150 

46  14 

41  15 

36  56 

33  16 

29  49 

26  21 

36 

40 

50  56 

45  36 

41  04 

36  48 

32  32 

40 

44 

55  10 

49  41 

44  32 

39  22 

44 

48 

59  08 

52  59 

46  51 

48 

52 

62  11 

54  59 

52 

56 

63  46 

56 

60 

60    • 

n 

It 

It 

It 

If 

n 

If 

n 

If 

If 

It 

If 

Ajh     i 

1.85 

4.12 

3.55 

3.09 

2.72 

2.40 

2.14 

1.91 

1.71 

1.54 

1.38 

1.22 

Ajh 

( 
Log. 

).685 

0.614 

0.550 

0.489 

0.434 

0.380 

0.330 

0.281 

0.233 

0.187 

0.139 

0.086 

Log. 

74 

90 

23 

96 

57 

21 

41 

03 

00 

52 

88 

36 

Limit 

18 

21 

23 

25 

27 

29 

32 

34 

37 

39 

43 

44 

Min- 
utes 

Merid- 
ian 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

73° 

72° 

Alti- 
tudes 

Latitude  53°  Declination  Contrary  Name. 


319 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

76 

8° 

9° 

10° 

IP 

Hour 

Angles 

Min. 

/       /' 

/     // 

/      // 

/        n 

/     // 

/     II 

/          IT 

/     // 

/     II 

/      // 

/      // 

/     // 

Min. 

4 

0  23 

0  23 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  21 

0  21 

0  20 

4 

8 

135 
3  34 

134 
3  31 

133 
3  28 

131 
3  25 

130 
3  23 

1  29 
3  20 

128 
3(27 

1  26j 

_i-2^ 

.    1  24 

1  23 

1  23 

8          r 

12 

)  3  14 

3  13 

3  10 

3  08 

3  06 

12         ^ 

16 

6  18 

6  13 

6  08 

6  03 

6  01 

5  56 

5  51 

5  46 

5  43 

5  38 

5  36 

5  30 

16 

20 

9  52 

9  44 

9  36 

9  28 

9  24 

9  16 

9  08 

9  00 

8  56 

8  48 

8  44 

8  36 

20 

24 

14  12 

14  01 

13  49 

13  38 

13  32 

13  21 

13  09 

12  58 

12  52 

12  41 

12  35 

12  23 

24 

28 

19  21 

19  05 

18  49 

18  34 

18  26 

18  10 

17  54 

17  38 

17  30 

17  15 

17  07 

16  52 

28 

32 

25  16 

24  55 

24  35 

24  14 

24  04 

23  43 

23  23 

23  02 

22  52 

22  31 

22  21 

22  01 

32 

36 

3158 

31  32 

3106 

30  40 

30  27 

30  02 

29  36 

29  10 

28  57 

28  31 

28  18 

27  52 

36 

40 

39  28 

38  56 

38  24 

37  52 

37  36 

37  04 

36  32 

36  00 

35  44 

35  12 

34  56 

34  24 

40 

44 

47  45 

47  06 

46  27 

45  49 

45  29 

44  51 

44  13 

43  34 

43  14 

42  36 

42  16 

41  37 

44 

48 

56  50 

56  04 

55  18 

54  32 

54  09 

53  22 

52  36 

51  50 

5127 

50  41 

50  18 

49  32 

48 

52 

66  42 

65  48 

64  54 

64  00 

63  33 

62  38 

61  44 

60  50 

60  23 

59  29 

59  02 

58  08 

52 

56 

77  21 

76  18 

75  15 

74  13 

73  41 

72  39 

71  37 

70  34 

70  02 

69  00 

68  28 

67  25 

56 

60 

88  48 

87  36 

86  24 

85  12 

84  36 

83  24 

82  12 

8100 

80  24 

79  12 

78  36 

77  24 

60 

n 

It 

IT 

If 

It 

n 

It 

n 

n 

n 

n 

n 

Ajh 

1.48 

1.46 

1.44 

1.425 

1.41 

1.39 

1.37 

1.35 

1.34 

1.32 

1.31 

1.29 

A,h 

Log. 

0.170 

0.164 

0.158 

0.153 

0.149 

0.143 

0.136 

0.130 

0.127 

0.120 

0.117 

0.110 

Log. 

26 

35 

36 

81 

22 

01 
58 

72 

33 

10 

57 

27 

59 

Limit 

55 

55 

56 

56 

57 

58 

59 

60 

61 

62 

62 

Min- 
utes 

Merid- 
ian 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15°      16° 

17° 

18° 

19^ 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
.    24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/       // 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 

1.28 

/      // 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 
16  28 
2130 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 
75  36 

H 

1.26 

/     // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
21  20 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 
75  00 

H 

1.245 

0  19 

1  19 

2  57 
5  15 

8  12 
1148 
16  05 
2100 
26  34 
32  48 
39  41 
47  14 
55  26 
64  17 
73  48 

H 

1.23 

/        n 

0  19 

1  18 

2  56 
5  12 

8  08 

1143 

15  57 

20  49 

26  21 

32  32 

39  22 

46  51 

54  59 

63  46 

73  12 
II 

1.22 

1     II 

0  19 

117 

2  53 

5  07 

8  00 

1131 

15  41 

20  29 

25  55 

32  00 

38  43 

46  05 

54  05 

62  43 

72  00 
It 

1.205 

/      // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 
15  33 
20  18 
25  43 
31  44 
38  24 
45  41 
53  37 
62  12 
71  24 

n 

1.19 

I  II 

0  19 

1  15 

2  48 
5  00 
7  48 

II  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 
70  12 

n 

1.175 

/        n 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 
69  36 

n 

1.16 

1      II 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 
69  00 

n 

1.145 

1      II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 
67  48 

IT 

1.13 

1     II 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46' 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
It 

1.12 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.107 
21 

0.100 
37 

0.095 
17 

0.089 
91 

0.086 
36 

0.080 
99 

0.075 
55 

0.070 
04 

0.064 
46 

0.058 
81 

0.053 
08 

0.049 
22 

Log. 

Limit 

63 

64 

65 

65 

65 

65 

66 

67 

68 

69 

70 

71 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

320 


Latitude  53"  Decimation  Contrary  Name. 


Declinations. 


Hour 
Angles 

24» 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 
66  36 

n 
1.11 

/       n 

0  17 

1  10 

2  37 
4  39 

7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

4151 

49  07 

56  58 

65  24 
It 

1.09 

/        n 

0  17 

109 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

n 

1.07 

1     " 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

n 

1.06 

/       n 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

n 

1.05 

/     II 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  47 

33  33 

39  56 

46  52 

54  21 

62  24 
It 

1.04 

0  17 
105 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 

1.03 

/       n 

0  16 

105 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
It 

1.01 

/       n 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

2136 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

It 

1.00 

/      // 

It 
0.99 

It 

/ 

It 

Min, 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.045 
32 

0.037 
43 

0.029 
38 

0.025 
31 

0.021 
19 

0.017 
03 

0.012 
84 

0.004 
32 

0.00 

9.995 
64 

Log. 

Limit 

72 

72 

73 

74 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

A 

° 

3° 

2° 

Alti- 
tudes 

Declinations. 

—  Inferior  Meridlajj 

• 

Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 
n 

II 

If 

// 

/ 

It 

// 

It 

// 

1 

/ 

II 

It 

/     // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
It 

0.88 

/     // 

0  14 
0  56 

2  05 

3  43 
5  48 
8  21 

1122 

14  51 

18  48 

23  12 

28  05 

33  24 

39  12 

45  20 

52  12 
It 

0.87 

/      // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 

51  36 

It 

0.86 

/      // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
It 

0.84 

/      // 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
It 

0.83 

/      // 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 
13  59 
17  43 
2152 
26  28 
3129 
36  57 
42  52 
49  12 

0.82 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.944 

48 

9.939 
52 

9.924 
50 

9.924 

28 

9.919 
08 

9.913     - 
81     ^°«- 

Limit 

76 

76 

76       76        76 

rja        Min- 
'^        utes 

Merid- 
ian 

1' 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7°        8° 

9° 

TAO        Alti- 

^^        tudes 

Latitude  53°  Decimation  Contfary  Name. 

Declinations.  —  Inferior  Meridian. 


321 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/  '/ 

1        n 

1      II 

/      II 

/  // 

/  // 

/  // 

1     II 

1     II 

/  // 

/  // 

/  // 

Min. 

4 

0  13 

0  12 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

0  11 

4 

8 

0  52 

0  51 

0  50 

0  49 

0  48 

0  48 

0  46 

0  46 

0  45 

0  44 

0  44 

0  42 

8 

12 

156 

154 

153 

150 

148 

147 

1  44 

142 

141 

139 

136 

1  35 

12 

16 

3  28 

3  22 

3  19 

3  14 

3  12 

3  09 

3  04 

3  02 

2  59 

2  57 

2  52 

2  49 

16 

20 

5  24 

5  16 

5  12 

5  04 

5  00 

4  56 

4  48 

4  44 

4  40 

4  46 

4  28 

4  24 

20 

24 

7  47 

7  35 

7  29 

7  18 

7  12 

7  06 

6  55 

6  49 

6  43 

6  38 

6  26 

6  21 

24 

28 

10  35 

10  20 

10  12 

9  56 

9  48 

9  40 

9  25 

9  17 

9  09 

9  01 

8  45 

8  37 

28 

32 

13  49 

13  29 

13  19 

12  58 

12  48 

12  38 

12  17 

12  07 

1157 

1146 

11  26 

11  15 

32 

36 

17  30 

17  04 

16  51 

16  25 

16  12 

15  59 

15  33 

15  20 

15  07 

14  55 

14  29 

14  16 

36 

40 

21  36 

21  04 

20  48 

20  16 

20  00 

19  44 

19  12 

18  56 

18  40 

18  24 

17  52 

17  36 

40 

44 

26  08 

25  29 

25  10 

24  31 

24  12 

23  52 

23  14 

22  54 

22  35 

22  16 

2138 

21  18 

44 

48 

31  06 

30  18 

29  55 

29  09 

28  46 

28  23 

27  37 

27  14 

26  51 

26  29 

25  43 

25  20 

48 

52 

36  30 

35  36 

35  09 

34  15 

33  48 

33  21 

32  27 

32  00 

3133 

3105 

30  11 

29  44 

52 

56 

42  20 

41  17 

40  46 

39  44 

39  12 

38  40 

37  38 

37  06 

36  35 

36  04 

35  02 

34  30 

56 

60 

48  36 

47  24 

46  48 

45  36 

45  00 

44  24 

43  12 

42  36 

42  00 

41  24 

40  12 

39  36 

60 

n 

It 

n 

It 

It 

It 

It 

It 

" 

" 

It 

It 

Ajh 

0.81 

0.79 

0.78 

0.76 

0.75 

0.74 

0.72 

0.71 

0.70 

0.69 

0.67 

0.66 

Ajh 

Log. 

9.908 

9.897 

9.892 

9.880 

9.875 

9.869 

9.857 

9.851 

9.845 

9.838 

9.826 

9.819 

Log. 

49 

63 

09 

81 

06 

23 

33 

26 

10 

85 

07 

54 

Limit 

76 

76 

76 

76 

76 

76 

76 

76 

76 

76 

76 

76 

Min- 
utes 

Merid- 
ian 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

Alti- 
tudes 

Declinations 

.  — Inferior  Meridian 

• 

Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/   // 

/  // 

/  // 

/  // 

1     II 

/  /' 

/  // 

1      II 

/  II 

/  // 

/  // 

/  // 

Min. 

4 

Oil 

Oil 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

4 

8 

0  41 

0  41 

0  40 

0  38 

0  37 

0  37 

0  36 

0  35 

0  33 

0  32 

0  31 

0  30 

8 

12 

1  32 

1  30 

1  27 

125 

124 

121 

1  19 

1  18 

1  15 

1  12 

1  09 

107 

12 

16 

2  44 

2  42 

2  37 

2  31 

2  28 

2  23 

2  21 

2  18 

2  13 

2  08 

2  03 

157 

16 

20 

4  16 

4  12 

4  04 

3  56 

3  52 

3  44 

3  40 

3  36 

3  28 

3  20 

3  12 

3  04 

20 

24 

6  09 

6  03 

5  52 

5  40 

5  32 

5  23 

5  17 

5  11 

5  00 

4  48 

4  36 

4  25 

24 

28 

8  21 

8  14 

7  58 

7  43 

7  35 

7  19 

7  11 

7  03 

6  48 

6  32 

6  16 

6  01 

28 

32 

10  55 

10  45 

10  24 

10  04 

9  54 

9  33 

9  23 

9  13 

8  52 

8  32 

8  12 

7  51 

32 

36 

13  50 

13  37 

13  11 

12  45 

12  32 

12  06 

11  23 

1140 

11  14 

10  48 

10  22 

9  56 

36 

40 

17  04 

16  48 

16  16 

15  44 

15  28 

14  56 

14  40 

14  24 

13  52 

13  20 

12  48 

12  16 

40 

44 

20  39 

20  20 

19  41 

19  02 

18  43 

18  04 

17  45 

17  25 

16  47 

16  08 

15  29 

14  51 

44 

48 

24  34 

24  11 

23  25 

22  39 

22  16 

21  30 

21  07 

20  44 

19  58 

19  12 

18  26 

17  40 

48 

52 

28  50 

28  23 

27  29 

26  35 

26  08 

25  14 

24  47 

24  20 

23  26 

22  32 

21  38 

20  44 

52 

56 

33  27 

32  56 

31  53 

30  50 

30  19 

29  16 

28  45 

28  13 

27  11 

26  08 

25  05 

24  02 

56 

60 

38  24 

37  48 

36  36 

35  24 

34  48 

33  36 

33  00 

32  24 

31  12 

30  00 

28  48 

27  36 

60 

n 

It 

It 

It 

It 

It 

n 

It 

It 

It 

It 

It 

Ajh 

0.64 

0.63 

0.61 

0.59 

0.58 

0.56 

0.55 

0.54 

0.52 

0.50 

0.48 

0.46 

A,h 

9.806 

9.799 

9.785 

9.770 

9.763 

9.748 

9.740 

9.732 

9.716 

9.698 

9.681 

9.662 

Log. 

Log. 

18 

34 

33 

85 

43 

19 

36 

39 

00 

97 

24 

76 

Limit 

76 

76 

76 

76 

76 

76 

77 

78 

79 

80 

81 

81 

Min- 
utes 

Merid- 
ian 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

Alti- 
tudes 

322 


Latitude  54°  Declination  Same  Name. 

Declinations. 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Anglos 

/   '/ 

/  /' 

Min. 

Min. 

4 

0  22 

0  22 

0  23 

0  23 

0  24 

0  24 

0  25 

0  25 

0  25 

0  26 

0  27 

0  27 

4 

8 

1  32 

133 

134 

1  35 

1  36 

1  37 

139 

1  41 

142 

1  42 

145 

146 

8 

12 

3  24 

3  28 

3  31 

3  34 

3  36 

3  39 

3  42 

3  46 

3  49 

3  51 

3  56 

3  59 

12 

16 

6  06 

6  08 

6  13 

6  18 

6  24 

6  29 

6  34 

6  42 

6  47 

6  53 

7  00 

7  05 

16 

20 

9  32 

9  36 

9  44 

9  52 

10  00 

10  08 

10  16 

10  28 

10  36 

10  44 

10  56 

1104 

20 

24 

13  43 

13  49 

14  01 

14  12 

14  24 

14  36 

14  47 

15  04 

15  16 

15  28 

15  45 

15  57 

24 

28 

18  42 

18  49 

19  05 

19  21 

19  36 

19  52 

20  07 

20  31 

20  47 

21  02 

21  25 

21  41 

28 

32 

24  25 

24  35 

24  55 

25  16 

25  36 

25  56 

26  17 

26  48 

27  08 

27  28 

27  59 

28  19 

32 

36 

30  53 

3106 

31  32 

3158 

32  24 

32  50 

33  16 

33  55 

34  21 

34  47 

35  26 

35  52 

36 

40 

38  08 

38  24 

38  56 

39  28 

40  00 

40  32 

41  04 

4152 

42  24 

42  56 

43  44 

44  16 

40 

44 

46  08 

46  27 

47  06 

47  45 

48  24 

49  03 

49  41 

50  40 

51  18 

5157 

52  55 

53  34 

44 

48 

54  55 

55  18 

56  04 

56  50 

57  36 

58  22 

59  08 

60  17 

6103 

61  49 

62  58 

63  44 

48 

52 

64  27 

64  54 

65  48 

66  42 

67  36 

68  30 

69  24 

70  45 

71  39 

72  33 

73  54 

74  48 

52 

56 

74  44 

75  15 

76  18 

77  21 

78  24 

79  27 

80  29 

82  04 

83  06 

84  09 

85  43 

86  46 

56 

60 

85  48 

86  24 

87  36 

88  48 

90  00 

91  12 

92  24 

94  12 

95  24 

96  36 

98  24 

99  36 

60 

n 

It 

" 

n 

n 

n 

n 

n 

K 

n 

H 

n 

A,h 

1.43 

1.44 

1.46 

1.48 

1.50 

1.52 

1.54 

1.57 

1.59 

1.61 

1.64 

1.66 

Ajh 

Log. 

0.155 

0.158 

0.164 

0.170 

0.176 

0.181 

0.187 

0.195 

0.201 

0.206 

0.214 

0.220 

Log. 

34 

36 

35 

26 

09 

84 

52 

90 

40 

83 

84 

11 

Limit 

56 

56 

55 

54 

54 

54 

53 

52 

52 

51 

51 

50 

Min- 
utes 

Merid- 
ian 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
CO 

A,h 

0  27 

1  48 
4  03 
7  13 

11  16 
16  14 
22  05 
28  50 
36  31 
45  04 
54  32 
64  53 
76  09 
88  20 
101  24 

1.69 

/  II 

0  27 

150 

4  06 

7  18 

11  24 

16  25 

22  21 

29  11 

36  56 

45  36 

55  10 

65  38 

77  04 

89  22 

102  36 
It 

1.71 

/   // 

0  28 

152 

4  11 

7  25 

11  36 

16  42 

22  44 

29  42 

37  35 

46  24 

56  08 

66  47 

78  25 

90  56 

104  24 
It 

1.74 

/  // 

0  28 

154 

4  16 

7  33 

1148 

16  59 

23  08 

30  13 

38  14 

47  12 

57  07 

67  56 

79  46 

92  31 

106  12 
It 

1.77 

/  // 

0  29 

1  55 
4  19 
7  41 

12  00 
17  17 
23  31 
30  43 
38  53 
48  00 
58  05 
69  07 
81  07 
94  05 
108  00 

1.80 

0  29 

1  57 
4  23 
7  49 

12  12 
17  34 
23  55 
31  13 
39  32 
48  48 
59  03 
70  16 
82  28 
95  39 
109  48 

n 

1.83 

/  // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

3155 

40  24 

49  52 

60  21 

71  48 

84  16 

97  45 

112  12 

" 
1.87 

/  // 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

4102 

50  40 

61  18 

72  58 

85  38 

99  18 

114  00 
It 

1.90 

/   // 

0  31 

2  04 

4  40 

8  16 

12  56 

18  37 

25  21 

33  07 

4154 

51  44 

62  35 

74  30 

87  26 

10123 

It 
1.94 

/  // 

0  31 

2  06 

4  46 

8  26 

13  12 

19  00 

25  53 

33  48 

42  46 

52  48 

63  53 

76  02 

89  14 

103  29 

n 

1.98 

/  // 

0  32 

2  09 

4  51 

8  37 

13  28 

19  24 

26  24 

34  28 

43  38 

53  52 

65  11 

77  34 

91  02 

105  35 

2.02 

/  // 

0  33 

2  12 

4  57 

8  47 

13  44 

19  47 

26  55 

35  09 

44  30 

54  56 

66  28 

79  06 

92  50 

106  06 

n 

2.06 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.227 
89 

0.233 
00 

0.240 
55 

0.247 
97 

0.255 
27 

0.262 
45 

0.271 
84 

0.278 
75 

0.287 
80 

0.296 
67 

0.305 
35 

0.313 

87 

Log. 

Limit 

49 

49 

48 

48 

47 

46 

46 

45 

45 

44 

43 

42 

Min- 
utes 

Merid- 
ian 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Alti- 
tudes 

Latitude  54"  Declination  Same  Name. 


323 


Declinatioxs. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      1 

/           H 

/     // 

/     // 

/      // 

1     II 

/     // 

/      // 

1     II 

/      // 

/     // 

Min. 

4 

0  34 

0  34 

0  35 

0  36 

0  38 

0  39 

0  40 

0  40 

0  43 

0  43 

0  45 

0  47 

4 

8 

2  14 

2  18 

2  22 

2  26 

2  28 

2  33 

2  37 

2  42 

2  48 

2  53 

2  59 

3  06 

8 

12 

5  05 

5  10 

5  18 

5  27 

5  35 

5  45 

5  54 

6  06 

6  17 

6  30 

6  43 

6  59 

12 

16 

8  59 

9  12 

9  26 

9  41 

9  52 

10  11 

10  30 

10  48 

11  07 

11  32 

1156 

12  22 

16 

20 

14  04 

14  23 

14  44 

15  08 

15  28 

15  56 

16  24 

16  52 

17  24 

18  00 

18  39 

19  20 

20 

24 

20  15 

20  45 

21  13 

21  48 

22  16 

22  56 

23  38 

24  17 

25  04 

25  56 

26  53 

27  50 

24 

28 

27  33 

28  13 

28  53 

29  40 

30  18 

31  14 

32  08 

33  04 

34  07 

35  16 

36  35 

37  54 

28 

32 

36  01 

36  51 

37  43 

38  44 

39  36 

40  48 

44  58 

43  11 

44  32 

46  05 

47  47 

49  30 

32 

36 

45  35 

46  40 

47  44 

49  02 

50  07 

51  37 

53  09 

54  39 

56  23 

58  19 

60  29 

62  38 

36 

40 

56  16 

57  36 

58  56 

60  32 

6152 

63  44 

65  36 

67  28 

69  36 

72  00 

74  40 

77  20 

40 

44 

68  05 

69  42 

71  18 

73  15 

74  52 

77  07 

79  22 

8138 

44 

48 

8101 

82  56 

84  52 

48 

52 

52 

56 

56 

60 

60 

It 

* 

If 

» 

H 

H 

It 

It 

It 

It 

» 

It 

Aih 

2.11 

2.16 

2.21 

2.27 

2.32 

2.39 

2.46 

2.53 

2.61 

2.70 

2.80 

2.90 

A]h 

Log. 

0.324 

0.334 

0.344 

0.356 

0.365 

0.378 

0.390 

0.403 

0.416 

0.431 

0.447 

0.462 

Log. 

28 

45 

39 

03 

49 

40 

94 

12 

64 

36 

16 

40 

Limit 

41 

40 

39 

38 

37 

37 

36 

35 

34 

33 

32 

32 

Min- 
utes 

Merid- 
ian 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

'   36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Anglea 

Min. 

/     // 

/      // 

/       n 

/          H 

/     // 

/        ir 

t     II 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  48 

0  50 

0  53 

0  56 

0  58 

102 

106 

1  10 

1  17 

1  24 

1  32 

143 

4 

8 

3  14 

3  22 

3  31 

3  42 

3  54 

4  07 

4  23 

4  43 

5  06 

5  34 

6  08 

6  53 

8 

12 

7  15 

7  34 

7  55 

8  19 

8  46 

9  17 

9  53 

10  36 

1128 

12  32 

13  50 

15  31 

12 

16 

12  54 

13  27 

14  04 

14  48 

15  35 

16  31 

17  35 

18  51 

20  22 

22  16 

24  34 

27  34 

16 

20 

20  09 

2100 

21  59 

23  07 

24  20 

25  47 

27  28 

29  27 

3152 

35  48 

38  24 

43  04 

20 

24 

29  00 

30  14 

31  39 

33  18 

35  03 

37  09 

39  34 

42  26 

45  53 

50  07 

55  18 

24 

28 

39  28 

4108 

43  07 

45  21 

47  41 

50  34 

53  50 

57  46 

28 

32 

51  31 

53  45 

56  19 

59  14 

62  17 

66  03 

32 

36 

65  14 

68  03 

71  17 

36 

40 

. . . 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

n 

It 

It 

It 

" 

n 

It 

" 

II 

It 

It 

Ajh 

3.02 

3.15 

3.30 

3.47 

3.65 

3.87 

4.12 

4.42 

4.78 

5.22 

5.76 

6.46 

Ajh 

Log. 

0.480 

0.498 

0.518 

0.540 

0.562 

0.587 

0.614 

0.645 

0.679 

0.717 

0.760 

0.810 

Log. 

01 

31 

51 

33 

29 

71 

90 

42 

43 

67 

42 

23 

Limit 

31 

30 

29 

28 

27 

26 

24 

23 

21 

20 

19 

18 

Min- 
utes 

Merid- 
ian 

72° 

73° 

740 

75° 

76° 

77° 

78° 

79° 

80° 

8P 

82° 

83° 

Alti- 
tudes 

324 


Latitude  54°  Decimation  Same  Name. 

Declinations. 


Hour 
Aiifjlcs 

48" 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Mln. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

1 
7 

17 
31 
49 

It 
7.3 

/f 

58 
52 
44 
32 
16 

9 

1         H 

2  20 

9  16 

20  51 

37  05 

H 

8.69 

1 

/r 

ff 

f 

If 

/ 

n 

/ 

n 

1 

n 

n 

1 

H 

1 

1 

H 

1 

H 

1 

/r 

1  49 

7  16 

16  22 

29  06 

It 
6.82 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.868 
64 

0.939 
02 

0.833 

78 

Log. 

Limit 

16 

13 

10 

8 

6 

3 

0 

3 

5 

8 

11 

14 

Min- 
utes 

Merid- 
ian 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/      // 

/     /' 

/      // 

/      // 

/     /' 

/     // 

/     // 

/      // 

Min. 

Min. 

4 

1  28 

1  14 

102 

0  53 

0  47 

0  41 

0  36 

0  32 

0  28 

0  26 

0  23 

0  20 

4 

8 

5  53 

4  54 

4  09 

3  34 

3  06 

2  44 

2  25 

2  08 

155 

142 

132 

121 

8 

12 

13  15 

11  01 

9  19 

8  00 

6  59 

6  09 

5  26 

4  48 

4  18 

3  50 

3  24 

3  02 

12 

16 

23  33 

19  35 

16  35 

14  18 

12  25 

10  55 

9  38 

8  32 

7  38 

6  50 

6  06 

5  22 

16 

20 

36  48 

30  36 

25  56 

22  20 

19  24 

17  04 

15  04 

13  20 

1156 

10  40 

9  32 

8  24 

20 

24 

44  04 

37  21 

32  10 

27  56 

24  35 

21  42 

19  12 

17  11 

15  22 

13  43 

12  06 

24 

28 

43  46 

38  02 

33  27 

29  32 

26  08 

23  24 

20  54 

18  42 

16  28 

28 

32 

43  41 

38  34 

34  08 

30  33 

27  18 

24  25 

21  30 

32 

36 

48  49 

43  12 

38  40 

34  34 

30  53 

27  13 

36 

40 

53  20 

47  44 

42  40 

38  08 

33  36 

40 

44 

57  45 

5138 

46  08 

40  39 

44 

48 

6126 

54  55 

48  23 

48 

52 

56  47 

52 

56 

56 

60 

60 

It 

It 

It 

It 

It 

* 

It 

It 

It 

It 

It 

" 

A,h 

5.52 

4.59 

3.89 

3.35 

2.91 

2.56 

2.26 

2.00 

1.79 

1.60 

1.43 

1.26 

A,li 

Log. 

0.741 

0.661 

0.589 

0.525 

0.463 

0.408 

0.354 

0.301 

0.252 

0.204 

0.155 

0.100 

Log. 

94 

81 

95 

04 

89 

24 

11 

03 

85 

12 

34 

37 

Limit 

16 

19 

21 

23 

25 

28 

31 

33 

36 

39 

41 

43 

Min- 
utes 

Merid- 
ian 

84 

0 

83° 

82 

o 

81° 

80 

o 

79 

o 

78° 

77° 

76° 

75° 

74° 

73° 

Alti- 
tu.l.-s 

Latitude  54°  Declination  Contrary  Name. 

Declinations. 


S2l 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
X  ngles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/   // 

0  22 

1  32 
3  24 
6  06 
9  32 

13  43 

18  42 

24  25 

30  53 

38  08 

46  08 

54  55 

64  27 

74  44 

85  48 
It 

1.43 

/  II 

0  22 

130 

3  23 

6  01 

9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 

1.41 

0  22 

129 

3  20 

5  56 

9  16 

13  21 

18  10 

23  43 

30  02 

37  04 

44  51 

53  22 

62  38 

72  39 

83  24 

n 

1.39 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 
17  54 
23  23 
29  36 
36  32 
44  13 
52  36 
61  44 
71  37 
82  12 

n 

1.37 

/  // 

0  22 
127 
3  16 

5  48 
9  04 
13  04 
17  46 
23  12 
29  23 
36  16 
43  53 
52  13 
61  17 
7105 
8136 

n 

1.36 

/  // 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

5127 

60  23 

70  02 

80  24 
It 

1.34 

/  // 

0  21 

1  25 
3  11 
5  41 
8  52 

12  46 
17  23 
22  42 
28  44 
35  28 
42  55 
5104 
59  56 
69  31 
79  48 

n 

1.33 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 

n 

1.31 

/  // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

4137 

49  32 

58  08 

67  25 

77  24 
If 

1.29 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 
16  44 
2151 
27  39 
34  08 
41  18 
49  09 
57  41 
66  54 
76  48 

n 

1.28 

/  // 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

21  30 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
It 

1.26 

/  // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 

16  20 

21  20 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
If 

1.25 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.155 
34 

0.149 
22 

0.143 
01 

0.136 

72 

0.133 
54 

0.127 
10 

0.123 
85 

0.117 

27 

0.110 
59 

0.107 
21 

0.100 
37 

0.096 
91 

Log. 

Limit 

56 

56 

57 

58 

59 

60 

60 

61 

62 

63 

63 

63 

Min- 
utes 

Merid- 
ian 

36° 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  20 

1  20 

2  59 
5  17 
8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
It 

1.24 

/   // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

If 

1.22 

/  // 

0  19 
117 

2  54 

5  10 

8  04 

11  37 

15  49 

20  39 

26  08 

32  16 

39  02 

46  28 

54  32 

63  14 

72  36 
It 

1.21 

/  // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
7124 

n 

1.19 

I  II 

0  19 

1  15 

2  50 
5  02 
7  52 

II  20 

15  25 

20  08 

25  30 

3128 

38  05 

45  18 

53  10 

61  41 

70  48 
It 

1.18 

1        n 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  45 

52  43 

61  10 

70  12 
It 

1.17 

/  // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

5149 

60  07 

69  00 
It 

1.15 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
It 

1.14 

/  // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
It 

1.13 

/  // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
It 

1.12 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
It 

1.10 

/  // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 

65  24 

It 

1.09 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.093 
42 

0.086 
36 

0.082 
79 

0.075 
55 

0.071 
88 

0.068 
19 

0.060 
70 

0.056 
90 

0.053 
08 

0.049 
22 

0.041 
39 

0.037 
43 

Log. 

Limit 

64 

65 

66 

66 

66 

66 

67 

68 

69 

69 

71 

72 

Min- 
utes 

Merid- 
ian 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

Alti- 
tudes 

326 


Latitude  54°  Decimation  Contrary  Name. 

Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  II 

0  17 

1  09 

2  35 
4  36 
7  12 

10  22 
14  07 
18  26 
23  20 
28  48 
34  51 
4128 
48  40 
56  27 
64  48 

H 

1.08 

/  n 

0  17 

1  08 

2  33 
4  31 
7  04 

10  11 
13  51 
18  05 
22  54 
28  16 
34  12 
40  42 
47  46 
55  24 
63  36 

n 

1.06 

/  It 

0  17 

^07 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

n 

1.04 

0.17 

<C05 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 

n 

1.03 

/  // 

0  16 

^  105 

2  27 

4  22 

6  50 

9  50 

13  23 

17  30 

22  07 

27  20 

33  04 

39  22 

46  12 

53  34 

61  30 

n 

1.02 

/  It 

0  16 

1  05 

2  26 
4  20 
6  48 
9  48 

13  18 
17  24 
22  00 
27  12 
32  55 
39  10 
45  58 
53  19 
61  12 

1.01 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
It 

1.00 

/  // 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  33 

26  24 

31  56 

38  01 

44  37 

51  44 

59  24 
It 

0.99 

0  15 

1  02 

2  22 
4  10 
6  32 
9  24 

12  49 
16  44 
21  10 
26  08 
31  37 
37  38 
44  10 
51  13 

58  48 

It 

0.98 

/ 

It 

1 

1 

n 

r 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.033 
42 

0.025 
31 

0.017 
03 

0.012 
84 

0.008 
60 

0.004 
32 

0.00 

9.995 
64 

9.991 
23 

Log. 

Limit 

73 

74 

75 

76 

77 

78 

79 

80 

81 

Min- 
utes 

Merid- 
ian 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40°   41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

t 

f 

II 

It 

1 

// 

1 

II 
It 

/  // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

It 

0.89 

/  // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
II 

0.88 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

5136 
II 

0.86 

t     II 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
II 

0.85 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
II 

0.84 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 
II 

0.83 

/  // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26'08 

31  06 

36  30 

42  20 

48  36 
II 

0.81 

/   // 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
41  49 
48  00 

n 

0.80 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.949 
39 

9.944 
48 

9.934 
50 

9.929 
42 

9.924 
28 

9.919 
08 

9.908 
49 

9.903 
09 

Log. 

Limit 

79 

79 

79 

79 

79 

79 

79 

7Q   Min- 
'**   utes 

Merid- 
ian 

0° 

1° 

2° 

3° 

4°  1  5° 

6° 

7° 

8° 

9° 

10° 

i-io   Alti- 
•'•■'•    tudes 

Latitude  54°  Declination  Contrary  Name. 
Declinations.  —  Inferior  Meridian. 


327 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/     // 

/      // 

/       n 

/      " 

/      // 

/       n 

/     /' 

t       n 

/     // 

/     // 

/     // 

'     II 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

0  12 

Oil 

■Oil 

Oil 

0  11 

Oil 

Oil 

Oil 

4 

8 

0  51 

0  50 

0  49 

0  48 

0  48 

0  46 

0  46 

0  44 

0  44 

0  42 

0  42 

0  41 

8 

12 

154 

153 

150 

148 

147 

144 

142 

139 

1  38 

136 

135 

1  32 

12 

16 

3  22 

3  19 

3  14 

3  12 

3  09 

3  04 

3  02 

2  57 

2  54 

2  52 

2  49 

2  44 

16 

20 

5  16 

5  12 

5  04 

5  00 

4  56 

4  48 

4  44 

4  36 

4  32 

4  28 

4  24 

4  16 

20 

24 

7  35 

7  29 

7  18 

7  12 

7  06 

6  55 

6  49 

6  38 

6  32 

6  26 

6  21 

6  09 

24 

28 

10  20 

10  12 

9  56 

9  48 

9  40 

9  25 

9  17 

9  01 

8  53 

8  45 

8  37 

8  21 

28 

32 

13  29 

13  19 

12  58 

12  48 

12  38 

12  17 

12  07 

1146 

1136 

11  26 

11  15 

10  55 

32 

36 

17  04 

16  51 

16  25 

16  12 

15  59 

15  33 

15  20 

14  55 

14  42 

14  29 

14  16 

13  50 

36 

40 

2104 

20  48 

20  16 

20  00 

19  44 

19  12 

18  56 

18  24 

18  08 

17  52 

17  36 

17  04 

40 

44 

25  29 

25  10 

24  31 

24  12 

23  52 

23  14 

22  54 

22  16 

21  57 

2138 

21  18 

20  39 

44 

48 

30  18 

29  55 

29  09 

28  46 

28  23 

27  37 

27  14 

26  29 

26  08 

25  43 

25  20 

24  34 

48 

52 

35  36 

35  09 

34  15 

33  48 

33  21 

32  27 

32  00 

31  05 

30  38 

30  11 

29  44 

28  50 

52 

56 

41  17 

40  46 

39  44 

39  12 

38  40 

37  38 

37  06 

36  04 

35  33 

35  02 

34  30 

33  27 

56 

60 

47  24 

46  48 

45  36 

45  00 

44  24 

43  12 

42  36 

41  24 

n 

40  48 

40  12 

39  36 
It 

38  24 

n 

60 

A,h 

0.79 

0.78 

0.76 

0.75 

0.74 

0.72 

0.71 

0.69 

0.68 

0.67 

0.66 

0.64 

A,h 

Log. 

9.897 

9.892 

9.880 

9.875 

9.869 

9.857 

9.851 

9.838 

9.832 

9.826 

9.819 

9.806 

Log. 

63 
79 

09 

81 

06 

23 

33 

26 

85 

51 

07 

54 

18 

Limit 

79 

79 

79 

79 

79 

79 

79 

79 

79 

79 

79 

Min- 
utes 

Merid- 
ian 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1     II 

/     // 

1     II 

/      // 

1     II 

/      II 

1     II 

/     // 

1     II 

/      // 

/     // 

/      // 

Min. 

4 

Oil 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

0  07 

4 

8 

0  41 

0  39 

0  38 

0  38 

0  37 

0  36 

0  35 

0  35 

0  32 

0  32 

0  31 

0  29 

8 

12 

1  30 

1  29 

1  26 

1  24 

122 

1  19 

1  18 

1  16 

1  13 

1  11 

1  08 

1  05 

12 

16 

2  42 

2  39 

2  34 

2  28 

2  26 

2  21 

2  18 

2  16 

2  11 

2  05 

2  00 

1  55 

16 

20 

4  12 

4  08 

4  00 

3  52 

3  48 

3  40 

3  36 

3  32 

3  24 

3  16 

3  03 

3  00 

20 

24 

6  03 

5  58 

5  46 

5  32 

5  28 

5  17 

5  11 

5  05 

4  54 

4  42 

4  30 

4  19 

24 

28 

8  14 

8  06 

7  50 

7  35 

7  27 

7  11 

7  03 

6  56 

6  40 

6  25 

6  09 

5  53 

28 

32 

10  45 

10  34 

10  14 

9  54 

9  44 

9  23 

9  13 

9  03 

8  42 

8  22 

8  02 

7  41 

32 

36 

13  37 

13  24 

12  58 

12  32 

12  19 

1153 

1140 

11  27 

11  01 

10  35 

10  09 

9  43 

36 

40 

16  48 

16  32 

16  00 

15  28 

15  12 

14  40 

14  24 

14  08 

13  36 

13  04 

12  32 

12  00 

40 

44 

20  20 

20  01 

19  22 

18  43 

18  24 

17  45 

17  25 

17  06 

16  27 

15  48 

15  10 

14  31 

44 

48 

24  11 

23  48 

23  02 

22  16 

21  53 

2107 

20  44 

20  21 

19  35 

18  49 

18  03 

17  17 

48 

52 

28  23 

27  56 

27  02 

26  08 

25  41 

24  47 

24  20 

23  53 

22  59 

22  05 

21  11 

20  17 

52 

56 

35  26 

32  25 

31  22 

30  19 

29  48 

28  45 

28  13 

27  42 

26  39 

25  36 

24  34 

23  31 

56 

60 

37  48 

37  12 

36  00 

34  48 

34  12 

33  00 

32  24 

3148 

30  36 

29  24 

28  12 

27  00 

60 

n 

If 

n 

II 

n 

" 

It 

It 

It 

It 

n 

It 

Ajh 

0.63 

0.62 

0.60 

0.58 

0.57 

0.55 

0.54 

0.53 

0.51 

0.49 

0.47 

0.45 

Ajh 

Log. 

9.799 

9.792 

9.778 

9.763 

9.755 

9.740 

9.732 

9.724 

9.707 

9.690 

9.672 

9.653 

Log. 

34 

39 

15 

43 

87 

36 

39 

28 

57 

20 

10 

21 

Limit 

79 

79 

79 

79 

79 

79 

79 

79 

79 

80 

81 

81 

Min- 
utes 

Merid- 
ian 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Alti- 
tudes 

328 


Latitude  55"  Declination  Same  Name. 


DlCCLIXATIONf^ 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/   '/ 

/  // 

/  " 

1       n 

/  // 

/  // 

/  // 

/   n 

/  // 

/  // 

/  * 

/  // 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  23 

0  23 

0  23 

0  24 

0  24 

0  25 

0  25 

0  25 

4 

8 

1  28 

1  29 

1  30 

1  32 

1  33 

1  34 

1  35 

1  36 

1  37 

139 

141 

1  42 

8 

12 

3  17 

3  20 

3  23 

3  24 

3  29 

3  31 

3  34 

3  36 

3  39 

3  43 

3  46 

3  49 

12 

16 

5  51 

5  56 

6  01 

6  06 

6  11 

6  13 

6  18 

6  24 

6  29 

6  37 

6  42 

6  47 

16 

20 

9  08 

9  16 

9  24 

9  32 

9  40 

9  44 

9  52 

10  00 

10  08 

10  20 

10  28 

10  36 

20 

24 

13  09 

13  21 

13  32 

13  43 

13  55 

14  01 

14  12 

14  24 

14  36 

14  53 

15  04 

15  16 

24 

28 

17  54 

18  10 

18  26 

18  42 

18  57 

19  05 

19  21 

19  36 

19  52 

20  15 

20  31 

20  47 

28 

32 

23  23 

23  43 

24  04 

24  25 

24  45 

24  55 

25  16 

25  36 

25  56 

26  27 

26  48 

27  08 

32 

36 

29  36 

30  02 

30  27 

30  53 

31  19 

31  32 

31  58 

32  24 

32  50 

33  29 

33  55 

34  21 

36 

40 

36  32 

37  04 

37  36 

38  08 

38  40 

38  56 

39  28 

40  00 

40  32 

41  20 

41  52 

42  24 

40 

44 

44  13 

44  51 

45  29 

46  08 

46  47 

47  06 

47  45 

48  24 

49  03 

50  01 

50  40 

51  18 

44 

48 

52  36 

53  22 

54  09 

54  55 

55  41 

56  04 

56  50 

57  36 

58  22 

59  31 

60  17 

61  03 

48 

52 

61  44 

62  38 

63  33 

64  27 

65  21 

65  48 

66  42 

67  36 

68  30 

69  51 

70  45 

71  39 

52 

56 

71  37 

72  39 

73  41 

74  44 

75  37 

76  18 

77  21 

78  24 

79  27 

81  01 

82  04 

83  06 

56 

60 

82  12 

83  24 

84  36 

85  48 

87  00 

87  36 

88  48 

90  00 

91  12 

93  00 

94  12 

95  24 

60 

It 

It 

ft 

It 

It 

It 

It 

It 

It 

It 

" 

It 

A,h 

1.37 

1.39 

1.41 

1.43 

1.45 

1.46 

1.48 

1.50 
0.176 

1.52 

1.55 

1.57 

1.59 

A,h 

Log. 

0.136 

0.143 

0.149 

0.155 

0.161 

0.164 

0.170 

0.181 

0.190 

0.195 

0.201 

Log. 

72 

01 

22 

34 
56 

37 

35 

26 

09 

84 

33 

90 

40 

Limit 

58 

58 

57 

56 

55 

55 

54 

53 

52 

52 

51 

Min- 
utes 

Merid- 
ian 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/   // 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 
It 

1.62 

0.209 

52 

1     " 

0  27 

145 

3  56 

7  00 

10  56 

15  45 

21  25 

27  59 

35  26 

43  44 

52  55 

62  58 

73  54 

85  43 

98  24 
It 

1.64 

I  II 

0  27 
147 
4  00 
7  08 

II  08 
16  02 
21  49 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 
87  18 

100  12 

It 

1.67 

/  // 

0  27 

1  48 
4  03 
7  13 

11  16 
16  14 
22  05 
28  50 
36  31 
45  04 
54  32 
64  53 
76  09 
88  20 

101  24 

It 

1.69 

/  // 

0  27 

1  50 
4  08 
7  20 

11  28 
16  31 
22  29 
29  21 
37  09 
45  52 
55  30 
66  01 
77  31 
89  54 

103  12 

It 

1.72 

/  // 

0  28 

1  52 
4  12 
7  28 

11  40 
16  48 
22  52 
29  52 
37  48 
46  40 
56  28 
67  10 
78  52 
91  28 

105  00 

It 

1.75 

1     II 

0  28 

154 

4  17 

7  35 

1152 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

80  13 

93  02 

106  48 
It 

1.78 

/  // 

0  29 

156 

4  20 

7  44 

12  04 

17  23 

23  39 

30  53 

39  06 

48  16 

58  24 

69  30 

8134 

94  36 

108  36 
It 

1.81 

1     II 

0  30 

1  58 
4  26 
7  54 

12  20 

17  46 

24  10 

31  34 

39  58 

49  20 

59  42 

7102 

83  22 

96  42 

11100 
It 

1.85 

/   // 

0  30 

2  00 

4  31 

8  01 

12  32 

18  03 

24  34 

32  05 

40  37 

50  08 

60  40 

72  11 

84  43 

98  15 

112  48 
It 

1.88 

/     It 

0  30 

2  02 

4  37 

8  11 

12  48 

18  26 

25  06 

32  46 

41  28 

51  12 

61  57 

73  44 

86  32 

100  21 

It 
1.92 

/  // 

0  31 

2  05 

4  43 

8  21 

13  04 

18  49 

25  37 

33  27 

42  20 

52  16 

63  14 

75  16 

88  20 

102  26 

1.96 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.214 
84 

0.222 

72 

0.227 
89 

0.235 
53 

0.243 
04 

0.250 

42 

0.257 

68 

0.267 
17 

0.274 
16 

0.283 
30 

0.292 
26 

Log. 

Limit 

50 

50 

49 

49 

48 

47 

47 

46 

46 

45 

44 

43 

Jlin- 
utes 

Merid- 
ian 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

Alti- 
tudes 

Latitude  55°  Decimation  Same  Name 


329 


Declinations. 


Hour 
Angles 

24°   1    25° 

26° 

27° 

28° 

29° 

30° 

31°  1    32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  32 

2  08 

4  48 

8  32 

13  20 

19  12 

26  08 

34  08 

43  12 

53  20 

64  32 

76  48 

90  08 

It 
2.00 

/        n 

0  32 

2  10 

4  53 

8  39 

13  32 

19  29 

26  31 

34  39 

43  51 

54  08 

65  30 

77  57 

9129 

It 
2.03 

/       n 

0  33 

2  14 

5  01 

8  55 

13  56 

20  04 

27  19 

35  40 

45  09 

55  44 

67  26 

80  15 

H 

2.09 

/     II 

0  34 

2  17 
5  08 
9  08 
14  16 
20  33 
27  57 
36  31 
46  14 
57  04 
69  03 
82  10 

* 
2.14 

1     II 

0  35 

2  20 
5  15 
9  21 

14  36 
21  02 
28  37 
37  22 
47  19 
58  24 
70  40 
84  05 

It 
2.19 

/      /' 

0  36 

2  25 
5  24 
9  36 
15  00 
21  36 
29  24 
38  24 
48  36 
60  00 
72  36 

2.25 

/      // 

0  37 

2  28 

5  32 

9  52 

15  24 

22  11 

30  11 

39  25 

49  54 

61  36 

74  32 

It 
2.31 

0  38 
2  32 
5  41 
10  07 
15  48 
22  46 
30  58 
40  26 
51  12 
63  12 
76  39 

It 
2.37 

/      II 

0  39 
2  36 
5  51 
10  24 
16  15 
23  24 
3151 
4139 
52  42 
65  04 

2.44 

0  40 
2  41 
6  03 
10  45 
16  48 
24  11 
32  56 
42  59 
54  26 
67  12 

It 
2.52 

I  II 

0  42 

2  47 
6  15 

II  06 
17  20 
24  58 
33  58 
44  22 
56  10 
69  20 

It 
2.60 

/       n 

0  43 
2  53 
6  29 
11  31 
18  00 
25  55 
35  17 
46  05 
58  19 
72  00 

It 
2.70 

Min. 
4 

8 
12 
16 
20 
24 
28. 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.301 
03 

0.307 
50 

0.320 
15 

0.330 
41 

0.340 
44 

0.352 
18 

0.363 
61 

0.374 
75 

0.387 
39 

0.401 
40 

0.414 
97 

0.431 
36 

Log. 

Limit 

42 

42 

41 

40 

39 

38 

37 

37 

36 

35 

34 

33 

Min- 
utes 

Merid- 
ian 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67'' 

68 

0 

69° 

70 

o 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/     // 

/     " 

/     II 

/      // 

/      '/ 

/     // 

/     // 

/     // 

/     // 

/     // 

/     It 

Min. 

4 

0  45 

0  47 

0  49 

0  51 

0  53 

0  56 

0  59 

103 

108 

1  14 

120 

128 

4 

8 

2  58 

3  06 

3  14 

3  24 

3  33 

3  45 

3  58 

4  14 

4  32 

4  54 

5  20 

5  53 

8 

12 

6  42 

6  59 

7  17 

7  39 

8  00 

8  25 

•8  56 

9  30 

10  12 

1101 

12  00 

13  15 

12 

16 

1154 

12  25 

12  58 

13  36 

14  13 

14  58 

15  52 

16  54 

18  08 

19  35 

21  20 

23  33 

16 

20 

18  35 

19  24 

20  15 

21  12 

22  12 

23  23 

24  48 

26  24 

28  20 

30  35 

33  20 

36  48 

20 

24 

26  45 

27  56 

29  09 

30  32 

3158 

33  42 

35  43 

38  00 

40  47 

44  04 

48  00 

53  00 

24 

28 

36  28 

38  02 

39  43 

41  34 

43  30 

45  52 

48  37 

5145 

55  32 

28 

32 

47  37 

49  40 

5153 

54  16 

56  50 

59  54 

63  29 

32 

36 

60  16 

62  51 

65  40 

68  42 

36 

40 

74  24 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

It 

It 

It 

It 

It 

H 

It 

It 

It 

It 

/f 

Ajh 

2.79 

2.91 

3.04 

3.18 

3.33 

3.51 

3.72 

3.96 

4.25 

4.59 

5.00 

5.52 

Ajh 

Log. 

0.445 

0.463 

0.482 

0.502 

0.522 

0.545 

0.570 

0.597 

0.628 

0.661 

0.698 

0.741 

Log, 

60 

89 

87 

43 

44 

31 

54 

70 

39 

81 

97 

94 

Limit 

32 

31 

30 

29 

28 

27 

25 

24 

23 

22 

22 

21 

Min- 
utes 

Merid- 
ian 

71° 

72° 

73° 

74° 

75 

o 

76° 

77 

0 

78 

0 

79° 

80 

o 

81° 

82 

o 

Alti- 
tudes 

330 


Latitude  55°  Declination  Same  Name. 
Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/      // 

/     // 

t       II 

/      // 

/      // 

/      // 

1     II 

/      // 

/      // 

/           // 

/     // 

/     '/ 

Min. 

4 

1  32 

1  54 

2  13 

4 

8 

6  33 

7  32 

8  52 

8 

12 

14  50    17  00 

19  57 

12 

16 

26  22    30  10 

35  28 

16 

20 

41  12 

47  08 

20 

24 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

ti 

It 

n 

* 

» 

If 

n 

H 

n 

f 

r 

» 

Ajh 

6.18 

7.07 

8.31 

A,h 

Log. 

0.790 
99 

0.849 
42 

0.863 
92 

Log. 

Limit 

18 

16 

13 

11 

9 

7 

3 

0 

3 

7 

9 

11 

Min- 
utes 

Merid- 
ian 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

Alti- 
tudes 

Declinatioxs. 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

r       n 

/     // 

/      // 

/      // 

/      // 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

143 

124 

109 

0  58 

0  50 

0  44 

0  38 

0  34 

0  30 

0  27 

0  23 

0  21 

4 

8 

6  53 

5  36 

4  38 

3  56 

3  22 

2  55 

2  33 

2  15 

2  00 

1  47 

136 

1  23 

8 

12 

15  31 

12  36 

10  24 

8  48 

7  35 

6  35 

5  46 

5  06 

4  31 

4  00 

3  35 

3  08 

12 

16 

27  34 

22  23 

18  30 

15  41 

13  29 

11  42 

10  15 

9  02 

8  01 

7  08 

6  21 

5  36 

16 

20 

35  00 

28  56 

24  29 

2103 

18  16 

16  01 

14  08 

12  32 

11  08 

9  56 

8  44 

20 

24 

35  14 

30  21 

26  19 

23  03 

20  21 

18  03 

16  02 

14  18 

12  35 

24 

28 

31  22 

27  41 

24  34 

21  49 

19  29 

17  07 

28 

32 

36  11 

32  05 

28  30 

25  26 

22  21 

32 

36 

40  37 

36  05 

32  11 

28  18 

36 

40 

44  32 

39  44 

34  56 

40 

44 

53  54 

48  04 

42  16 

44 

48 

57  13 

50  18 

48 

52 

59  02 

52 

56 

56 

60 

60 

IT 

n 

II 

» 

n 

* 

H 

H 

n 

H 

H 

H 

A,h 

6.46 

5.25 

4.34 

3.67 

3.16 

2.74 

2.40 

2.12 

1.88 

1.67 

1.49 

1.31 

A,h 

Log. 

0.810 

0.720 

0.637 

0.564 

0.499 

0.437 

0.380 

0.326 

0.274 

0.222 

0.173 

0.117 

Log. 

23 

16 

49 

67 

69 

75 

21 

34 

16 

72 

19 

27 

Limit 

13 

16 

18 

20 

21 

22 

25 

28 

32 

36 

40 

44 

Min- 
utes 

Merid- 
ian 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

74° 

Alti- 
tudes 

Latitude  55°  Declination  Contrary  Name. 


331 


Declinations. 


Hour 
Angles 

0°    1° 

2° 

3°   4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
It 

1.37 

/  // 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

8136 

It 

1.36 

t      II 

0  22 

126 

3  13 

5  43 

8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

5127 

60  23 

70  02 

80  24 

It 

1.34 

/  // 

0  21 

125 

3  11 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 

It 

1.33 

1     II 

0  21 

1  23 

3  08 
5  36 
8  44 
12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

1.31 

0  21 
123 
3  07 
5  33 

8  40 

12  29 

16  59 

22  11 

28  05 

34  40 

41  57 

49  55 

58  35 

67  57 

78  00 
It 

1.30 

/  n 

0  20 

122 

3  05 

5  27 

8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
It 

1.28 

/  // 

'  0  20 

121 

3  03 

j  5  25 

8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 

It 

1.27 

/  II 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 

16  20 

2120 

27  00 

33  20 

40  20 

48  00 

56  20 

65  20 

75  00 
It 

1.25 

/  // 

0  20 

1  20 

2  59 
5  17 
8  16 

11  54 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 
It 

1.24 

/  // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
64  59 
63  46 
73  12 

n 

1.22 

/  // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

It 

1.21 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.136 
72 

0.133 
54 

0.127 
10 

0.123 
85 

0.117 
27 

0.113 
94 

61 

0.107 
21 

0.103 
80 

0.096 
91 

0.093 
42 

0.086 
36 

0.082 
79 

Log. 

Limit 

58 

58 

59 

60 

61 

61 

62 

62 

63 

64 

64 

Min- 
utes 

Merid- 
ian 

35° 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/   // 

0  19 

1  17 

2  53 
5  07 
8  00 

11  31 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

n 

1.20 

I  II 

0  19 

1  15 

2  50 
5  02 
7  52 

II  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 
70  48 

1.18 

/  // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 

15  17 

19  58 

25  17 

31  12 

37  46 

44  55 

52  43 

61  10 

70  12 
It 

1.17 

I  II 

0  19 

1  14 

2  47 

4  57 
7  44 

II  09 

15  09 

19  47 

25  04 

30  56 

37  26 

44  32 

52  16 

60  38 

69  36 
II 

1.16 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 
14  53 
19  27 
24  38 
30  24 
36  47 
43  46 
51  22 
59  35 
68  24 

n 

1.14 

1     II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
It 

1.13 

1      II 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  38 
58  33 
67  12 

1.12 

1      II 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

It 

1.11 

1      II 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

It 

1.10 

/  // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 

1.08 

1     It 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 

It 

1.07 

0  17 

1  08 

2  33 
4  31 
7  04 

10  11 
13  51 
18  05 
22  54 
28  16 
34  12 
40  42 
47  46 
55  24 

63  36 

It 

1.06 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.079 
18 

0.071 

88 

0.068 
19 

0.064 
46 

0.056 
90 

0.053 
08 

0.049 
22 

0.045 
32 

0.041 
39 

0.033 
42 

0.029 
38 

0.025 
31 

Log. 

Limit 

65 

65 

66 

67 

67 

67 

68 

69 

70 

70 

71 

72 

Min- 
utes 

Merid- 
ian 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

Alti- 
tudes 

332 


Latitude  55°  Decimation  Contrary  Name. 


Declinations. 


y 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 

y  12 

'^    16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

017 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

n 

1.05 

0  17 

105 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 

n 

1.03 

0  16 
105 
2  26 

Tlir 

6  48 
9  48 
13  20 
17  24 
22  00 
27  12 
32  55 
39  10 
45  58 
53  19 

61  12 

It 

1.02 

0  16 

105 

2  25 

»   4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

n 

1.01 

/     // 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

It 

1.00 

'      "< 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

51  44 

59  24 

n 

0.99 

/      // 

0  15 

103 

2  21 

4  11 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 

ir 

0.98 

/ 

1 

/ 

/ 

n 

II 

/ 

r 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
56 

A,h 

Log. 

0.021 
19 

0.012 
84 

0.008 
60 

0.004 
32 

0.00 

9.995 
64 

9.991 
23 

\ 

Log. 

Limit 

73 

74 

75 

76 

77 

78 

80 

Min- 
uteg 

Merid- 
ian 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4 

t° 

° 

2= 

Y 

C 

1° 

Alti- 
tudes 

Declinations,  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1 

n 

// 

/ 

H 

// 

1 

It 

// 

It 

// 

/      // 

0  14 
0  56 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

n 

0.87 

/      // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 

14  30 

18  22 

22  40 

27  26 

32  38 

38  18 

44  26 

5100 
It 

0.85 

/      // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 

14  20 

18  09 

22  24 

27  06 

32  15 

37  51 

43  54 

50  24 
It 

0.84 

/     // 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 
It 

0.83 

/      // 

0  13 

0  52 

1  58 
3  30 
5  28 
7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

3129 

36  57 

42  52 

49  12 
It 

0.82 

/     // 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

3106 

36  30 

42  20 

48  36 
It 

0.81 

/      // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 

0.79 

/     // 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
It 

0.78 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.939 
52 

9.929 
42 

9.924 
28 

9.919 
08 

9.913 
81 

9.908 
49 

9.897 
63 

9.892 
09 

Log. 

Limit 

80 

79 

78 

77 

76 

75 

74 

73 

Min- 
utes 

Merid- 
ian 

1° 

2« 

3« 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

IP 

12° 

Alti- 
tudes 

Latitude  55°  Declination  Contfary  Name* 

Declinations.  —  Inferior  Meridian. 


333 


Hour 

Angles 

48= 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Auglea 

r       n 

/  // 

/   // 

1     II 

/   // 

Min. 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

0  11 

0  11 

4 

8 

0  50 

0  48 

0  48 

0  47 

0  46 

0  46 

0  44 

0  44 

0  43 

0  42 

0  41 

0  40 

8 

12 

1  51 

148 

147 

1  45 

144 

1  42 

1  39 

1  38 

1  36 

1  35 

1  33 

130 

12 

16 

3  17 

3  12 

3  09 

3  07 

3  04 

3  02 

2  57 

2  54 

2  52 

2  49 

2  47 

2  42 

16 

20 

5  08 

5  00 

4  56 

4  52 

4  48 

4  44 

4  36 

4  32 

4  28 

4  24 

4  20 

4  12 

20 

24 

7  23 

7  12 

7  06 

7  00 

6  55 

6  49 

6  38 

6  32 

6  26 

6  21 

6  15 

6  03 

24 

28 

10  04 

9  48 

9  40 

9  33 

9  25 

9  17 

9  01 

8  53 

8  45 

8  37 

8  29 

8  14 

28 

32 

13  09 

12  48 

12  38 

12  28 

12  17 

12  07 

1146 

1136 

11  26 

11  15 

11  05 

10  45 

32 

36 

16  38 

16  12 

15  59 

15  46 

15  33 

15  20 

14  55 

14  42 

14  29 

14  16 

14  03 

13  37 

36 

40 

20  32 

20  00 

19  44 

19  28 

19  12 

18  56 

18  24 

18  08 

17  52 

17  36 

17  20 

16  48 

40 

44 

24  51 

24  12 

23  52 

23  33 

23  14 

22  54 

22  16 

21  57 

2138 

21  18 

20  59 

20  20 

44 

48 

29  32 

28  46 

28  23 

28  00 

27  37 

27  14 

26  29 

26  06 

25  43 

25  20 

24  57 

24  11 

48 

52 

34  42 

33  48 

33  21 

32  54 

32  27 

32  00 

31  05 

30  38 

30  11 

29  44 

29  17 

28  23 

52 

56 

40  15 

39  12 

38  40 

38  09 

37  38 

37  06 

36  04 

35  33 

35  02 

34  30 

33  59 

32  56 

56 

60 

46  12 

45  00 

44  24 

43  48 

43  12 

42  36 

4124 

40  48 

40  12 

39  36 

39  00 

37  48 

60 

* 

// 

ir 

H 

H 

It 

n 

It 

It 

It 

It 

It 

Ajh 

0.77 

0.75 

0.74 

0.73 

0.72 

0.71 

0.69 

0.68 

0.67 

0.66 

0.65 

0.63 

A,h 

Log. 

9.886 

9.875 

9.869 

9.863 

9.857 

9.851 

9.838 

9.832 

9.826 

9.819 

9.812 

9.799 

Log. 

49 

06 

23 

32 

33 

26 

85 

51 

07 

54 

91 

34 

Limit 

80 

80 

80 

80 

80 

80 

80 

80 

80 

80 

80 

80 

Min- 
utes 

Merid- 
ian 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

Alti- 
tudes 

Declinations.  — ^  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

1       II 

/  // 

/  // 

1     II 

/  // 

/  // 

/  // 

/  // 

/  // 

/  1/ 

/  // 

/  // 

Min. 

4 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  08 

0  07 

0  07 

4 

8 

0  39 

0  39 

0  38 

0  37 

0  37 

0  35 

0  35 

0  33 

0  32 

0  31 

0  30 

0  29 

8 

12 

129 

1  27 

125 

122 

121 

1  18 

1  16 

1  15 

1  12 

1  09 

107 

104 

12 

16 

2  39 

2  37 

2  31 

2  26 

2  23 

2  18 

2  16 

2  13 

2  08 

2  03 

157 

152 

16 

20 

4  08 

4  04 

3  56 

3  48 

3  44 

3  36 

3  32 

3  28 

3  20 

3  12 

3  04 

2  56 

20 

24 

5  58 

5  52 

5  40 

5  28 

5  23 

5  11 

5  05 

5  00 

4  48 

4  36 

4  25 

4  13 

24 

28 

8  06 

7  58 

7  43 

7  27 

7  19 

7  03 

6  56 

6  48 

6  32 

6  16 

6  01 

5  45 

28 

32 

10  34 

10  24 

10  04 

9  44 

9  33 

9  13 

9  03 

8  52 

8  32 

8  12 

7  51 

7  31 

32 

36 

13  24 

13  11 

12  45 

12  19 

12  06 

1140 

1127 

11  14 

10  48 

10  22 

9  56 

9  30 

36 

40 

16  32 

16  16 

15  44 

15  12 

14  56 

14  24 

14  08 

13  52 

13  20 

12  48 

12  16 

1148 

40 

44 

20  01 

19  41 

19  02 

18  24 

18  04 

17  25 

17  06 

16  47 

16  08 

15  29 

14  50 

14  11 

44 

48 

23  48 

23  25 

22  39 

2153 

2130 

20  44 

20  21 

19  58 

19  12 

18  26 

17  40 

16  54 

48 

52 

27  56 

27  29 

26  35 

25  41 

25  14 

24  20 

23  53 

23  26 

22  32 

21  38 

20  46 

19  50 

52 

56 

32  25 

31  53 

30  50 

29  48 

29  16 

28  13 

27  42 

27  11 

26  08 

25  05 

24  04 

22  59 

56 

60 

37  12 

36  36 

35  24 

34  12 

33  16 

32  24 

3148 

31  12 

30  00 

28  48 

27  36 

26  24 

60 

H 

" 

It 

" 

It 

It 

It 

It 

It 

It 

It 

It 

Aih 

0.62 

0.61 

0.59 

0.57 

0.56 

0.54 

0.53 

0.52 

0.50 

0.48 

0.46 

0.44 

A,h 

Log. 

9.792 

9.785 

9.770 

9.755 

9.748 

9.732 

9.724 

9.716 

9.698 

9.681 

9.662 

9.643 

Log. 

39 

33 

85 

87 

19 

39 

28 

00 

97 

24 

76 

45 

Limit 

80 

80 

80 

80 

80 

80 

80 

80 

80 

80 

80 

81 

Min- 
utes 

Merid- 
ian 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

Alti- 
tudes 

334 


Latitude  56°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

Min. 

/       // 

/     // 

/      " 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     It 

/     // 

Min. 

4 

0  21 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  23 

0  23 

0  24 

0  24 

4 

8 

124 

126 

127 

128 

129 

1  30 

132 

1  33 

134 

135 

136 

137 

8 

12 

3  10 

3  13 

3  16 

3  17 

3  20 

3  23 

3  24 

3  28 

3  31 

3  34 

3  36 

3  39 

12 

16 

5  38 

5  43 

5  48 

5  51 

5  56 

6  01 

6  06 

6  08 

6  13 

6  18 

6  24 

6  29 

16 

20 

8  48 

8  56 

9  04 

9  08 

9  16 

9  24 

9  32 

9  36 

9  44 

9  52 

10  00 

10  08 

20 

24 

12  41 

12  52 

13  04 

13  09 

13  21 

13  32 

13  43 

13  49 

14  01 

14  12 

14  24 

14  36 

24 

28 

17  15 

17  30 

17  46 

17  54 

18  10 

18  26 

18  42 

18  49 

19  05 

19  21 

19  36 

19  52 

28 

32 

22  31 

22  52 

23  12 

23  23 

23  43 

24  04 

24  25 

24  35 

24  55 

25  16 

25  36 

25  56 

32 

36 

28  31 

28  57 

29  23 

29  36 

30  02 

30  27 

30  53 

31  06 

31  32 

3158 

32  24 

32  50 

36 

40 

35  12 

35  44 

36  16 

36  32 

37  04 

37  36 

38  08 

38  24 

38  56 

39  28 

40  00 

40  32 

40 

44 

42  36 

43  14 

43  53 

44  13 

44  51 

45  29 

46  08 

46  27 

47  06 

47  45 

48  24 

49  03 

44 

48 

50  41 

5127 

52  13 

52  36 

53  22 

54  09 

54  55 

55  18 

56  04 

56  50 

57  36 

58  22 

48 

52 

59  29 

60  23 

61  17 

6144 

62  38 

63  33 

64  27 

64  54 

65  48 

66  42 

67  36 

68  30 

52 

56 

69  00 

70  02 

7105 

7137 

72  39 

73  41 

74  44 

75  15 

76  18 

77  21 

78  24 

79  27 

56 

60 

79  12 

80  24 

8136 

82  12 

83  24 

84  36 

85  48 

86  24 

87  36 

88  48 

90  00 

91  12 

60 

" 

It 

n 

It 

It 

It 

K 

It 

It 

* 

It 

n 

A,h 

1.32 

1.34 

1.36 

1.37 

1.39 

1.41 

1.43 

1.44 

1.46 

1.48 

1.50 

1.52 

A,h 

Log. 

0.120 

0.127 

0.133 

0.136 

0.143 

0.149 

0.155 

0.158 

0.164 

0.170 

0.176 

0.181 

Log. 

57 

10 

54 

72 

01 

22 

34 

36 

35 

26 

09 

84 

Limit 

59 

59 

58 

57 

57 

56 

56 

55 

55 

54 

54 

53 

Min- 
utes 

Merid- 
ian 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       II 

0  25 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

8101 

93  00 

It 

1.55 

t     II 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41  52 

50  40 

60  17 

70  45 

82  04 

94  12 
It 

1.57 

1     II 

0  25 

142 

3  49 

6  47 

10  36 

15  16 

20  47 

27  08 

34  21 

42  24 

51  18 

61  03 

7139 

83  06 

95  24 

It 

1.59 

0  26 

143 

3  53 

6  55 

10  48 

15  34 

21  10 

27  38 

35  00 

43  12 

52  17 

62  12 

73  00 

84  41 

97  12 

It 

1.62 

/      // 

0  27 

1  45 
3  56 
7  00 

10  56 
15  45 
2125 
27  59 
35  26 
43  44 
52  55 
62  58 
73  54 
85  43 

98  24 

It 

1.64 

/     // 

0  27 

147 

4  00 

7  08 

1108 

16  02 

21  49 

28  30 

36  05 

44  32 

53  54 

64  07 

75  15 

87  18 

100  12 

It 

1.67 

/     // 

0  27 

149 

4  03 

7  15 

11  20 

16  19 

22  13 

29  01 

36  43 

45  20 

54  51 

65  15 

76  37 

88  51 

102  00 

1.70 

/      // 

0  27 

151 

4  09 

7  23 

11  32 

16  36 

22  37 

29  32 

37  22 

46  08 

55  49 

66  24 

77  58 

90  25 

103  48 
It 

1.73 

I  II 

0  28 
153 
4  14 
7  30 

II  44 
16  54 
23  00 
30  02 
38  01 
46  56 
56  47 
67  33 
79  19 
9159 

105  36 

It 

1.76 

0  28 

155 

4  18 

7  38 

1156 

17  11 

23  24 

30  33 

38  40 

47  44 

57  45 

68  42 

80  40 

93  33 

107  24 

It 

1.79 

1     II 

0  29 

156 

4  22 

7  46 

12  08 

17  29 

23  47 

31  03 

39  19 

48  32 

58  44 

69  53 

82  01 

95  08 

109  12 

It 

1.82 

0  30 

159 

4  28 

7  56 

12  24 

17  52 

24  18 

31  44 

40  11 

49  36 

60  01 

71  25 

83  49 

97  13 

111  36 

It 

1.86 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.190 
33 

0.195 
90 

0.201 
40 

0.209 
52 

0.214 
84 

0.222 
72 

0.230 
45 

0.238 
05 

0.245 
51 

0.252 
85 

0.260 
07 

0.269 
51 

Log. 

Limit 

52 

52 

51 

51 

50 

49 

49 

48 

47 

46 

45 

44 

Min- 
utes 

Merid- 
ian 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

Alti- 
tudes 

Latitude  56°  Declination  Same  Name. 


335 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  30 

2  01 

4  32 

8  04 

12  36 

18  09 

24  42 

32  15 

40  50 

50  24 

60  59 

72  34 

85  10 

1.89 

0  31 

2  03 
4  39 
8  14 
12  52 
18  31 
25  13 
32  57 
41  41 
51  28 
62  16 
74  07 
86  59 

1.93 

/           H 

0  32 

2  06 
4  44 
8  24 
13  08 
18  44 
25  45 
33  38 
42  33 
52  32 
63  34 
75  39 

It 
1.97 

/      // 

0  32 

2  09 

4  51 

8  37 

13  28 

19  23 

25  25 

34  29 

43  38 

53  52 

65  11 

77  34 

n 

2.02 

/     // 

0  33 

2  11 
4  58 
8  46 
13  44 
19  46 
26  55 
35  10 
44  30 
54  56 
66  28 
79  06 

n 

2.06 

/      // 

0  34 

2  15 

5  04 

9  01 

14  04 

20  16 

27  34 

36  00 

45  35 

56  16 

68  05 

8101 

It 
2.11 

/      // 

0  35 

2  18 
5  13 
9  15 
14  28 
20  50 
28  21 
37  02 
46  53 
57  52 
70  02 
83  19 

It 
2.17 

/     // 

0  36 

2  23 

5  21 

9  31 

14  53 

21  25 

29  09 

38  03 

48  10 

59  28 

7157 

It 
2.23 

/      // 

0  37 

2  27 

5  29 

9  47 

15  16 

22  00 

29  55 

39  05 

49  28 

6104 

73  53 

It 
2.29 

/      // 

0  38 
2  32 
5  39 
10  05 
15  44 
22  40 
30  50 
40  16 
50  59 
62  56 
76  09 

It 
2.36 

/      // 

0  39 
2  35 
5  49 
10  23 
16  12 
23  20 
31  45 
41  28 
52  29 
64  48 

It 
2.43 

/      // 

0  40 
2  40 
6  01 

10  44 
16  42 
24  06 
23  48 
42  50 
54  13 
66  56 

It 
2.51 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.276 
46 

0.285 
56 

0.294 
47 

0.305 
35 

0.313 

87 

0.324 

28 

0.336 
46 

0.348 
30 

0.359 

84 

0.372 
91 

0.385 
61 

0.399 
67 

Log. 

Limit 

43 

43 

42 

41 

41 

40 

39 

38 

37 

37 

36 

35 

Min- 
utes 

Merid-     cqo 
ian        50 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/      // 

I          H 

/      II 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

/     // 

/      // 

Min. 

4 

0  42 

0  43 

0  45 

0  47 

0  49 

0  51 

0  54 

0  57 

101 

105 

1  10 

1  17 

4 

8 

2  47 

2  52 

3  00 

3  07 

3  15 

3  25 

3  36 

3  48 

4  04 

4  20 

4  41 

5  06 

8 

12 

6  15 

6  27 

6  44 

7  00 

7  19 

7  41 

8  06 

8  34 

9  08 

9  46 

10  33 

11  29 

12 

16 

11  06 

11  28 

11  58 

12  27 

12  59 

13  40 

14  24 

15  13 

16  14 

17  22 

18  45 

20  25 

16 

20 

17  20 

17  55 

18  41 

19  28 

20  20 

21  21 

22  29 

23  47 

25  21 

27  08 

29  17 

31  56 

20 

24 

24  58 

25  48 

26  54 

28  02 

29  17 

30  44 

32  22 

34  16 

36  30 

39  05 

42  09 

45  59 

24 

28 

33  58 

35  09 

36  36 

38  10 

39  51 

41  49 

44  02 

46  39 

49  39 

53  11 

57  22 

62  34 

28 

32 

44  22 

45  55 

47  47 

49  50 

52  03 

54  37 

57  31 

60  56 

32 

36 

56  10 

58  07 

60  29 

63  04 

65  53 

69  07 

36 

40 

69  20 

7144 

40 

44 

44 

48 

48 

52 

52 

5fe 

56 

60 

60 

It 

It 

It 

It 

It 

It 

It 

It 

It 

» 

It 

It 

Ajh 

2.60 

2.69 

2.80 

2.92 

3.05 

3.20 

3.37 

3.57 

3.80 

4.07 

4.39 

4.79 

A,h 

Log. 

0.414 

0.429 

0.447 

0.465 

0.484 

0.505 

0.527 

0.552 

0.579 

0.609 

0.642 

0.680 

97 

75 

16 

38 

30 

15 

63 

67 

78 

59 

46 

34 

Log. 

Limit 

34 

33 

32 

31 

30 

29 

28 

26 

25 

24 

22 

20 

Min- 
utes 

Merid- 
ian 

70° 

71° 

72° 

73° 

74° 

75° 

76 

°l 

7 

7° 

78 

° 

79 

° 

80 

o 

81 

o 

Alti- 
tudes 

336 


Latitude  56"  Declination  Same  Name 

Declinations. 


Hour 

Aiiylos 


48" 


Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


1  24 
5  37 
12  41 
22  30 
35  12 
50  41 


5.28 


49= 


134 

6  18 

14  12 

25  14 

39  24 


91 


50° 


148 

7  13 

16  12 

28  48 

45  00 


75 


51" 


2  07 

8  27 

18  59 

33  50 


93 


52° 


53° 


54° 


55= 


56° 


57° 


58° 


59° 


Hour 

Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 


Limit 


Merid- 


0.722 
^63 

20 


0.771 
59 


0.829 
30 


0.899 
27 


Log. 


18 


16 


14 


12 


Min- 
utes 


82° 


83° 


84° 


85° 


86° 


87° 


88° 


89° 


90° 


89° 


88° 


87° 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

60° 

61° 

B2° 

B3°      6 

4° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

//    / 

//    / 

It 

/     // 

/     // 

/     // 

/      // 

1     II 

/      // 

/     // 

Min. 

I\Iin. 

4 

137 

1  19 

106     C 

55 

0  47 

0  41 

0  36 

0  31 

0  27 

0  25 

0  22 

4 

8 

6  30 

5  19 

4  22     I 

41 

3  10J 

2  45 

2  25 

2  06 

152 

1  39 

1  26 

8 

12 

14  39    1 

158 

9  49     i 

19 

7  08 

6  10 

5  24 

4  46 

4  12 

3  43 

3  14 

12 

16 

26  05    2 

1  14    1 

12h    U 

45 

12  40 

10  58 

9  36 

8  26 

7  28 

6  37 

5  46 

16 

20 

■3 

3  12    2 

7  16   22 

04 

19  48 

17  08 

15  00 

13  12 

1140 

10  20 

9  00 

20 

24 

J 

9  16   33 

13 

28  30 

24  40 

2136 

19  00 

16  48 

14  53 

12  58 

24 

28 

..       45 

13 

38  49 

33  35 

29  24 

25  53 

22  52 

20  15 

17  38 

28 

32 

43  52 

38  24 

33  48 

29  52 

26  27 

23  02 

32 

36 

48  36 

42  46 

37  48 

33  29 

29  10 

36 

40 

52  48 

46  40 

41  20 

36  00 

40 

44 

56  28 

50  01 

43  34 

44 

48 

59  31 

5150 

48 

52 

60  50 

52 

56 

56 

60 

60 

T 

It 

It 

n 

» 

II 

It 

It 

It 

n 

' 

n 

Ajh 

6.11     ^ 

L98     4 

.09      3. 

46 

2.97 

2.57 

2.25 

1.98 

1.75 

1.55 

1.35 

A,h 

0.786   C 

.697    C 

.611    0. 

539 

0.472 

0.409 

0.352 

0.296 

0.243 

0.190 

0.130 

Log. 

Log. 

04 

23 

72 

08 

76 

93 

18 

67 

04 

33 

33 

Limit 

12 

14 

18 

20        2 

2 

24 

27 

30 

33 

36 

39 

42 

Min- 
utes 

Merid- 
ian 

85° 

85° 

84° 

83°      8 

2° 

81° 

80° 

79° 

78° 

77° 

76° 

75° 

Alti- 
tudes 

Latitude  56°  Declination  Contrary  Namei 

Declinations. 


337 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min, 

/       // 

/     // 

/     // 

/     It 

/     // 

/     // 

/     // 

/      // 

/     // 

/     // 

/     /' 

/     // 

Min. 

4 

0  21 

0  21 

0  20 

0  20 

0  20 

0  20 

0  20 

0  19 

0  19 

0  19 

0  19 

0  19 

4 

8 

124 

123 

123 

1  22 

121 

1  20 

1  20 

1  18 

1  17 

1  17 

1  15 

1  15 

8 

12 

3  10 

3  08 

3  06 

3  05 

3  02 

3  00 

2  59 

2  56 

2  54 

2  53 

2  50 

2  48 

12 

16 

5  38 

5  36 

5  30 

5  27 

5  22 

5  20 

5  17 

5  12 

5  10 

5  07 

5  02 

5  00 

16 

20 

8  48 

8  44 

8  36 

8  32 

8  24 

8  20 

8  16 

8  08 

8  04 

8  00 

7  52 

7  48 

20 

24 

12  41 

12  35 

12  23 

12  17 

12  06 

12  00 

11  54 

11  43 

11  37 

1131 

11  20 

11  14 

24 

28 

17  15 

17  07 

16  52 

16  44 

16  28 

16  20 

16  12 

15  57 

15  49 

15  41 

15  25 

15  17 

28 

32 

22  31 

22  21 

22  01 

2151 

2130 

2120 

21  10 

20  49 

20  39 

20  29 

20  08 

19  58 

32 

36 

28  31 

28  18 

27  52 

27  39 

27  13 

27  00 

26  47 

26  21 

26  08 

25  55 

25  30 

25  17 

36 

40 

35  12 

34  56 

34  24 

34  08 

33  36 

33  20 

33  04 

32  32 

32  16 

32  00 

31  28 

31  12 

40 

44 

42  36 

42  16 

4137 

41  18 

40  39 

40  20 

40  00 

39  22 

39  02 

38  43 

38  05 

37  46 

44 

48 

50  41 

50  18 

49  32 

49  09 

48  23 

48  00 

47  37 

46  51 

46  28 

46  05 

45  18 

44  55 

48 

52 

59  29 

59  02 

58  08 

57  41 

56  47 

56  20 

55  53 

54  59 

54  32 

54  05 

53  10 

52  43 

52 

56 

69  00 

68  28 

67  25 

66  54 

65  51 

65  20 

64  48 

63  46 

63  14 

62  43 

6141 

61  10 

56 

60 

79  12 

78  36 

77  24 

76  48 

75  36 

75  00 

74  24 

73  12 

72  36 

72  00 

70  48 

70  12 

60 

It 

" 

It 

It 

" 

It 

It 

It 

It 

It 

n 

It 

A,h 

1.32 

1.31 

1.29 

1.28 

1.26 

1.25 

1.24 

1.22 

1.21 

1.20 

1.18 

1.17 

Ajh 

Log. 

0.120 

0.117 

0.110 

0.107 

0.100 

0.096 

0.093 

0.086 

0.082 

0.079 

0.071 

0.068 

Log. 

57 

27 

59 

21 

37 

91 

42 

36 

79 

18 

88 

19 

Limit 

59 

59 

60 

61 

62 

62 

62 

63 

64 

65 

65 

65 

Min- 
utes 

Merid- 
ian 

34° 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 
69  36 

n 

1.16 

/     // 

0  19 

1  13 

2  45 
4  55 
7  40 

1103 
15  01 
19  37 
24  51 
30  40 
37  07 
44  09 
5149 
60  07 

69  00 

It 

1.15 

/     // 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 

67  48 

It 

1.13 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

It 

1.12 

/     // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

It 

1.11 

/     // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

It 

1.10 

/     // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

It 

1.09 

/      // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 
It 

1.07 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

It 

1.06 

/     // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 
It 

1.05 

/      // 

0  17 

1  07 

2  30 
4  26 
6  56 
9  59 

13  35 
17  45 
22  28 
27  44 
33  33 
39  56 
46  52 
54  21 

62  24 

It 

1.04 

/      // 

0  16 

1  06 

2  28 
4  24 
6  52 
9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 
It 

1.03 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.064 
46 

0.060 
70 

0.053 
08 

0.049 
22 

0.045 
32 

0.041 
39 

0.037 
43 

0.029 
38 

0.250 
31 

0.021 
19 

0.017 
03 

0.012 
89 

Log. 

Limit 

66 

67 

68 

68 

68 

69 

70 

71 

72 

72 

73 

74 

Min- 
utes 

Merid- 
ian 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

Alti- 
tudes 

338 


Latitude  56°  Declination  Contrary  Name. 


Declinations. 


Hour  1     ntp 
AnglesI    ^* 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  16 

1  05 

2  27 
4  21 
6  48 
9  48 

13  20 
17  24 
22  02 
27  12 
32  55 
39  10 
45  58 
53  19 

61  12 

It 

1.02 

/       n 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

2136 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

n 

1.00 

/     // 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

2123 

26  24 

3156 

38  01 

44  37 

5144 

59  24 

0.99 

/     // 

0  15 
103 

2  21 

411 

6  32 

'    9  24 

12  49 

16  42 

21  08 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 

n 

0.98 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

n 

0.97 

1       n 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

n 

0.96 

1 

// 

// 

// 

/ 

If 

II 

/ 

1 

1 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.008 
60 

0.00 

9.995 
64 

9.991 
23 

9.986 
77 

9.982 
27 

Log. 

Limit 

75 

75 

76 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 
•      8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

// 

It 

// 

/ 

I  II 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

II  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 
5136 

n 

0.86 

/     // 

0  14 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 
50  24 

IT 

0.84 

1      II 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 

n 

0.83 

/     // 

0  13 
0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

It 

0.82 

/     // 

0  13 

0  52 

1  56 
3  28 
5  24 
7  47 

10  35 

13  49 

17  30 

21  36 

26  08 

31  06 

36  30 

42  20 

48  36 
It 

0.81 

/      // 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
41  49 

48  00 

It 

0.80 

/     // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 

n 

0.79 

/     // 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

0.78 

/     // 

0  12 

0  50 

1  51 
3  17 
5  08 
7  23 

10  04 
13  09 
16  38 
20  32 
24  51 
29  32 
34  42 
40  15 
4612 

0.77 

Min. 
4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.934 
50 

9.924 

28 

9.919 
08 

9.913 
81 

9.908 
49 

9.903 
09 

9.897 
63 

9.892 
09 

9.886 
49 

Log. 

Limit 

83 

83 

83 

83 

83 

83 

83 

83 

83 

Min- 
utes 

Merid- 
ian 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

Alti- 
tudes 

Latitude  56°  Decimation  Contrary  Name. 


339 


Declixations.  —  Inferior  Meridian 

Hour 
Angles 

48° 

49° 

50° 

51° 

52°      53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 

Angles 

Min. 

/     // 

/     II 

/      // 

/      II 

/      //    /      // 

/      // 

1     II 

/      // 

/      // 

/      /' 

/      '/ 

Min. 

4 

0  12 

0  12 

0  12 

0  11 

Oil      Oil 

Oil 

Oil 

Oil 

0  11 

0  11 

0  10 

4 

8 

0  48 

0  48 

0  47 

0  46 

0  46     0  45 

0  44 

0  43 

0  42 

0  41 

0  40 

0  39 

8 

12 

148 

147 

145 

144 

1  42      1  41 

139 

1  36 

135 

1  33 

130 

129 

12 

16 

3  12 

3  09 

3  07 

3  04 

3  02 

2  59 

2  57 

2  52 

2  49 

2  47 

2  42 

2  39 

16 

20 

5  00 

4  56 

4  52 

4  48 

4  44 

4  40 

4  36 

4  28 

4  24 

4  20 

4  12 

4  08 

20 

24 

7  12 

7  06 

7  00 

6  55 

6  49 

6  43 

6  38 

6  26 

6  21 

6  15 

6  03 

5  58 

24 

28 

9  48 

9  40 

9  33 

9  25 

9  17 

9  09 

9  01 

8  45 

8  37 

8  29 

8  14 

8  06 

28 

32 

12  48 

12  38 

12  28 

12  17 

12  07 

11  57 

1146 

1126 

11  15 

11  05 

10  45 

10  34 

32 

36 

16  12 

15  59 

15  46 

15  33 

15  20 

15  07 

14  55 

14  29 

14  16 

14  03 

13  37 

13  24 

36 

40 

20  00 

19  44 

19  28 

19  12 

18  56 

18  40 

18  24 

17  52 

17  36 

17  20 

16  48 

16  32 

40 

44 

24  12 

23  52 

23  33 

23  14 

22  54 

22  35 

22  16 

2138 

21  18 

20  59 

20  20 

20  01 

44 

48 

28  46 

28  23 

28  00 

27  37 

27  14 

26  51 

26  29 

25  43 

25  20 

24  57 

24  11 

23  48 

48 

52 

33  48 

33  21 

32  54 

32  27 

32  00 

3133 

3105 

30  11 

29  44 

29  17 

28  33 

27  56 

52 

56 

39  12 

38  40 

38  09 

37  38|  37  06]  36  35 

36  04 

35  02 

34  30 

33  59 

32  56 

32  25 

56 

60 

45  00 

44  24 

43  48 

43  12 

42  36,  42  00 

4124 

40  12 

39  36 

39  00 

37  48 

37  12 

60 

It 

n 

n 

n 

n 

" 

n 

It 

II 

It 

It 

" 

A,h 

0T5 

0.74 

0.73 

0.72 

0.71 

0.70 

0.69 

0.67 

0.66 

0.65 

0.63 

0.62 

Ajh 

Log. 

9.875 

9.859 

9.863 

9.857 

9.851 

9.845 

9.838 

7.826 

9.819 

9.812 

9.799 

9.792 

Log. 

06 

23 

32 

33 

26 

10 

85 

07 

54 

91 

34 

39 

Limit 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

Min- 
utes 

Merid- 
ian 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

Alti- 
tudes 

Declination.? 

.  —  Inferior  Meridian 

• 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

1     II 

/     // 

/   ^// 

Min. 

Min. 

4 

0  10 

0  10 

0  09 

0  09 

0  09 

•    0  09 

0  09 

0  08 

0  08 

0  07 

0  07 

0  07 

4 

8 

0  39 

0  38 

0  38 

0  37 

0  37 

0  36 

0  35 

0  32 

0  31 

0  31 

0  30 

0  29 

8 

12 

1  27 

126 

124 

122 

121 

1  18 

1  16 

1  13 

1  11 

1  08 

107 

104 

12 

16 

2  37 

2  34 

2  28 

2  26 

2  23 

2  18 

2  16 

2  11 

2  05 

2  00 

157 

152 

16 

20 

4  04 

4  00 

3  52 

3  48 

3  44 

3  36 

3  32 

3  24 

3  16 

3  08 

3  04 

2  56 

20 

24 

5  52 

5  46 

5  34 

5  28 

5  23 

5  11 

5  05 

4  54 

4  42 

4  30 

4  25 

4  13 

24 

28 

7  58 

7  50 

7  35 

7  27 

7  19 

7  03 

6  56 

6  40 

6  25 

6  09 

6  01 

5  45 

28 

32 

10  24 

10  14 

9  54 

9  44 

9  33 

9  13 

9  03 

8  42 

8  22 

8  02 

7  51 

7  31 

32 

36 

13  11 

12  58 

12  32 

12  19 

12  06 

11  40 

1127 

11  01 

10  35 

10  09 

9  56 

9  30 

36 

40 

16  16 

16  00 

15  28 

15  12 

14  56 

14  24 

14  08 

13  36 

13  04 

12  32 

12  16 

1144 

40 

44 

19  41 

19  22 

18  43 

18  24 

18  04 

17  25 

17  06 

16  27 

15  48 

15  10 

14  50 

14  11 

44 

48 

23  25 

23  02 

22  16 

"2153 

21  30 

20  44 

20  21 

19  35 

18  49 

18  03 

17  40 

16  54 

48 

52 

27  29 

27  02 

26  08 

25  41 

25  14 

24  20 

23  53 

22  59 

22  05 

21  11 

20  46 

19  50 

52 

56 

3153 

31  22 

30  19 

29  48 

29  16 

28  13 

27  42 

26  39 

25  36 

24  34 

24  02 

22  59 

56 

60 

36  36 

36  00 

34  48 

34  12 

33  36 

32  24 

3148 

30  36 

29  24 

28  12 

27  36 

26  24 

60 

" 

It 

It 

n 

It 

It 

It 

It 

II 

It 

It 

n 

Ajh 

0.61 

0.60 

0.58 

0.57 

0.56 

0.54 

0.53 

0.51 

0.49 

0.47 

0.46 

0.44 

A,h 

Log. 

9.785 

9.778 

9.763 

9.755 

9.748 

9.732 

9.724 

9.707 

9.690 

9.672 

9.662 

9.643 

Log. 

33 

15 

43 

87 

19 

39 

28 

57 

20 

10 

76 

45 

Limit 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

83 

Min- 
utes 

Merid- 
ian 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

Alti- 
tudes 

340 


Latitude  57°  Declination  Same  Name* 


Declinations. 


Honr 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 

16  44 

2151 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
It 

1.28 

/     // 

0  20 

1  23 
3  06 
5  30 
8  36 

12  23 
16  52 
22  01 
27  52 
34  24 
41  37 
49  32 
58  08 
67  25 
77  24 

n 

1.29 

/     // 

0  21 

1  23 
3  07 
5  33 
8  40 

12  29 
16  59 
22  11 
28  05 
34  40 
4157 
49  55 
58  35 
67  57 
78  00 

1.30 

/       n 

0  21 

124 

3  10 

5  38 

8  48 

12  41 

17  15 

22  31 

28  31 

35  12 

42  36 

50  41 

59  29 

69  00 

79  12 

It 

1.32 

/     II 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 

17  30 

22  52 

28  57 

35  44 

43  14 

5127 

60  23 

70  02 

80  24 
It 

1.34 

/     // 

0  22 

1  26 
3  14 
5  46 
9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

51  50 

60  50 

70  34 

8100 
It 

1.35 

/     // 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
It 

1.37 

/     It 

0  22 

1  29 
3  20 
5  56 
9  16 

13  21 

18  10 

23  43 

30  02 

37  04 

44  51 

53  22 

62  38 

72  39 

83  24 
It 

1.39 

/     // 

0  22 

1  30 
3  22 

5  58 

9  20 

13  26 

18  18 

23  54 

30  14 

37  20 

45  10 

53  46 

63  06 

73  10 

84  00 
II 

1.40 

/     II 

0  22 

131 

3  25 

6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 
It 

1.42 

/       n 

0  22 
133 

3  28 

6  08 

9  36 

13  49 

18  49 

24  35 

31  06 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 
It 

1.44 

/     II 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 

1.46 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.107 
21 

0.110 
59 

0.113 
94 

0.120 
57 

0.127 
10 

0.130 
33 

0.136 
72 

0.143 
01 

0.146 
13 

0.152 
29 

0.158 
36 

0.164 
35 

Log. 

Min- 
utes 

Alti- 
tudes 

Limit 

60 

60 

59 

58 

58 

57 

57 

56 

56 

55 

55 

54 

Merid- 
ian 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 
4 

0  23 

0  24 

/      // 
0  24 

/     // 
0  25 

/     // 
0  25 

0  25 

/     // 
0  26 

/     // 
0  27 

/      II 
0  27 

0  27 

0  27 

0  28 

Min. 
4 

8 

1  35 

1  36 

137 

139 

141 

1  42 

143 

145 

147 

149 

151 

1  53 

8 

12 

3  34 

3  36 

3  39 

3  42 

3  46 

3  49 

3  53 

3  56 

4  00     4  05 

4  09 

4  14 

12 

16 

6  18 

6  24 

6  29 

6  34 

6  42 

6  47 

6  55 

7  00 

7  08     7  15 

7  23 

7  30 

16 

20 

9  52 

10  00 

10  08 

10  16 

10  28 

10  36 

10  48 

10  56 

1108 

11  20 

11  32 

11  44 

20 

24 

14  12 

14  24 

14  36 

14  47 

15  04 

15  16 

15  34 

15  45 

16  02 

16  19 

16  36 

16  54 

24 

28 

19  21 

19  36 

19  52 

20  07 

20  31 

20  47 

21  10 

21  25 

2149 

22  13 

22  37 

23  00 

28 

32 

25  16 

25  36 

25  56 

26  17 

26  48 

27  08 

27  38 

27  59 

28  30 

29  01 

29  32 

30  02 

32 

36 

3158 

32  24 

32  50 

33  16 

33  55 

34  21 

35  00 

35  26 

36  05 

36  43    37  22 

38  01 

36 

40 

39  28 

40  00 

40  32 

41  04 

4152 

42  24 

43  12 

43  44 

44  32 

45  20 

46  08 

46  56 

40 

44 

47  45 

48  24 

49  03 

49  41 

50  40 

51  18 

52  17 

52  55 

53  54 

54  51 

55  49 

56  47 

44 

48 

56  50 

57  36:  58  22 

59  08 

60  17 

6103 

62  12 

62  58 

64  07 

65  15    66  24 

67  33 

48 

52 

66  42 

67  36    68  30 

69  24 

70  45 

7139 

73  00 

73  54 

75  15 

76  37,  77  58 

79  19 

52 

56 

77  21 

78  24    79  27 

80  29 

82  04 

83  06 

84  41 

85  43 

87  18 

88  5l'  90  25 

91  59 

56 

60 

88  48 

90  00   91  12 

92  24 

94  12 

95  24 

97  12 

98  24 

100  12 

102  00  103  48 

105  36 

60 

It 

It 

It 

It 

It 

It 

It 

n 

It 

It 

It 

It 

A,h 

1.48 

1.50 

1.52 

1.54 

1.57 

1.59 

1.62 

1.64 

1.67 

1.70 

1.73 

1.76 

A,h 

Log. 

0.170 

0.176 

0.181 

0.187 

0.195 

0.201 

0.209 

0.214 

0.222 

0.230   0.238 

0.245 

Log. 

26 

09 

84 

52 

90 

40 

52 

84 

72 

45 

05 

51 

Limit 

54 

53 

52 

52 

51 

50 

50 

49 

49 

48 

47 

46 

Min- 
utes 

Merid- 
ian 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

Alti- 
tudes 

Latitude  57*  Declination  Same  Name* 


341' 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

oKo       Hour 
•^^       Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

0  28 

1  55 
4  18 
7  38 

11  56 
17  11 
23  24 
30  33 
38  40 
47  44 
57  45 
68  42 
80  40 

1.79 

/      // 

0  28 

1  56 
4  22 
7  46 

12  08 
17  29 
23  47 
31  03 
39  19 
48  32 
58  44 
69  53 
82  01 

It 
1.82 

/      // 

0  30 

2  00 

4  29 

7  59 

12  28 

17  57 

24  26 

31  55 

40  24 

49  52 

60  21 

7148 

84  16 

n 

1.87 

0  30 

2  02 

4  35 

8  09 

12  44 

18  20 

24  58 

32  36 

41  15 

50  56 

6137 

73  21 

86  05 

n 

1.91 

/      II 

0  31 

2  04 
4  41 
8  19 
13  00 
18  43 
25  29 
33  17 
42  07 
52  00 
62  55 
74  53 

n 

1.95 

/      // 

0  31 
2  07 

4  47 
8  29 
13  16 
19  06 
26  01 
33  58 
42  59 
53  04 
64  12 
76  25 

n 

1.99 

/      // 

0  33 

2  11 

4  54 

8  42 

13  36 

19  35 

26  39 

34  49 

44  04 

54  24 

65  49 

78  20 

It 
2.04 

/      // 

0  33 
2  14 
5  01 

8  55 
13  56 
20  04 
27  19 
35  40 
45  09 
55  44 
67  26 
80  15 

It 
2.09 

/      // 

0  35 

2  17 

5  09 

9  11 

14  20 

20  39 

28  05 

36  41 

46  27 

57  20 

69  23 

82  33 

It 
2.15 

/      // 

0  3-5 
2  22 

5  18 
9  26 
14  44 
21  13 
28  53 
37  43 
47  44 
58  56 
71  18 

It 
2.21 

/     // 

0  36 
2  25 

7  27 
9  40 
15  08 
2145 
29  40 
38  45 
49  02 
60  32 
73  15 

It 
2.27 

0  37 
2  30 
5  37 
10  00 
15  36 
22  27 
30  33 
39  56 
50  33 
62  24 
75  30 

It 
2.34 

Min. 

4 

8 
12 
16 
20 
24 
28 
^32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.252 

85 

0.260 
07 

0.271 

84 

0.281 
03 

0.290 
03 

0.298 
85 

0.309 
63 

0.320 
15 

0.332 
44 

0.344 
39 

0.356 
03 

0.369 
22 

Log. 

Limit 

45 

44 

44 

43 

42 

41 

41 

40 

39 

38 

37 

36 

Min- 
utes 

Merid- 
ian 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/       // 

/     // 

/     // 

/      // 

r       II 

/     // 

/      // 

Min. 

Min. 

4 

0  38 

0  41 

0  41 

0  43 

0  45 

0  47 

0  49 

0  51 

0  55 

0  58 

1  02 

107 

4 

8 

2  35 

2  40 

2  45 

2  52 

3  00 

3  08 

3  17 

3  26 

3  38 

3  54 

4  09 

4  30 

8 

12 

5  47 

6  02 

6  12 

6  29 

6  44 

7  01 

7  23 

7  44 

8  12 

8  45 

9  21 

10  05 

12 

16 

10  17 

10  38 

11  02 

1128 

1158 

12  30 

13  06 

13  46 

14  36 

15  32 

16  36 

17  54 

16 

20 

16  04 

16  40 

17  16 

17  55 

18  41 

19  52 

20  28 

21  30 

22  48 

24  16 

25  56 

28  00 

20 

24 

23  08 

24  00 

24  52 

25  48 

26  54 

28  08 

29  28 

30  57 

32  50 

34  57 

37  21 

40  19 

24 

28 

31.30 

32  40 

33  51 

35  09 

36  36 

38  18 

40  07 

42  13 

44  52 

47  33 

50  50 

54  53 

28 

32 

4108 

42  40 

44  12 

45  54 

47  47 

50  01 

52  24 

55  08 

58  22 

62  07 

32 

36 

52  03 

54  00 

55  57 

58  07 

60  29 

63  17 

66  19 

36 

40 

64  16 

66  40 

69  04 

7144 

74  40 

40 

44 

77  45 

44 

48 

48 

52 

52 

56 

56 

60 

60 

H 

n 

It 

It 

It 

It 

It 

n 

K 

It 

It 

It 

A,h 

2.41 

2.50 

2.59 

2.69 

2.80 

2.93 

3.07 

3.23 

3.42 

3.64 

3.89 

4.20 

A,h 

Log. 

0.382 

0.397 

0.413 

0.429 

0.447 

0.466 

0.487 

0.509 

0.534 

0.561 

0.589 

0.623 

Log. 

02 

94 

30 

75 

16 

87 

14 

20 

03 

10 

95 

25 

Limit 

36 

35 

34 

33 

32 

31 

30 

28 

27 

26 

24 

22 

Min- 
utes 

Merid- 
ian 

69° 

70* 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

Alti- 
tudes 

342 


Latitude  57°  Decimation  Same  Name. 

Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56°      £ 

7°      5 

8° 

cQo      Hour 
^^       Angles 

Min. 

/      // 

/      // 

1        n 

/      // 

/      // 

1     II    t 

II 

1     II    1 

//    / 

II    / 

// 

1 

"      Min. 

4 

1  13 

121 

131 

143 

2  00 

4 

8 

4  53 

5  22 

6  01 

6  52 

8  03 

8 

12 

1100 

12  04 

13  32 

15  28 

18  07 

12 

16 

19  30 

21  30 

24  04 

27  28 

32  13 

16 

20 

30  28 

33  36 

37  36 

42  56 

20 

24 

43  52 

48  23 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

n 

* 

K 

It 

H 

n 

" 

# 

n 

» 

Ajh 

4.57 

5.04 

5.64 

6.44 

7.55 

A  ,h 

liOg. 

0.659 
92 

0.702 
43 

0.751 

28 

0.808 
89 

0.877 
95 

Log. 

Limit 

21 

19 

18 

17 

14 

11 

8 

6 

3 

0 

3 

e         Min- 
"         utes 

Merid- 
ian 

81° 

82° 

83° 

84° 

85° 

86° 

J7° 

88° 

59°      g 

0°      8 

9° 

BOO       Alti- 
'*'        tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

•  65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/      // 

/     // 

/     // 

/     // 

1     II 

/      // 

/      // 

/      // 

/     // 

Min. 

Min. 

4 

132 

1  15 

102 

0  52 

0  44 

0  38 

0  34 

0  30 

0  26 

0  22 

4 

8 

6  10 

5  00 

4  07 

3  28 

2  58 

2  35 

2  14 

1  58 

1  44 

131 

8 

12 

13  48 

11  15 

9  15 

7  48 

6  40 

5  47 

5  02 

4  25 

3  54 

3  25 

12 

16 

24  34 

20  00 

16  26 

13  52 

1152 

10  17 

8  58 

7  51 

6  58 

6  03 

16 

20 

38  24 

31  16 

25  40 

21  40 

18  32 

16  04 

14  00 

12  14 

10  52 

9  58 

20 

24 

36  58 

31  12 

26  41 

23  08 

20  10 

17  40 

15  39 

13  38 

24 

28 

42  28 

36  18 

3130 

27  26 

24  02 

21  18 

18  34 

28 

32 

47  27 

4108 

35  50 

31  24 

27  49 

24  14 

32 

36 

52  03 

45  22 

39  45 

35  13 

30  40 

36 

40 

56  00 

49  04 

43  28 

37  52 

40 

44 

59  22 

52  36 

45  49 

44 

48 

62  35 

54  32 

48 

52 

64  00 

52 

56 

56 

60 

60 

n 

1 

n 

n 

n 

H 

It 

It 

It 

It 

IT 

If 

A,h 

5.76 

4.69 

3.85 

3.25 

2.78 

2.41 

2.10 

1.84 

1.63 

1.42 

A]h 

0.760 

0.671 

0.585 

0.511 

0.444 

0.382 

0.322 

0.264 

0.212 

0.152 

Log. 

Log. 

42 

17 

46 

88 

04 

02 

22 

82 

19 

29 

Limit 

9 

12 

15 

18 

20 

22 

25 

28 

31 

34 

37 

40 

Min- 
utes 

Merid- 
ian 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

77° 

76° 

Alti- 
tudes 

Latitude  57°  Declination  Contfary  Name. 


343 


Declinations. 


Hour 

Augles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  20 
122 
3  05 
5  27 

8  32 

12  17 

16  44 

21  51 

27  39 

34  08 

41  18 

49  09 

57  41 

66  54 

76  48 
It 

1.28 

t       n 

0  20 

121 

3  02 

5  22 

8  24 

12  06 

16  28 

2130 

27  13 

33  36 

40  39 

48  23 

56  47 

65  51 

75  36 
It 

1.26 

/      // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
21  20 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 
75  00 

1.25 

/      // 

0  19 

1  19 

2  57 
5  15 
8  12 

1148 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
It 

1.23 

/      // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

It 

1.22 

I  II 

0  19 

1  17 

2  54 
5  10 
8  04 

II  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

If 

1.21 

/     It 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

31  44 

38  24 

45  41 

53  37 

62  12 

7124 
It 

1.19 

/     // 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 

15  25 

20  08 

25  30 

3128 

38  05 

45  18 

53  10 

61  41 

70  48 
It 

1.18 

/      // 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

It 

1.17 

/      // 

0  19 

1  14 

2  47 
4  57 
7  44 

11  09 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

It 

1.16 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
It 

1.14 

/       n 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
It 

1.13 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.107 
21 

0.100 
37 

0.096 
91 

0.089 
91 

0.086 
36 

0.082 
79 

0.075 
55 

0.071 

88 

0.068 
19 

0.064 
46 

0.056 
90 

0.053 
08 

Log. 

Limit 

61 

61 

62 

I  63 

64 

64 

64 

64 

65 

66 

66 

66 

Min- 
utes 

Merid- 
ian 

33° 

32° 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Anglea 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t     II 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
It 

1.12 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 

14  30 

18  56 

25  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 
It 

1.11 

1       n 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 
66  00 

1.10 

1       n 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

4151 

49  07 

56  58 

65  24 
It 

1.09 

1     II 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

41  05 

48  13 

55  56 

64  12 

1.07 

/      // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
It 

1.06 

/      II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

It 

1.05 

/      II 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 
It 

1.04 

0  16 

1  06 

2  28 
4  24 
6  52 
9  53 

13  28 
17  35 
22  15 
27  28 
33  14 
39  33 
46  25 
53  50 
6148 

n 

1.03 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
It 

1.02 

r       II 

0  16 

1  04 

2  25 
4  19 
6  44 
9  42 

13  12 
17  14 
2149 
26  56 
32  35 
38  47 
45  31 
52  47 
60  36 

1.01 

1      II 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
It 

1.00 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

Ajh 

Log. 

0.049 
22 

0.045 
32 

0.041 
39 

0.037 
43 

0.029 
38 

0.025 
31 

0.021 
19 

0.017 
03 

0.012 

84 

0.008 
60 

0.004 
32 

0.00 

Log. 

Limit 

67 

68 

69 

70 

70 

70 

71 

72 

73 

73 

74 

75 

Min- 
utes 

Merid- 
ian 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10" 

Alti- 
tudes 

344 


Latitude  57"  Declination  Ojntrary  Name 


Declinations. 


Hour 
Angles 

24° 

25°      26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

5144 

59  24 

H 

0.99 

/       n 

0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 
16  34 
20  57 
25  52 
31  18 
37  15 
43  43 
50  42 
58  12 

n 

0.97 

/       n 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 
It 

0.96 

/       v 

0  15 

100 

2  16 

4  03 

6  22 

9  10 

12  29 

16  18 

20  37 

25  28 

30  49 

36  40 

43  02 

49  39 

57  18 

n 

0.955 

0  15 

100 

2  16 

4  02 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

n 

0.95 

/ 

n 

It 

1 

1 

1 

H 

// 

H 

n 

// 

/ 

n 

// 

n 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.995 
64 

9.986 

77 

9.982 
27 

9.980 
00 

9.977 
72 

Log. 

Limit 

76 

77 

77 

78 

79 

Min- 
utes 

Merid- 
ian 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

Alti- 
tudes 

Declinations.  — Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 
4 

/       '/ 

/     // 

/     // 
0  14 

0  14 

/      // 
0  13 

1     1' 
0  13 

1     II 
0  13 

/      // 
0  12 

/      // 
0  12 

0  12 

/      // 
0  12 

0  12 

Min, 
4 

8 

0  54 

0  53 

0  52 

0  52 

0  51 

0  51 

0  50 

0  50 

0  49 

0  48 

8 

12 

2  01 

159 

158 

156 

155 

154 

153 

151 

150 

148 

12 

16 

3  35 

3  33 

3  30 

3  28 

3  25 

3  22 

3  19 

3  17 

3  14 

3  12 

16 

20 

5  36 

5  32 

5  28 

5  24 

5  20 

5  16 

5  12 

5  08 

5  04 

5  00 

20 

24 

8  04 

7  58 

7  53 

7  47 

7  41 

7  35 

7  29 

7  23 

7  18 

7  12 

24 

28 

10  58 

10  51 

10  43 

10  35 

10  27 

10  20 

10  12 

10  04 

9  56 

9  48 

28 

32 

14  20 

14  10 

13  59 

13  49 

13  39 

13  29 

13  19 

13  09 

12  58 

12  48 

32 

36 

18  09 

17  56 

17  43 

17  30 

17  17 

17  04 

16  51 

16  38 

16  25 

16  12 

36 

40 

22  24 

22  08 

21  52 

21  36 

21  20 

2104 

20  48 

20  32 

20  16 

20  00 

40 

44 

27  06 

26  47 

26  28 

26  08 

25  49 

25  29 

25  10 

24  51 

24  31 

24  12 

44 

48 

32  15 

3152 

3129 

3106 

30  43 

30  18 

29  55 

29  32 

29  09 

28  46 

48 

52 

37  51 

37  24 

36  57 

36  30 

36  03 

35  36 

35  09 

34  42 

34  15 

33  48 

52 

56 

43  54 

43  23 

42  52 

42  20 

4149 

41  17 

40  46 

40  15 

39  44 

39  12 

56 

60 

50  24 

49  48 

49  12 

48  36 

48  00 

47  24 

46  48 

46  12 

45  36 

45  00 

60 

n 

H 

n 

n 

It 

n 

n 

n 

If 

n 

n 

n 

A,h 

0.84 

0.83 

0.82 

0.81 

0.80 

0.79 

0.78 

^.11 

0.76 

0.75 

A,h 

9.924 

9.919 

9.913 

9.908 

9.903 

9.897 

9.892 

9.886 

9.880 

9.875 

Log. 

28 

08 

81 

49 

09 

63 

09 

49 

81 

06 

Limit 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

Min- 
utes 

Merid- 
ian 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

Alti- 
tudes 

Latitude  57°  Decimation  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


345 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/   '/ 

/  // 

/  n 

1     II 

/  // 

/  It 

/  // 

/  n 

/  // 

/  '/ 

/  II 

/  II 

Min. 

4 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

0  11 

Oil 

0  10 

0  10 

4 

8 

0  48 

0  47 

0  46 

0  45 

0  45 

0  44 

0  43 

0  42 

0  41 

0  40 

0  39 

0  39 

8 

12 

147 

1  45 

1  44 

142 

141 

139 

136 

1  35 

1  33 

1  30 

1  29 

1  27 

12 

16 

3  09 

3  07 

3  04 

3  02 

2  59 

2  57 

2  52 

2  49 

2  47 

2  42 

2  39 

2  37 

16 

20 

4  56 

4  52 

4  48 

4  44 

4  40 

4  36 

4  28 

4  24 

4  20 

4  12 

4  08 

4  04 

20 

24 

7  06 

7  00 

6  55 

6  49 

6  43 

6  38 

6  26 

6  21 

6  15 

G03 

5  58 

5  52 

24 

28 

9  40 

9  33 

9  25 

9  17 

9  09 

9  01 

8  45 

8  37 

8  29 

8  14 

8  06 

7  58 

28 

32 

12  38 

12  28 

12  17 

12  07 

1157 

1146 

1126 

11  15 

11  05 

10  45 

10  34 

10  24 

32 

36 

15  59 

15  46 

15  33 

15  20 

15  07 

14  55 

14  29 

14  16 

14  03 

13  37 

13  04 

13  11 

36 

40 

19  44 

19  28 

19  12 

18  56 

18  40 

18  24 

17  52 

17  36 

17  20 

16  48 

16  32 

16  16 

40 

44 

23  52 

23  33 

23  14 

22  54 

22  35 

22  16 

2138 

21  18 

20  59 

20  20 

20  01 

19  41 

44 

48 

28  23 

28  00 

27  37 

27  14 

26  51 

26  29 

25  43 

25  20 

24  57 

24  11 

23  48 

23  25 

48 

52 

33  21 

32  54 

32  27 

32  00 

31  33 

3105 

30  11 

29  44 

29  17 

28  23 

27  56 

27  29 

52 

56 

38  40 

38  09 

37  38 

37  06 

36  35 

36  04 

35  02 

34  30 

33  59 

32  56 

32  25 

31  53 

56 

60 

44  24 

43  48 

43  12 

42  36 

42  00 

41  24 

40  12 

39  36 

39  00 

37  48 

37  12 

36  36 

60 

It 

If 

n 

n 

It 

It 

It 

II 

II 

It 

It 

n 

'  A,h 

0.74 

0.73 

0.72 

0.71 

0.70 

0.69 

0.67 

0.66 

0.65 

0.63 

0.62 

0.61 

Ajh 

Log. 

9.869 

9.863 

9.857 

9.851 

9.845 

9.838 

9.826 

9.819 

9.812 

9.799 

9.792 

9.785 

Log. 

23 

32 

33 

26 

10 

85 

07 

54 

91 

34 

39 

33 

Limit 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

Min- 
utes 

Merid- 
ian 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1     II 

0  10 
0  38 
126 
2  34 

4  00 

5  46 
7  50 

10  14 

12  58 

16  00 

19  22 

23  02 

27  02 

31  22 

36  00 
It 

0.60 

0  09 

0  38 

1  25 

2  31 

3  56 
5  40 
7  43 

10  04 

12  45 

15  44 

19  02 

22  39 

26  35 

30  50 

35  24 
It 

0.59 

0  09 
0  37 
122 

2  26 

3  48 
5  28 
7  27 
9  44 

12  09 

15  12 

18  24 

2153 

25  41 

29  48 

34  12 
It 

0.57 

/  // 

0  09 

0  37 

1  21 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
21  30 
25  14 
29  16 

33  36 

It 

0.56 

1     II 

0  09 

0  36 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

1153 
14  40 
17  45 
2107 
24  47 
28  45 

33  00 

It 

0.55 

/  // 

0  09 

0  35 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

11  27 

14  08 

17  06 

20  21 

23  53 

27  42 

31  48 
It 

0.53 

I  II 

0  09 

0  33 

1  15 

2  13 

3  28 

5  00 

6  48 
8  52 

II  14 

13  52 

16  47 

19  58 

23  26 

27  11 

31  12 
It 

0.52 

0  08 

0  32 

1  12 

2  08 

3  20 

4  48 
6  32 
8  32 

10  48 
13  20 
16  08 
19  12 
22  32 
26  08 
30  00 

n 

0.50 

1     II 

0  08 

0  31 

1  09 

2  03 

3  12 

4  36 
6  16 
8  12 

10  22 
12  48 
15  29 
18  26 
21  38 
25  05 
28  48 

0.48 

/  n 

0  07 
0  30 
107 
157 

3  04 

4  25 

6  01 

7  51 
9  56 

12  16 
14  50 
17  40 
20  44 
24  04 

27  36 

It 

0.46 

/  // 

0  07 

0  29 

1  05 
155 

3  00 

4  19 

5  53 
7  41 
9  43 

12  00 
14  31 
17  17 
20  17 
23  31 

27  00 

It 

0.45 

>     II 

0  07 

0  29 

1  04 

1  52 

2  56 

4  13 

5  45 
7  31 
9  30 

1144 

14  11 

16  54 

19  50 

22  59 

26  24 
It 

0.44 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.778 
15 

9.770 
85 

9.755 

87 

9.748 
19 

9.740 
36 

9.724 

28 

9.716 
00 

9.698 
97 

9.681 
24 

9.662 
76 

9.653 

21 

9.643 
45 

Log. 

Limit 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

86 

Min- 
utes 

Merid- 
ian 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

Alti- 
tudes 

346 


Latitude  58°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

I     0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Miu. 

/      II 

/      // 

/      // 

/      '/ 

/       n 

/     // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

Min. 

4 

0  19 

0  20 

0  20 

0  20 

0  20 

0  21 

0  21 

0  21 

0  22 

0  22 

0  22 

0  22 

4 

8 

1  19 

120 

1  20 

121 

122 

123 

123 

125 

126 

127 

1  28 

130 

8 

12 

2  57 

2  59 

3  00 

3  03 

3  05 

3  07 

3  08 

3  11 

3  14 

3  16 

3  19 

3  22 

12 

16 

5  15 

5  17 

5  20 

5  25 

5  27 

5  33 

5  36 

5  41 

5  46 

5  48 

5  53 

5  58 

16 

20 

8  12 

8  16 

8  20 

8  28 

8  32 

8  40 

8  44 

8  52 

9  00 

9  04 

9  12 

9  20 

20 

24 

1148 

1154 

12  00 

12  11 

12  17 

12  29 

12  35 

12  46 

12  58 

13  04 

13  15 

13  26 

24 

28 

16  05 

16  12 

16  20 

16  36 

16  44 

16  59 

17  07 

17  23 

17  38 

17  46 

18  02 

18  18 

28 

32 

2100 

21  10 

21  20 

21  41 

2151 

22  11 

22  21 

22  42 

23  02 

23  12 

23  33 

23  54 

32 

36 

26  34 

26  47 

27  00 

27  26 

27  39 

28  05 

28  18 

28  44 

29  10 

29  23 

29  49 

30  14 

36 

40 

32  48 

33  04 

33  20 

33  52 

34  08 

34  40 

34  56 

35  28 

36  00 

36  16 

36  48 

37  20 

40 

44 

39  41 

40  00 

40  20 

40  59 

41  18 

4157 

42  16 

42  55 

43  34 

43  53 

44  32 

45  10 

44 

48 

47  14 

47  37 

48  00 

48  46 

49  09 

49  55 

50  18 

5104 

51  50 

52  13 

52  59 

53  46 

48 

52 

55  26 

55  53 

56  20 

57  14 

57  41 

58  35 

59  02 

59  56 

60  50   61  17 

62  11 

63  06 

52 

56 

64  17 

64  48 

65  20 

66  23 

66  54 

67  57 

68  28 

69  31 

70  34 

7105 

72  08 

73  10 

56 

60 

73  48 

74  24 

75  00 

76  12 

76  48 

78  00 

78  36 

79  48 

8100 

8136 

82  48 

84  00 

60 

" 

It 

» 

n 

It 

It 

It 

" 

It 

It 

" 

n 

A,h 

1.23 

1.24 

1.25 

1.27 

1.28 

1.30 

1.31 

1.33 

1.35 

1.36 

1.38 

1.40 

A,h 

I<og. 

0.089 

0.093 

0.096 

0.103 

0.107 

0.113 

0.117 

0.123 

0.130 

0.133 

0.139 

0.146 

Log. 

91 

42 

91 

80 

21 

94 

27 

85 

33 

54 

88 

13 

Limit 

62 

62 

61 

60 

59 

59 

58 

57 

57 

56 

56 

55 

Min- 
utes 

Merid- 
ian 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

1      II 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min, 

/      // 

t     II 

/      // 

1     II 

/     // 

/      // 

/      /' 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

0  22 

0  22 

0  23 

0  23 

0  23 

0  24 

0  25 

0  25 

0  25 

0  26 

0  27 

0  27 

4 

8 

130 

132 

133 

134 

136 

137 

1  39 

140 

1  42 

142 

1  45 

147 

8 

12 

3  23 

3  24 

3  29 

3  32 

3  35 

3  39 

3  42 

3  45 

3  49 

3  51 

3  56 

4  00 

12 

16 

6  01 

6  06 

6  11 

6  16 

6  21 

6  29 

6  34 

6  39 

6  47 

6  53 

7  00 

7  08 

16 

20 

9  24 

9  32 

9  40 

9  48 

9  56 

10  08 

10  16 

10  24 

10  36 

10  44 

10  56 

11  08 

20 

24 

13  32 

13  43 

13  55 

14  06 

14  18 

14  36 

14  47 

14  59 

15  16 

15  28 

15  45 

16  02 

24 

28 

18  26 

18  42 

18  57 

19  13 

19  29 

19  52 

20  07 

20  23 

20  47 

2102 

21  25 

2149 

28 

32 

24  04 

24  25 

24  45 

25  06 

25  26 

25  56 

26  17 

26  37 

27  08 

27  28 

27  59 

28  30 

32 

36 

30  27 

30  53 

31  19 

3145 

32  11 

32  50 

33  16 

33  42 

34  21 

34  47 

35  26 

36  05 

36 

40 

37  36 

38  08 

38  40 

39  12 

39  44 

40  32 

4104 

41  36 

42  24 

42  56 

43  44 

44  32 

40 

44 

45  29 

46  08 

46  47 

47  26 

48  04 

49  03 

49  41 

50  20 

51  18 

51  57 

52  55 

53  54 

44 

48 

54  09 

54  55 

55  41 

56  27 

57  13 

58  22 

59  08 

59  54 

6103 

6149 

62  58 

64  07 

48 

52 

63  33 

64  27 

65  21 

66  15 

67  09 

68  30 

69  24 

70  18 

7139 

72  33 

73  54 

75  15 

52 

56 

73  41 

74  44 

75  37 

76  50 

77  52 

79  27 

80  29 

8132 

83  06 

84  09 

85  43 

87  18 

56 

60 

84  36 

85  48 

87  00 

88  12 

89  24 

91  12 

92  24 

93  36 

95  24 

96  36 

98  24 

100  12 

60 

n 

It 

IT 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

1.41 

1.43 

1.45 

1.47 

1.49 

1.52 

1.54 

1.56 

1.59 

1.61 

1.64 

1.67 

A,h 

Log. 

0.149 

0.155 

0.161 

0.167 

0.173 

0.181 

0.187 

0.193 

0.201 

0.206 

0.214 

0.222 

Log. 

22 

34 

37 

32 

19 

84 

52 

12 

40 

83 

84 

72 

Limit 

55 

54 

53 

53 

52 

51 

51 

50 

50 

49 

48 

47 

Min- 
utes 

Merid- 
ian 

44° 

45° 

46° 

47° 

48° 

40° 

50° 

51° 

52° 

53° 

54° 

55° 

Alti- 
tudes 

Latitude  58**  Declination  Same  Name* 

Declinations. 


347 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/   // 

f        n 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

Min. 

4 

0  27 

0  27 

0  28 

0  28 

0  30 

0  30 

0  31 

0  31 

0  32 

0  33 

0  34 

0  35 

4 

8 

1  49 

151 

153 

1  55 

158 

2  00 

2  02 

2  05 

2  09 

2  12 

2  15 

2  19 

8 

12 

4  05 

4  09 

4  14 

4  19 

4  25 

4  31 

4  37 

4  43 

4  49 

4  58 

5  06 

5  14 

12 

16 

7  15 

7  23 

7  30 

7  41 

7  51 

8  01 

8  11 

8  21 

8  35 

8  46 

9  02 

9  18 

16 

20 

11  20 

11  32 

11  44 

12  00 

12  16 

12  32 

12  48 

13  24 

13  24 

13  44 

14  08 

14  32 

20 

24 

16  19 

16  36 

16  54 

17  17 

17  40 

18  03 

18  26 

18  49 

19  18 

19  46 

20  21 

20  56 

24 

28 

22  13 

22  37 

23  00 

23  31 

24  02 

24  34 

25  06 

25  37 

26  16 

26  55 

27  41 

28  29 

28 

32 

29  01 

29  32 

30  03 

30  43 

3124 

32  05 

32  46 

33  27 

34  18 

35  10 

36  10 

37  12 

32 

36 

36  43 

37  22 

38  01 

38  53 

39  45 

40  37 

4128 

42  20 

43  25 

44  30 

45  58 

47  06 

36 

40 

45  20 

46  08 

46  56 

48  00 

49  04 

50  08 

51  12 

52  16 

53  36 

54  56 

56  32 

58  08 

40 

44 

54  51 

55  49 

56  47 

58  05 

59  22 

60  40 

6157 

63  14 

64  51 

66  28 

68  25 

70  21 

44 

48 

65  15 

66  24 

67  33 

69  07 

70  39 

72  11 

73  44 

75  16 

77  11 

79  06 

48 

52 

76  37 

77  58 

79  19 

8107 

82  55 

84  43 

86  32 

52 

56 

88  51 

90  25 

9159 

56 

60 

60 

It 

It 

It 

It 

It 

It 

It 

It 

It 

II 

It 

It 

A,h 

1.70 

1.73 

1.76 

1.80 

1.84 

1.88 

1.92 

1.96 

2.01 

2.06 

2.12 

2.18 

A,h 

Log. 

0.230 

0.238 

0.245 

0.255 

0.264 

0.274 

0.283 

0.292 

0.303 

0.313 

0.326 

0.338 

Log. 

46 

05 

51 

27 

82 

16 

30 

26 

20 

87 

34 

46 

Limit 

46 

46 

45 

44 

43 

42 

42 

41 

40 

39 

38 

37 

Min- 
utes 

Merid- 
ian 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

/  // 

/  // 

/  // 

/   // 

/  // 

/  // 

/  // 

/  // 

/  // 

Min. 

Min. 

4 

0  36 

0  38 

0  39 

0  40 

0  41 

0  44 

0  45 

0  47 

0  49 

0  52 

0  56 

1  00 

4 

8 

2  25 

2  28 

2  33 

2  39 

2  45 

2  51 

2  59 

3  09 

3  18 

3  29 

3  44 

3  58 

8 

12 

5  24 

5  35 

5  45 

5  57 

6  12 

6  27 

6  43 

7  04 

7  25 

7  50 

8  22 

8  55 

12 

16 

9  36 

9  52 

10  15 

10  35 

1100 

11  25 

11  56 

12  32 

13  10 

13  56 

14  50 

15  52 

16 

20 

15  00 

15  28 

16  00 

16  32 

17  12 

17  52 

18  39 

19  37 

20  36 

21  48 

23  13 

24  48 

20 

24 

21  36 

22  16 

23  03 

23  48 

24  46 

25  44 

26  53 

28  15 

29  40 

31  23 

33  25 

35  43 

24 

28 

29  24 

30  18 

31  21 

32  25 

33  43 

35  02 

36  35 

38  26 

40  23 

42  44 

45  28 

48  37 

28 

32 

38  24 

39  36 

40  57 

42  20 

44  02 

45  44 

47  47 

50  11 

52  44 

55  49 

59  24 

63  29 

32 

36 

48  36 

50  07 

51  50 

53  34 

55  44 

57  54 

60  29 

63  00 

66  45 

36 

40 

60  00 

6152 

64  00 

66  08 

68  48 

71  28 

40 

44 

72  36 

74  52 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

It 

It 

It 

It 

It 

n 

It 

It 

It 

It 

It 

A,h 

2.25 

2.32 

2.40 

2.48 

2.58 

2.68 

2.80 

2.94 

3.09 

3.27 

3.48 

3.72 

A,h 

Log. 

0.352 

0.365 

0.380 

0.394 

0.411 

0.428 

0.447 

0.468 

0.489 

0.514 

0.541 

0.570 

Log. 

18 

49 

21 

45 

62 

13 

16 

35 

96 

55 

58 

54 

Limit 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

26 

25 

Min- 
utes 

Merid- 

iMU 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

Alti- 
tudes 

348 


Latitude  SS**  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54°      5 

5°      56° 

57° 

58°      59 

o    1  Hour 
Angles 

Mln.      ' 

It 

/          H 

/     It 

/     II 

/     // 

/     // 

/     It    1 

II 

/       n 

/        n 

1 

//    / 

"     Min. 

4 

104 

1  10 

1  17 

126 

138 

155 

4 

8 

4  16 

4  39 

5  08 

5  45 

6  33 

7  40 

8 

12 

9  37 

10  29 

11  32 

12  53 

14  43 

17  15 

12 

16       1 

7  06 

18  37 

20  32 

22  55 

26  10 

30  41 

16 

20       2 

6  44 

29  04 

32  04 

35  48 

40  52 

47  56 

20 

24       2 

8  30 

4152 

46  11 

5133 

24 

28 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

n 

It 

" 

n 

It 

It 

t 

T 

1 

It         It 

A,h     4 

.01 

4.36 

4.81 

5.37 

6.13 

7.19 

Ajh 

Log.      ^ 

.603 
14 

0.639 
49 

0.682 
15 

0.729 
97 

0.787 
46 

0.856 
73 

Log. 

Limit 

22 

21 

20 

19 

17 

15 

12        1 

0 

6 

3 

0          3 

Min- 
utes 

Merid-     , 
ian        * 

io 

3 

81° 

82 

3 

83° 

84° 

85 

0 

86°      8 

7° 

8 

8° 

89° 

90°      89 

0       Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

/      '/ 

/     // 

/     // 

/      // 

/     // 

:Miu. 

4 

127 

1  10 

1  00 

0  48 

0  42 

0  36 

0  31 

0  27 

0  23 

4 

8 

5  47 

4  39 

3  51 

3  15 

2  46 

2  24 

2  05 

150 

1  34 

8 

12 

13  00 

10  29 

8  40 

7  18 

6  14 

5  22 

4  41 

4  07 

3  32 

12 

16 

23  06 

18  37 

15  24 

12  59 

1106 

9  33 

8  20 

7  19 

6  16 

16 

20 

36  08 

29  04 

24  03 

20  16 

17  19 

14  55 

13  01 

11  25 

9  48 

20 

24 

34  39 

29  11 

24  58 

2130 

18  44 

16  27 

14  06 

24 

28 

39  42 

33  58 

29  16 

25  29 

22  23 

19  13 

28 

32 

44  22 

38  14 

33  17 

29  11 

25  06 

32 

36 

48  23 

42  06 

36  57 

3145 

36 

40 

52  00 

45  36 

39  12 

40 

44 

55  10 

47  26 

44 

48 

56  27 

48 

52 

52 

56 

56 

60 

60 

» 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

5.42 

4.36 

3.61 

3.04 

2.60 

2.24 

1.95 

1.71 

1.47 

A,h 

Log. 

0.734 

0.639 

0.557 

0.482 

0.414 

0.350 

0.290 

0.233 

0.167 

Log. 

00 

49 

51 

87 

97 

25 

03 

00 

32 

Limit 

6 

9 

12 

15 

18 

20 

23 

26 

29 

32 

36 

40 

Min- 
utes 

Merid- 
ian 

8 

8° 

S 

7° 

36 

9 

85° 

84° 

83° 

82° 

81 

0 

80° 

79° 

78° 

77° 

Alti- 
tudes 

Latitude  58°  Declination  Contrary  Name. 

Declinations. 


349 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Anglo* 

/           H 

/     * 

/        n 

/     It 

1        ir 

/       n 

/      // 

/     // 

Min. 

Min. 

4 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  18 

0  18 

0  18 

0  17 

4 

8 

1  19 

1  17 

1  17 

1  16 

1  15 

1  14 

1  13 

1  13 

1  12 

1  11 

1  11 

1  10 

8 

12 

2  57 

2  54 

2  53 

2  51 

2  50 

2  47 

2  45 

2  44 

2  42 

2  41 

2  39 

2  37 

12 

16 

5  15 

5  10 

5  07 

5  05 

5  02 

4  57 

4  55 

4  52 

4  50 

4  47 

4  45 

4  39 

16 

20 

8  12 

8  04 

8  00 

7  56 

7  52 

7  44 

7  40 

7  36 

7  32 

7  28 

7  24 

7  16 

20 

24 

11  48 

1137 

1131 

1126 

1120 

11  09 

1103 

10  57 

10  51 

10  46 

10  40 

10  28 

24 

28 

16  05 

15  49 

15  41 

15  33 

15  25 

15  09 

15  01 

14  53 

14  46 

14  38 

14  30 

14  15 

28 

32 

2100 

20  39 

20  29 

20  18 

20  08 

19  47 

19  37 

19  27 

19  17 

19  06 

18  56 

18  36 

32 

36 

26  34 

26  08 

25  55 

25  43 

25  30 

25  04 

24  51 

24  38 

24  25 

24  12 

23  59 

23  33 

36 

40 

32  48 

32  16 

32  00 

31  44 

31  28 

30  56 

30  40 

30  24 

30  08 

29  52 

29  36 

29  04 

40 

44 

39  41 

39  02 

38  43 

38  24 

38  05 

37  26 

37  07 

36  47 

36  28 

36  09 

35  49 

35  10 

44 

48 

47  14 

46  28 

46  05 

45  41 

45  18 

44  32 

44  09 

43  46 

43  23 

43  00 

42  37 

41  51 

48 

52 

55  26 

54  32 

54  05 

53  37 

53  10 

52  16 

5149 

51  22 

50  55 

50  28 

50  01 

49  07 

52 

56 

64  17 

63  14 

62  43 

62  12 

6141 

60  38 

60  07 

59  35 

39  04 

58  33 

58  01 

56  58 

56 

60 

73  48 

72  36 

72  00 

7124 

70  48 

69  36 

69  00 

68  24 

67  48 

67  12 

66  36 

65  24 

60 

H 

K 

H 

n 

It 

It 

It 

It 

H 

It 

It 

It 

A,h 

1.23 

1.21 

1.20 

1.19 

1.18 

1.16 

1.15 

1.14 

1.13 

1.12 

1.11 

1.09 

A,h 

Log. 

0.089 

0.082 

0.079 

0.075 

0.071 

0.064 

0.060 

0.056 

0.053 

0.049 

0.045 

0.037 

Log. 

91 

79 

18 

55 

88 

46 

70 

90 

08 

22 

32 

43 

Limit 

62 

63 

64 

64 

65 

65 

65 

66 

66 

67 

68 

68 

Min- 
utes 

Merid- 
ian 

32° 

31" 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

Alti- 
tudes 

Declinations. 


Hour  1    1  no 
Angles     ^^ 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour' 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1      II 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 

1.08 

/      // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

It 

1.07 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

1.06 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

II 

1.05 

/      // 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

1.04 

1      II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 

H 

1.03 

/     // 

0  16 

1  05 

2  27 
4  21 
6  48 
9  48 

13  20 
17  24 
22  02 
27  12 
32  55 
39  10 
45  58 
53  19 
61  12 

1.02 

1     II 

0  16 

1  04 

2  25 
4  19 
6  44 
9  42 

13  12 
17  14 
2149 
26  56 
32  35 
38  47 
45  31 
52  47 

60  36 

It 

1.01 

/      // 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 
17  04 
2136 
26  40 
32  16 
38  24 
45  04 
52  16 

60  00 

It 

1.00 

/      // 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  10 

44  37 

5144 

59  24 
It 

0.99 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 
It 

0.98 

/     // 

0  15 
102 
2  20 

4  08 
6  28 
9  18 
12  41 
16  34 
20  57 
25  52 
31  18 
37  15 
43  43 
50  42 

58  12 

It 

0.97 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.033 
42 

0.029 
38 

0.025 
31 

0.021 
19 

0.017 
03 

0.012 
84 

0.008 
60 

0.004 
32 

0.000 

9.995 
64 

9.991 
23 

9.986 
77 

Log. 

Limit 

69 

70 

71 

71 

71 

71 

72 

73 

74 

75 

76 

77 

Min- 
utes 

Merid- 
ian 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

Alti- 
tudes 

350 


Latitude  58°  Decimation  Contrary  Name. 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      // 

/      " 

/      // 

/      // 

1     II 

/     II 

/     // 

/      /' 

/      // 

/      '/ 

Min. 

4 

0  15 

015 

0  15 

0  14 

4 

8 

101 

100 

100 

0  59 

8 

12 

2  19 

2  16 

2  14 

2  13 

12 

16 

4  05 

4  02 

4  00 

3  57 

16 

20 

6  24 

6  20 

6  16 

6  12 

20 

24 

9  13 

9  07 

9  01 

8  56 

24 

28 

12  33 

12  25 

12  17 

12  09 

28 

32 

16  23 

16  13 

16  03 

15  52 

32 

36 

20  44 

20  31 

20  18 

20  05 

36 

40 

25  36 

25  20 

25  04 

24  48 

40 

44 

30  58 

30  39 

30  19 

30  00 

44 

48 

36  52 

36  29 

36  06 

35  43 

48 

52 

43  16 

42  49 

42  22 

4155 

52 

56 

50  10 

49  39 

49  07 

48  36 

56 

60 

57  36 

57  00 

56  24 

55  48 

60 

It 

n 

n 

H 

/ 

1 

" 

n 

H 

n 

A,h 

0.96 

0.95 

0.94 

0.93 

Ajh 

Log. 

9.982 
27 

9.977 
72 

9.973 
13 

9.968 
48 

Log. 

Limit 

78 

78 

79 

80 

Min- 
utes 

Merid- 
ian 

8° 

7° 

6° 

5° 

4 

t° 

3= 

2° 

1° 

0° 

1 

o 

i 

° 

a 

° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

0  14 

0  53 

159 

3  33 

5  32 

7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

3152 

37  24 

43  23 

49  48 

n 

0.83 

1     " 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

2152 

26  28 

31  29 

36  57 

42  52 

49  12 
n 

0.82 

1     II 

0  13 

0  52 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 

II 

0.81 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
4149 
48  00 

n 

0.80 

/      // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
II 

0.79 

/      // 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

n 

0.78 

/      // 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

0.77 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  44 

45  36 

n 

0.76 

/      // 

0  12 

0  49 

1  49 
3  13 
5  02 
7  15 
9  52 

12  53 
16  18 
20  08 
24  21 
28  55 
34  02 
39  28 
45  18 

n 

0.755 

1     II 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 

n 

0.75 

/      // 

0  12 
0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 

n 

0.74 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.919 
08 

9.913 
81 

9.908 
49 

9.903 
09 

9.897 
63 

9.892 
09 

9.886 
49 

9.880 
81 

9.877 
95 

9.875 
06 

9.869 
23 

Log. 

Limit 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

Min- 
utes 

Merid- 1      jq    \      ko 

ian         *      1      ^ 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

Alti- 
tudes 

Latitude  5S°  Decimation  Contrary  Name. 

Declixations.  —  Inferior  Meridian. 


351 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/      // 

/      // 

/     ff 

/      * 

/     f/ 

/     // 

/      // 

/     // 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  10 

4 

8 

0  47 

0  46 

0  46 

0  45 

0  44 

0  43 

0  42 

0  41 

0  41 

0  40 

0  39 

0  38 

8 

12 

1  45 

1  44 

1  42 

141 

139 

1  36 

135 

133 

1  30 

1  29 

1  27 

1  26 

12 

16 

3  07 

3  04 

3  02 

2  59 

2  57 

2  52 

2  49 

2  47 

2  42 

2  39 

2  37 

2  34 

16 

20 

4  52 

4  48 

4  44 

4  40 

4  36 

4  28 

4  24 

4  20 

4  12 

4  08 

4  04 

4  00 

20 

24 

7  00 

6  55 

6  49 

6  43 

6  38 

6  26 

6  21 

6  15 

6  03 

5  58 

5  52 

5  46 

24 

28 

9  33 

9  25 

9  17 

9  09 

9  01 

8  45 

8  37 

8  29 

8  14 

8  06 

7  58 

7  50 

28 

32 

12  28 

12  17 

12  07 

1157 

1146 

11  26 

11  15 

1105 

10  45 

10  34 

10  24 

10  14 

32 

36 

15  46 

15  33 

15  30 

15  07 

14  55 

14  29 

14  16 

14  03 

13  37 

13  24 

13  11 

12  58 

36 

40 

19  28 

19  12 

18  56 

18  40 

18  24 

17  52 

17  36 

17  20 

16  48 

16  32 

16  16 

16  00 

40 

44 

23  33 

23  14 

22  54 

22  35 

22  16 

2138 

21  18 

20  59 

20  20 

20  01 

19  41 

19  22 

44 

48 

28  00 

27  37 

27  14 

26  51 

26  29 

25  43 

25  20 

24  57 

24  11 

23  48 

23  25 

23  02 

48 

52 

32  54 

32  27 

32  00 

3133 

3105 

30  11 

29  44 

29  17 

28  23 

27  56 

27  29 

27  02 

52 

56 

38  09 

37  38 

37  06 

36  35 

36  04 

35  02 

34  30 

33  59 

32  56 

32  25 

3153 

31  22 

56 

60 

43  48 

43  12 

42  36 

42  00 

4124 

40  12 

39  36 

39  00 

37  48 

37  12 

36  36 

36  00 

60 

/r 

/r 

" 

If 

ff 

» 

* 

It 

It 

It 

It 

H 

A,h 

0.73 

0.72 

0.71 

0.70 

0.69 

0.67 

0.66 

0.65 

0.63 

0.62 

0.61 

0.60 

Ajh 

log. 

9.863 

9.857 

9.851 

9.845 

9.838 

9.826 

9.819 

9.812 

9.799 

9.792 

9.785 

•  9.778 

Log. 

32 

33 

26 

10 

85 

07 

54 

91 

34 

39 

33 

15 

Limit 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

Min- 
utes 

Merid- 
ian 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/      '/ 

/     // 

/      // 

/      // 

/      // 

1       n 

/     // 

t     II 

1     II 

/      // 

/      // 

1     II 

Min. 

4 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

4 

8 

0  38 

0  38 

0  37 

0  36 

0  35 

0  33 

0  32 

0  31 

0  31 

0  30 

0  29 

0  29 

8 

12 

125 

124 

122 

1  19 

1  18 

1  15 

1  13 

1  11 

109 

107 

105 

1  04 

12 

16 

2  31 

2  28 

2  26 

2  21 

2  18 

2  13 

2  11 

2  05 

2  03 

157 

155 

1  52 

16 

20 

3  56 

3  52 

3  48 

3  40 

3  36 

3  28 

3  24 

3  16 

3  12 

3  04 

3  00 

2  56 

20 

24 

5  40 

5  34 

5  28 

5  17 

5  11 

5  00 

4  54 

4  42 

4  36 

4  25 

4  19 

4  13 

24 

28 

7  43 

7  35 

7  27 

7  11 

7  03 

6  48 

6  40 

6  25 

6  16 

6  01 

5  53 

5  45 

28 

32 

10  04 

9  54 

9  44 

9  23 

9  13 

8  52 

8  42 

8  22 

8  12 

7  51 

7  41 

7  31 

32 

36 

12  45 

12  32 

12  19 

11  53 

1140 

11  14 

1101 

10  35 

10  22 

9  56 

9  43 

9  30 

36 

40 

15  44 

15  28 

15  12 

14  40 

14  24 

13  52 

13  36 

13  04 

12  48 

12  16 

12  00 

1144 

40 

44 

19  02 

18  43 

18  24 

17  45 

17  25 

16  47 

16  27 

15  48 

15  29 

14  50 

14  31 

14  11 

44 

48 

22  39 

22  16 

2153 

2107 

20  44 

19  58 

19  35 

18  49 

18  26 

17  40 

17  17 

16  54 

48 

52 

26  35 

26  08 

25  41 

24  47 

24  20 

23  26 

22  59 

22  05 

2138 

20  44 

20  17 

19  50 

52 

56 

30  50 

30  19 

29  48 

28  45 

28  13 

27  11 

26  39 

25  36 

25  05 

24  04 

23  31 

22  59 

56 

60 

35  24 

34  48 

34  12 

33  00 

32  24 

31  12 

30  36 

29  24 

28  48 

27  36 

27  00 

26  24 

60 

It 

It 

n 

It 

H 

It 

n 

It 

It 

It 

It 

It 

A,h 

0.59 

0.58 

0.57 

0.55 

0.54 

0.52 

0.51 

0.49 

0.48 

0.46 

0.45 

0.44 

Ajh 

Log. 

9.770 

9.763 

9.755 

9.740 

7.732 

9.716 

9.707 

9.690 

9.681 

9.662 

9.653 

9.643 

Log. 

85 

43 

87 

36 

39 

00 

57 

20 

24 

76 

21 

45 

Limit 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

89 

Min- 
utes 

Merid- 
ian 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

Alti- 
tudes 

352 


Latitude  59°  Declination  Same  Name 

Declinations. 


Hour 
Angles 

0° 

1» 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/      // 

/     // 

/      // 

/       n 

/       n 

/     // 

/        n 

/     // 

/     // 

/     // 

/       n 

/     // 

Min. 

4 

0  19 

0  19 

0  19 

0  19 

0  19 

0  20 

0  20 

0  20 

0  20 

0  21 

0  21 

0  22 

4 

8 

1  15 

116 

1  17 

1  18 

1  19 

120 

121 

1  21 

1  23 

1  23 

124 

126 

8 

12 

2  50 

2  51 

2  54 

2  56 

2  57 

3  00 

3  02 

3  03 

3  06 

3  07 

3  10 

3  13 

12 

16 

5  02 

5  05 

5  10 

5  12 

5  15 

5  20 

5  22 

5  25 

5  30 

5  33 

5  38 

5  43 

16 

20 

7  52 

7  56 

8  04 

8  08 

8  12 

8  20 

8  24 

8  28 

8  36 

8  40 

8  48 

8  56 

20 

24 

1120 

1126 

1137 

11  43 

11  48 

12  00 

12  06 

12  11 

12  23 

12  29 

12  41 

12  52 

24 

28 

15  25 

15  33 

15  49 

15  57 

16  05 

16  20 

16  28 

16  36 

16  52 

16  59 

17  15 

17  30 

28 

32 

20  08 

20  18 

20  39 

20  49 

2100 

21  20 

2130 

21  41 

22  01 

22  11 

22  31 

22  52 

32 

36 

25  30 

25  43 

26  08 

26  21 

26  34 

27  00 

27  13 

27  26 

27  52 

28  05 

28  31 

28  57 

36 

40 

3128 

3144 

32  16 

32  32 

32  48 

33  20 

33  36 

33  52 

34  24 

34  40 

35  12 

35  44 

40 

44 

38  05 

38  24 

39  02 

39  22 

39  41 

40  20 

40  39 

40  59 

4137 

41  57 

42  36 

43  14 

44 

48 

45  18 

45  41 

46  28 

46  51 

47  14 

48  00 

48  23 

48  46 

49  32 

49  55 

50  41 

51  17 

48 

52 

53  10 

53  37 

54  32 

54  59 

55  26 

56  20 

56  47 

57  14 

58  08 

58  35 

59  29 

60  23 

52 

56 

6141 

62  12 

63  14 

63  46 

64  17 

65  20 

65  51 

66  23 

67  25 

67  57 

69  00 

70  02 

56 

60 

70  48 

71  24 

72  36 

73  12 

73  48 

75  00 

75  36 

76  12 

77  24 

78  00 

79  12 

80  24 

60 

n 

n 

It 

n 

n 

n 

n 

II 

n 

H 

H 

H 

Aih 

1.18 

1.19 

1.21 

1.22 

1.23 

1.25 

1.26 

1.27 

1.29 

1.30 

1.32 

1.34 

A,h 

liOg. 

0.071 

0.075 

0.082 

0.086 

0.089 

0.096 

0.100 

0.103 

0.100 

0.113 

0.120 

0.127 

IiOg. 

88 

55 

79 

36 

91 

91 

37 

80 

59 

94 

57 

10 

Limit 

64 

64 

63 

62 

61 

60 

60 

59 

59 

58 

58 

57 

Min- 
utes 

Merid- 
ian 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

/       n 

/     // 

1     >i 

1     II 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

0  22 

0  22 

0  22 

0  22 

0  22 

0  23 

0  23 

0  23 

0  24 

0  24 

0  25 

0  25 

4 

8 

126 

128 

129 

130 

132 

133 

134 

136 

136 

138 

140 

1  41 

8 

12 

3  14 

3  17 

3  20 

3  23 

3  24 

3  29 

3  32 

3  35 

3  37 

3  40 

3  45 

3  48 

12 

16 

5  46 

5  51 

5  56 

6  01 

6  06 

6  11 

6  16 

6  21 

6  27 

6  32 

6  39 

6  44 

16 

20 

9  00 

9  08 

9  16 

9  24 

9  32 

9  40 

9  48 

9  56 

10  04 

10  12 

10  24 

10  32 

20 

24 

12  58 

13  09 

13  21 

13  32 

13  43 

13  55 

14  06 

14  18 

14  30 

14  41 

14  59 

15  10 

24 

28 

17  38 

17  54 

18  10 

18  26 

18  42 

18  57 

19  13 

19  29 

19  44 

20  00 

20  23 

20  39 

28 

32 

23  02 

23  23 

23  43 

24  04 

24  25 

24  45 

25  06 

25  26 

25  46 

26  07 

26  37 

26  58 

32 

36 

29  10 

29  36 

30  02 

30  27 

30  53 

31  19 

31  45 

32  11 

32  37 

33  03 

33  42 

34  08 

36 

40 

36  00 

36  32 

37  04 

37  36 

38  08 

38  40 

39  12 

39  44 

40  16 

40  48 

4136 

42  08 

40 

44 

43  34 

44  13 

44  51 

45  29 

46  08 

46  47 

47  26 

48  04 

48  43 

49  22 

50  20 

50  59 

44 

48 

5150 

52  36 

53  22 

54  09 

54  55 

55  41 

56  27 

57  13 

57  59 

58  45 

59  54 

60  40 

48 

52 

60  50 

61  44 

62  38 

66  33 

64  27 

65  21 

66  15 

67  09 

68  03 

68  57 

70  18 

71  12 

52 

56 

70  34 

7137 

72  39 

73  41 

74  44 

75  37 

76  50 

77  52 

78  55 

79  58 

8132 

82  25 

56 

60 

8100 

82  12 

83  24 

84  36 

85  48 

87  00 

88  12 

89  24 

90  36 

9148 

93  36 

94  48 

60 

It 

H 

n 

It 

It 

n 

It 

It 

It 

It 

n 

n 

A,h 

1.35 

1.37 

1.39 

1.41 

1.43 

1.45 

1.47 

1.49 

1.51 

1.53 

1.56 

1.58 

A,h 

Log. 

0.130 

0.136 

0.143 

0.149 

0.155 

0.161 

0.167 

0.173 

0.178 

0.184 

0.193 

0.198 

Log. 

33 

72 

01 

22 

34 

37 

32 

19 

98 

69 

12 

66 

Limit 

56 

56 

55 

55 

54 

53 

53 

52 

52 

51 

50 

49 

Min- 
utes 

Merid- 
ian 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

Alti- 
tudes 

Latitude  59®  Declination  Same  Name. 

Declinations. 


353 


Hour 
Angles 

24' 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

/      // 

/       n 

/     II 

/        n 

Min. 

Min. 

4 

0  26 

0  26 

0  27 

0  27 

0  28 

0  29 

0  29 

0  30 

0  30 

0  31 

0  32 

0  33 

4 

8 

143 

1  44 

147 

149 

151 

154 

156 

1  58 

2  01 

2  03 

2  06 

2  11 

8 

12 

3  51 

8  54 

4  00 

4  05 

4  09 

4  15 

4  20 

4  26 

4  32 

4  38 

4  46 

4  54 

12 

16 

6  53 

6  58 

7  08 

7  15 

7  23 

7  33 

7  44 

7  54 

8  04 

8  14 

8  26 

8  42 

16 

20 

10  44 

10  52 

1108 

11  20 

1132 

11  48 

12  04 

12  20 

12  36 

12  52 

13  12 

13  36 

20 

24 

15  28 

15  39 

16  02 

16  19 

16  36 

16  59 

17  23 

17  46 

18  09 

18  31 

19  00 

19  35 

24 

28 

2102 

21  18 

2149 

22  16 

22  37 

23  08 

23  39 

24  10 

24  42 

25  14 

25  53 

26  39 

28 

32 

27  28 

27  49 

28  30 

29  32 

29  32 

30  13 

30  53 

3134 

32  15 

32  5? 

33  48 

34  49 

32 

36 

34  47 

35  13 

36  05 

36  43 

37  22 

38  14 

39  06 

39  58 

40  50 

4141 

42  4G 

44  04 

36 

40 

42  56 

43  28 

44  32 

45  20 

46  08 

47  12 

48  16 

49  20 

50  24 

5128 

52  48 

54  24 

40 

44 

5157 

52  36 

53  54 

54  51 

55  49 

57  07 

58  24 

59  42 

60  59 

62  16 

63  53 

65  49 

44 

48 

6149 

62  35 

64  07 

65  15 

66  24 

67  56 

69  30 

7102 

72  34 

74  07 

76  02 

78  20 

48 

52 

72  33 

73  27 

75  15 

76  37 

77  58 

79  46 

8134 

83  22 

52 

56 

84  09 

85  12 

87  18 

88  51 

56 

60 

60 

H 

K 

It 

" 

n 

n 

» 

K 

If 

n 

» 

H 

A,h 

1.61 

1.63 

1.67 

1.70 

1.73 

1.77 

1.81 

1.85 

1.89 

1.93 

1.98 

2.04 

A,h 

I<og. 

0.206 

0.212 

0.222 

0.230 

0.238 

0.247 

0.257 

0.267 

0.276 

0.285 

0.296 

0.309 

Log. 

83 

19 

72 

45 

05 

97 

68 

17 

46 

56 

67 

63 

Limit 

48 

48 

47 

46 

45 

44 

43 

43 

42 

41 

40 

39 

Min- 
utes 

Merid- 
ian 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42°      43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/       // 

/      II 

/     II 

/      It 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

1     II 

1     II 

Min. 

4 

0  33 

0  34 

0  36 

0  37 

0  38 

0  39 

0  41 

0  44 

0  46 

0  48 

0  50 

0  54 

4 

8 

2  14 

2  18 

2  22 

2  27 

2  32 

2  38 

2  45 

2  53 

3  00 

3  10 

3  20 

3  33 

8 

12 

5  01 

5  10 

5  20 

5  31 

5  43 

5  55 

6  11 

6  27 

6  45 

7  07 

7  29 

8  00 

12 

16 

8  55 

9  12 

9  29 

9  48 

10  10 

10  32 

11  00 

1125 

12  00 

12  38 

13  18 

14  10 

16 

20 

13  56 

14  23 

14  49 

15  19 

15  53 

16  27 

17  12 

17  52 

18  45 

19  45 

20  46 

22  08 

20 

24 

20  04 

20  45 

2120 

22  05 

22  52 

23  41 

24  45 

25  44 

27  00 

28  26 

29  58 

31  52 

24 

28 

27  19 

28  13 

29  01 

30  03 

3105 

32  17 

33  43 

35  02 

36  43 

38  41 

40  46 

43  20 

28 

32 

35  40 

36  51 

37  53 

39  15 

40  38 

42  10 

44  02 

45  44 

47  57 

50  31 

53  14 

56  39 

32 

36 

45  09 

46  41 

47  56 

49  41 

51  25 

53  21 

55  44 

57  54 

60  42 

63  56 

36 

40 

55  44 

57  36 

59  12 

61  20 

63  28 

65  52 

68  48 

7128 

40 

44 

67  26 

69  42 

7138 

74  13 

76  48 

44 

48 

80  15 

82  56 

48 

52 

52 

56 

56 

60 

60 

H 

« 

n 

It 

H 

It 

It 

It 

n 

9 

if 

It 

A,h 

2.09 

2.16 

2.22 

2.30 

2.38 

2.47 

2.58 

2.68 

2.81 

2.96 

3.12 

3.32 

A,h 

Log. 

0.320 

0.334 

0.346 

0.361 

0.376 

0.392 

0.411 

0.428 

0.448 

0.471 

0.494 

0.521 

Log. 

15 

45 

35 

73 

58 

70 

62 

13 

71 

29 

15 

14 

Tiimit 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

28 

27 

Min- 
utes 

Merid- 
ian 

67° 

68° 

69° 

70° 

71° 

72« 

73° 

74° 

75° 

76° 

77° 

78° 

Alti- 
tudes 

354 


Latitude  59°  Decimation  Same  Name. 

Declinations. 


Hour       A 
Angles     * 

8° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
AnglM 

Min.      ' 

// 

/     // 

1     II 

/     // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

Min. 

4          ( 

)57 

101 

107 

1  13 

1  22 

134 

149 

4 

8      : 

!48 

4  04 

4  26 

4  52 

5  27 

6  16 

7  16 

8 

12          f 

i32 

9  10 

8  00 

10  57 

12  16 

14  06 

16  22 

12 

16        It 

)  11 

16  17 

17  45 

19  30 

21  49 

25  04 

29  06 

16 

20        2: 

40 

25  28 

27  44 

30  28 

34  05 

39  12 

45  28 

. 

20 

24        3^ 

105 

36  41 

39  56 

43  52 

49  04 

24 

28      4e 

)23 

49  55 

28 

32 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

•  • 

56 

60 

60 

' 

n 

* 

It 

It 

If 

" 

" 

' 

f 

r 

A,h      3. 

55 

3.82 

4.16 

4.57 

5.11 

5.88 

6.82 

A,h 

Log.      0. 

550 

0.582 

0.619 

0.659 

0.708 

0.769 

0.833 

Log. 

23 

06 

09 

92 

42 

38 

78 

Limit       2 

4 

23 

22 

21 

20 

18 

15 

12 

9 

6 

3 

0 

Min- 
utes 

Merid-      7 
ian          ' 

9° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

90° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

/     // 

/     // 

1     II 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

120 

105 

0  55 

0  45 

0  39 

0  33 

0  29 

0  24 

4 

8 

5  25 

4  22 

3  36 

3  02 

2  35 

2  14 

156 

1  38 

8 

12 

12  13 

9  49 

8  06 

6  50 

5  49 

5  01 

4  20 

3  40 

12 

16 

2143 

17  26 

14  23 

12  06 

10  20 

8  55 

7  44 

6  32 

16 

20 

33  56 

27  16 

22  28 

18  56 

16  08 

13  56 

12  04 

10  12 

20 

24 

32  21 

27  16 

23  14 

20  04 

17  23 

14  41 

24 

28 

37  06 

3138 

27  19 

23  39 

20  00 

28 

32 

41  18 

35  40 

30  53 

26  07 

32 

36 

45  09 

39  06 

33  03 

36 

40 

48  16 

40  48 

40 

44 

49  22 

44 

48 

48 

52 

52 

56 

56 

60 

60 

If 

n 

n 

11 

n 

n 

H 

n 

n 

n 

H 

n 

A,h 

5.09 

4.09 

3.37 

2.84 

2.42. 

2.09 

1.81 

1.53 

A,h 

Log. 

0.706 

0.611 

0.527 

0.453 

0.383 

0.320 

0.257 

0.184 

Log. 

72 

72 

63 

32 

82 

15 

68 

69 

Limit 

3 

6 

9 

12 

15 

18 

22 

25 

28 

31 

34 

36 

Min- 
utes 

Morid- 
ian 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

78° 

Alti- 
tudes 

Latitude  59°  Declination  Contrary  Name. 


355 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t      It 

0  19 

1  15 

2  50 
5  02 
7  52 

11  20 
15  25 
20  08 
25  30 
31  28 
38  05 
45  18 
53  10 
61  41 
70  48 

1.18 

/  n 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

It 

1.17 

/  // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

It 

1.16 

/  // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

5122 

59  35 

68  24 
It 

1.14 

/  It 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 
14  46 
19  17 
24  25 
30  08 
36  28 
43  23 
50  55 
59  04 

67  48 

If 

1.13 

/  II 

0  18 

1  11 

2  41 
4  47 

7  28 
10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 

67  12 

If 

1.12 

'  ti 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

It 

1.11 

/  // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
It 

1.10 

1      II 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

4151 

49  07 

56  58 

65  24 
It 

1.09 

/  It 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  30 

28  48 

34  51 

4128 

48  40 

56  27 

64  48 

1.08 

t     II 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
It 

1.07 

/  // 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 

It 

1.06 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,ll 

Log. 

0.071 

88 

0.068 
19 

0.064 
46 

0.056 
90 

0.053 
08 

0.049 
22 

0.045 
32 

0.041 
39 

0.037 
43 

0.033 
42 

0.029 
38 

0.025 
31 

Log. 

Limit 

64 

64 

65 

65 

66 

67 

67 

67 

68 

68 

69 

69 

Min- 
utes 

Merid- 
ian 

31° 

30° 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 
4 

8 

t      II 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

It 

1.05 

1     II 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 
It 

1.04 

r       II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 

1.03 

1     II 

0  16 

1  05 

2  27 
4  21 
6  48 
9  48 

13  20 
17  24 
22  02 
27  12 
32  55 
39  10 
45  58 
53  19 
61  12 

1.02 

/   // 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

1.01 

1     II 

0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 
It 

1.00 

1      II 

0  15 
103 

1     II 

0  15 

1  02 

/   // 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

0.97 

1     II 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

0.96 

/  // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
It 

0.95 

/  // 

0  15 
100 

Min. 

4 
8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

2  33 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

51  44 

59  24 

It 

0.99 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

3137 

37  38 

44  10 

51  13 

58  48 
It 

0.98 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
It 

0.94 

12 
16 
20 
24 

28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.021 
19 

0.017 
03 

0.012 

84 

0.008 
60 

0.004 
32 

0.00 

9.995 
64 

9.991 
23 

9.986 

77 

9.982 

27 

9.977 
72 

9.973 
13 

Log. 

Limit 

70 

71 

71 

72 

72 

72 

73 

74 

75 

76 

77 

78 

Min- 
utes 

Merid- 
ian 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

Alti- 
tudes 

356 


Latitude  59"  Declination  Contrary  Name. 


Declinations. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Honr 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

0  14 
0  59 

2  13 

3  57 
6  12 
8  56 

12  09 

15  52 

20  05 

24  48 

30  00 

35  43 

44  55 

48  36 

55  48 
It 

0.93 

/   n 

0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 

15  42 

19  52 

24  32 

29  41 

35  20 

4128 

48  05 

55  12 
n 

0.92 

/  It 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

n 

0.91 

/ 

It 

r 

It 

t 

It 

It 

/ 

r 

t 

1 

/ 

II 

1 

/ 

// 

r 

/ 

It 

1 

/ 

1 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.968 
48 

9.963 
79 

9.959 
04 

■ 

Log. 

Limit 

79 

80 

80 

Min- 
utes 

Merid- 
ian 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/  // 

/  // 

/  /' 

/   // 

/  // 

/  // 

/  // 

/  // 

Min. 

Min. 

4 

0  13 

0  13 

0  13 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

Oil 

4 

8 

0  52 

0  52 

0  51 

0  51 

0  50 

0  50 

0  50 

0  49 

0  48 

0  48 

0  47 

0  46 

8 

12 

158 

156 

155 

1  54 

153 

152 

151 

150 

148 

147 

145 

1  44 

12 

16 

3  30 

3  28 

3  25 

3  22 

3  19 

3  18 

3  17 

3  14 

3  12 

3  09 

3  07 

3  04 

16 

20 

5  28 

5  24 

5  20 

5  16 

5  12 

5  10 

5  08 

5  04 

5  00 

4  56 

4  52 

4  48 

20 

24 

7  53 

7  47 

7  41 

7  35 

7  29 

7  26 

7  23 

7  18 

7  12 

7  06 

7  00 

6  55 

24 

28 

10  43 

10  35 

10  27 

10  20 

10  12 

10  08 

10  04 

9  56 

9  48 

9  40 

9  33 

9  25 

28 

32 

13  59 

13  49 

13  39 

13  29 

13  19 

13  14 

13  09 

12  58 

12  48 

12  38 

12  28 

12  17 

32 

36 

17  43 

17  30 

17  17 

17  04 

16  51 

16  44 

16  38 

16  25 

16  12 

15  59 

15  46 

15  33 

36 

40 

21  52 

21  36 

21  20 

21  04 

20  48 

20  40 

20  32 

20  16 

20  00 

19  44 

19  28 

19  12 

40 

44 

26  28 

26  08 

25  49 

25  29 

25  10 

25  00 

24  51 

24  31 

24  12 

23  52 

23  33 

23  14 

44 

48 

31  29 

3106 

30  43 

30  18 

29  55 

29  44 

29  32 

29  09 

28  46 

28  23 

28  00 

27  37 

48 

52 

36  57 

36  30 

36  03 

35  36 

35  09 

34  55 

34  42 

34  15 

33  48 

33  21 

32  54 

32  27 

52 

56 

42  52 

42  20 

41  49 

41  17 

40  46 

40  30 

40  15 

39  44 

39  12 

38  40 

38  09 

37  38 

56 

60 

49  12 

48  36 

48  00 

47  24 

46  48 

46  30 

46  12 

45  36 

45  00 

44  24 

43  48 

43  12 

60 

It 

It 

It 

It 

It 

It 

It 

It 

" 

" 

H 

It 

A,h 

0.82 

0.81 

0.80 

0.79 

0.78 

^.llh 

^.11 

0.76 

0.75 

0.74 

0.73 

0.72 

A,h 

9.913 

9.908 

9.903 

9.897 

9.892 

9.889 

9.886 

9.880 

9.875 

9.869 

9.863 

9.857 

Log. 

81 

49 

09 

63 

09 

30 

49 

81 

06 

23 

32 

33 

Limit 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

Min- 
utes 

Merid- 
ian 

5° 

6° 

70 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

ICO   Alti- 
■^°   ^  tudes 

Latitude  59°  Declination  Q)ntfary  Namc« 

Declinations.  —  Inferior  Meridian. 


357 


Hour 
Angles 

48» 

49<' 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/           V 

oil 

0  46 
142 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  06 

42  36 

It 

0.71 

/        n 

Oil 

0  45 

141 

2  59 

4  40 

6  43 

9  09 

1157 

15  07 

18  40 

22  35 

26  51 

3133 

36  35 

42  00 
It 

0.70 

/       n 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

1146 

14  55 

18  24 

22  16 

26  29 

3105 

36  04 

41  24 

It 

0.69 

Oil 

0  44 

138 

2  54 

4  32 

6  32 

8  53 

1136 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 

n 

0.68 

/     // 

Oil 
0  44 
136 
2  52 

4  28 
6  26 
8  45 
1126 
14  29 
17  52 
2138 
25  43 
30  11 
35  02 
40  12 

0.67 

Oil 

0  42 

1  35 

2  49 
4  24 
6  21 
8  37 

11  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 

39  36 

It 

0.66 

/     // 

Oil 

0  41 

132 

2  44 

4  16 

6  09 

8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 

It 

0.64 

1     It 

Oil 

0  41 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  33 

32  56 

37  48 
It 

0.63 

1     It 

0  10 
0  40 
129 
2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

n 

0.62 

1     It 

0  10 

0  40 
127 
2  37 

4  04 

5  52 
7  58 

10  24 

13  11 

16  16 

19  41 

23  25 

27  29 

3153 

36  36 
It 

0.61 

/     // 

0  10 

0  39 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 

12  58 

16  00 

19  22 

23  02 

27  02 

3122 

36  00 
It 

0.60 

/     It 

0  09 
0  38 
125 

2  31 

3  56 
5  40 
7  43 

10  04 

12  45 

•15  44 

19  02 

22  39 

26  35 

30  50 

35  24 
It 

0.59 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.851 
26 

9.845 
10 

9.838 
85 

9,832 
51 

9.826 
07 

9.819 
54 

9.806 
18 

9.799 
34 

9.792 
39 

9.785 
33 

9.778 
15 

9.770 
85 

Log. 

Limit 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

Min- 
utes 

Merid- 
ian 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/      // 

/      // 

/      // 

/      // 

/      // 

/      /' 

/      // 

/      // 

/     // 

t       a 

/      // 

/      // 

Min. 

4 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

0  06 

4 

8 

0  38 

0  37 

0  37 

0  35 

0  35 

0  32 

0  32 

0  31 

0  31 

0  29 

0  28 

0  28 

8 

12 

124 

122 

121 

118 

1  16 

1  13 

1  12 

109 

108 

105 

104 

102 

12 

16 

2  28 

2  26 

2  23 

2  18 

2  16 

2  11 

2  08 

2  03 

2  00 

1  55 

152 

150 

16 

20 

3  52 

3  48 

3  44 

3  36 

3  32 

3  24 

3  20 

3  12 

3  08 

3  00 

2  56 

2  52 

20 

24 

5  34 

5  28 

5  23 

5  11 

5  05 

4  54 

4  48 

4  36 

4  30 

4  19 

4  13 

4  07 

24 

28 

7  35 

7  27 

7  19 

7  03 

6  56 

6  40 

6  32 

6  16 

6  09 

5  53 

5  45 

5  38 

28 

32 

9  54 

9  44 

9  33 

9  13 

9  03 

8  42 

8  32 

8  12 

8  02 

7  41 

7  31 

7  21 

32 

36 

12  32 

12  19 

12  06 

1140 

1127 

1101 

10  48 

10  22 

10  09 

9  43 

9  30 

9  17 

36 

40 

15  28 

15  12 

14  56 

14  24 

14  08 

13  36 

13  20 

12  48 

12  32 

12  00 

1144 

1128 

40 

44 

18  43 

18  24 

18  04 

17  25 

17  06 

16  27 

16  08 

15  29 

15  10 

14  31 

14  12 

13  52 

44 

48 

22  16 

21  53 

2130 

20  44 

20  21 

19  35 

19  12 

18  26 

18  03 

17  17 

16  54 

16  31 

48 

52 

26  08 

25  41 

25  14 

24  20 

23  53 

22  59 

22  32 

2138 

21  11 

20  17 

19  50 

19  23 

52 

56 

30  19 

29  48 

29  16 

28  13 

27  42 

26  39 

26  08 

25  05 

24  34 

23  31 

23  00 

22  28 

56 

60 

34  48 

34  12 

33  36 

32  24 

3148 

30  36 

30  00 

28  48 

28  12 

27  00 

26  24 

25  48 

60 

II 

It 

IT 

n 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

0.58 

0.57 

0.56 

0.54 

0.53 

0.51 

0.50 

0.48 

0.47 

0.45 

0.44 

0.43 

Ajh 

Log. 

9.763 

9.755 

9.748 

9.732 

9.724 

9.707 

9.698 

9.681 

9.672 

9.653 

9.643 

9.633 

43 

87 

19 

39 

28 

57 

97 

24 

10 

21 

45 

47  ""^• 

Limit 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

92 

Min- 
utes 

Merid- 
ian 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38= 

39° 

40° 

Alti- 
tudes 

358 


Latitude  60°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

o» 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  18 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  20 

0  20 

0  20 

4 

8 

1  12 

1  13 

1  14 

1  15 

1  15 

1  16 

1  17 

1  18 

1  19 

1  20 

121 

1  22 

8 

12 

2  42 

2  45 

2  47 

2  48 

2  50 

2  51 

2  54 

2  56 

2  57 

3  00 

3  02 

3  05 

12 

16 

4  50 

4  55 

4  57 

5  00 

5  02 

5  05 

5  10 

5  12 

5  15 

5  20 

5  22 

5  27 

16 

20 

7  32 

7  40 

7  44 

7  48 

7  52 

7  56 

8  04 

8  08 

8  12 

8  20 

8  24 

8  32 

20 

24 

10  51 

1103 

11  09 

11  14 

11  20 

11  26 

11  37 

1143 

1148 

12  00 

12  06 

12  17 

24 

28 

14  46 

15  01 

15  09 

15  17 

15  25 

15  33 

15  49 

15  57 

16  05 

16  20 

16  28 

16  44 

28 

32 

19  17 

19  37 

19  47 

19  58 

20  08 

20  18 

20  39 

20  49 

2100 

21  20 

2130 

21  51 

32 

36 

24  25 

24  51 

25  04 

25  17 

25  30 

25  43 

26  08 

26  21 

26  34 

27  00 

27  13 

27  39 

36 

40 

30  08 

30  40 

30  56 

31  12 

3128 

31  44 

32  16 

32  32 

32  48 

33  20 

33  36 

34  08 

40 

44 

36  28 

37  07 

37  26 

37  46 

38  05 

38  24 

39  02 

39  22 

39  41 

40  20 

40  39 

41  18 

44 

48 

43  23 

44  09 

44  32 

44  55 

45  18 

45  41 

46  28 

46  51 

47  14 

48  00 

48  23 

49  09 

48 

52 

50  55 

51  49 

52  16 

52  43 

53  10 

53  37 

54  32 

54  59 

55  26 

56  20 

56  47 

57  41 

52 

56 

59  04 

60  07 

60  38 

61  10 

6141 

62  12 

63  14 

63  46 

64  17 

65  20 

65  51 

66  54 

56 

60 

67  48 

69  00 

69  36 

70  12 

70  48 

7124 

72  36 

73  12 

73  48 

75  00 

75  36 

76  48 

60 

n 

n 

If 

tt 

n 

n 

» 

" 

" 

n 

i> 

It 

A,h 

1.13 

1.15 

1.16 

1.17 

1.18 

1.19 

1.21 

1.22 

1.23 

1.25 

1.26 

1.28 

Ajh 

Log. 

0.053 

0.060 

0.064 

0.068 

0.071 

0.075 

0.082 

0.086 

0.089 

0.096 

0.100 

0.107 

Log. 

08 

70 

46 

19 

88 

55 

79 

36 

91 

91 

37 

21 

Limit 

66 

66 

65 

64 

63 

62 

62 

61 

60 

60 

59 

58 

Min- 
utes 

Merid- 
ian 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

/     // 

/      // 

/     // 

/      // 

/      // 

/     // 

/      // 

/      // 

Min. 

Min, 

4 

0  20 

0  21 

0  21 

0  22 

0  22 

0  22 

0  22 

0  22 

0  22 

0  23 

0  23 

0  24 

4 

8 

1  23 

123 

124 

126 

127 

128 

130 

131 

133 

134 

135 

136 

8 

12 

3  06 

3  08 

3  10 

3  13 

3  16 

3  19 

3  22 

3  25 

3  28 

3  31 

3  34 

3  36 

12 

16 

5  30 

5  36 

5  38 

5  43 

5  48 

5  53 

5  58 

6  03 

6  08 

6  13 

6  18 

6  24 

16 

20 

8  36 

8  44 

8  48 

8  56 

9  04 

9  12 

9  20 

9  28 

9  36 

9  44 

9  52 

10  00 

20 

24 

12  23 

12  35 

12  41 

12  52 

13  04 

13  15 

13  36 

13  38 

13  49 

14  01 

14  12 

14  24 

24 

28 

16  52 

17  07 

17  15 

17  30 

17  46 

18  02 

18  18 

18  34 

18  49 

19  05 

19  21 

19  36 

28 

32 

22  01 

22  21 

22  31 

22  52 

23  12 

23  33 

23  54 

24  14 

24  35 

24  55 

25  16 

25  36 

32 

36 

27  52 

28  18 

28  31 

28  57 

29  23 

29  49 

30  14 

30  40 

3106 

31  32 

31  58 

32  24 

36 

40 

34  24 

34  56 

35  12 

35  44 

36  16 

36  48 

37  20 

37  52 

38  24 

38  56 

39  28 

40  00 

40 

44 

41  37 

42  16 

42  36 

43  14 

43  53 

44  32 

45  10 

45  49 

46  27 

47  06 

47  25 

48  24 

44 

48 

49  32 

50  18 

50  41 

5127 

52  13 

52  59 

53  46 

54  32 

55  18 

56  04 

56  50 

57  36 

48 

52 

58  08 

59  02 

59  29 

60  23 

61  17 

62  11 

63  06 

64  00 

64  54 

65  48 

66  42 

67  36 

52 

56 

67  25 

68  28 

69  00 

70  02 

71  05 

72  08 

73  10 

74  13 

75  15 

76  18 

77  21 

78  24 

56 

60 

77  24 

78  36 

79  12 

80  24 

8136 

82  48 

84  00 

85  12 

86  24 

87  36 

88  48 

90  00 

60 

n 

It 

It 

n 

n 

" 

It 

It 

It 

It 

It 

It 

A,h 

1.29 

1.31 

1.32 

1.34 

1.36 

1.38 

1.40 

1.42 

1.44 

1.46 

1.48 

1.50 

A,h 

Log. 

0.110 

0.117 

0.120 

0.127 

0.133 

0.139 

0.146 

0.152 

0.158 

0.164 

0.170 

0.176 

Log. 

59 

27 

57 

10 

54 

88 

13 

29 

36 

35 

26 

09 

Limit 

58 

57 

57 

56 

55 

55 

54 

53 

53 

52 

51 

50 

Min- 
utes 

Merid- 
ian 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

AUi- 
tuiles 

Latitude  60°  Declination  Same  Name. 


359 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

.Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      // 

0  25 

138 

3  40 

6  32 

10  12 

14  41 

20  00 

26  07 

33  03 

40  48 

49  22 

58  45 

68  57 

79  58 

91  48 
It 

1.53 

/     // 

0  25 

1  39 
3  43 
6  37 

10  20 
14  53 
20  15 
26  27 
33  29 
4120 
50  01 
59  31 
69  51 
8101 
93  00 

1.55 

t       n 

0  25 

1  41 
3  48 
6  44 

10  32 
15  10 
20  39 
26  58 
34  08 
42  08 
50  59 
60  40 
71  12 
82  35 
94  48 

n 

1.58 

/       n 

0  26 

143 
3  51 
6  53 
10  44 
15  28 
2102 
27  28 
34  47 
42  56 
51  57 
61  49 
72  33 
84  09 

It 
1.61 

/      // 

0  27 

1  45 
3  56 
7  00 

10  56 
15  45 
21  25 
27  59 
35  26 
43  44 
52  55 
62  58 
73  54 
85  43 

It 
1.64 

/      // 

0  27 

147 
4  00 
7  08 
11  08 
16  02 
2149 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 

1.67 

/     // 

0  27 

1  49 
4  05 
7  15 

11  20 
16  19 
22  13 
29  01 
36  43 
45  20 
54  51 
65  15 
76  37 

1.70 

/     // 

0  28 

1  52 
4  11 
7  25 

1136 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 

n 

1.74 

t     II 

0  29 

1  54 
4  15 
7  33 

1148 
16  59 
23  08 
30  13 
38  14 
47  12 
57  07 
67  56 
79  46 

It 

0  29 
156 
4  20 

7  44 
12  04 
17  23 
23  39 
30  53 
39  06 
48  16 
58  24 
69  30 

It 
1.81 

/     // 

0  30 
159 

4  28 
7  56 
12  24 
17  52 
24  18 
3144 
40  11 
49  36 
60  01 
7125 

It 
1.86 

/     // 

0  30 

2  01 

4  34 

8  06 

12  40 

18  14 

24  50 

32  26 

4102 

50  40 

61  18 

72  58 

It 
1.90 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.184 
69 

0.190 
33 

0.198 
66 

0.206 
83 

0.214 

84 

0.222 

72 

0.230 
45 

0.240 
55 

0.247 
97 

0.257 
68 

0.269 
51 

0.278 
75 

Log. 

Limit 

49 

49 

48 

47 

46 

45 

45 

44 

43 

42 

41 

41 

Min- 
utas 

Merid- 
ian 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

Min. 

/       // 

/     // 

/      // 

1     II 

/     // 

/      // 

/      // 

/      // 

1     II 

/      // 

/     // 

/       n 

Min. 

4 

0  31 

0  32 

0  33 

0  34 

0  35 

0  37 

0  38 

0  40 

0  41 

0  44 

0  46 

0  47 

4 

8 

2  04 

2  08 

2  12 

2  16 

2  21 

2  26 

2  32 

2  37 

2  44 

2  51 

3  02 

3  10 

8 

12 

4  41 

4  48 

4  59 

5  07 

5  17 

5  28 

5  39 

5  54 

6  09 

6  27 

6  48 

7  09 

12 

16 

8  19 

8  32 

8  49 

9  05 

9  23 

9  44 

10  05 

10  30 

10  55 

1125 

12  00 

12  42 

16 

20 

13  00 

13  20 

13  48 

14  16 

14  40 

15  12 

15  44 

16  24 

17  04 

17  52 

18  48 

19  50 

20 

24 

18  43 

19  12 

19  52 

20  27 

2107 

2154 

22  40 

23  38 

24  35 

25  44 

27  04 

28  36 

24 

28 

25  29 

26  08 

27  03 

27  49 

28  45 

29  47 

30  50 

32  08 

33  25 

35  02 

36  52 

38  57 

28 

32 

33  17 

34  08 

35  20 

36  21 

37  33 

38  55 

40  16 

41  58 

43  41 

45  44 

48  07 

50  52 

32 

36 

42  07 

43  12 

44  43 

46  01 

47  31 

49  15 

51  00 

53  08 

55  18 

57  44 

60  55 

64  22 

36 

40 

52  00 

53  20 

55  12 

56  48 

58  40 

60  48 

62  56 

65  36 

68  16 

71  28 

40 

44 

62  55 

64  32 

66  48 

68  44 

70  59 

44 

48 

74  53 

76  48 

48 

52 

52 

56 

56 

60 

60 

II 

It 

It 

It 

" 

It 

It 

ft 

It 

It 

It 

n 

Ajh 

1.95 

2.00 

2.07 

2.13 

2.20 

2.28 

2.36 

2.46 

2.56 

2.68 

2.82 

2.98 

Aih 

Log. 

0.290 

0.301 

0.315 

0.328 

0.342 

0.357 

0.372 

0.390 

0.408 

0.428 

0.450 

0.474 

Log. 

03 

03 

97 

38 

42 

93 

91 

94 

24 

13 

25 

22 

Limit 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

Min- 
utes 

Merid- 
ian 

66° 

67^ 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

Alti- 
tudes 

J60 


Latitude  60**  Decimation  Same  Name. 


Declinations. 


48" 


0  51 
3  22 
7  35 
13  28 
21  03 
30  21 
41  17 
53  55 


3.16 


0.499 
69 


26 


78° 


49° 


0  54 
3  36 
8  07 
14  25 
22  32 
32  27 
44  10 
57  41 


3.38 


0.528 
92 


25 


79= 


50° 


0  59 
3  52 
8  42 
15  30 
24  12 
34  51 
47  26 


3.63 


0.559 
91 


24 


80° 


51° 


103 
4  13 
9  31 
16  53 
26  24 
38  01 
51  45 


3.96 


0.597 
70 


23 


81° 


52° 


1  10 
4  38 
10  25 
18  31 
28  56 
41  40 
56  42 


34 


0.637 
49 


22 


82° 


53° 


1  18 
5  10 
11  38 
20  42 
32  20 
46  34 


4.85 


0.685 
74 


20 


83° 


54° 


1  28 
5  53 
13  15 
23  33 
36  48 
53  00 


5.52 


0.741 
94 


18 


84° 


55° 


143 

6  54 

15  31 

27  33 

43  04 


6.46 


0.810 
23 


15 


85° 


56° 


12 


86° 


57° 


87° 


58° 


88° 


59° 


89° 


Hour 
Angles 


Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 


Log. 


Min- 
utes 


Alti- 
tudes 


Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/      // 

/     // 

/      // 

/     // 

/      // 

/      // 

/     // 

/      // 

/     // 

/     // 

/      // 

/      // 

]Min. 

4 

1  16 

101 

0  50 

0  42 

0  36 

0  31 

0  26 

4 

8 

5  05 

4  05 

3  22 

2  49 

2  25 

2  03 

1  42 

8 

12 

11  26 

9  10 

7  34 

6  20 

5  24 

4  39 

3  51 

12 

16 

20  18 

16  18 

13  27 

11  15 

9  36 

8  14 

6  53 

16 

20 

31  44 

25  29 

2100 

17  36 

15  00 

12  52 

10  44 

20 

24 

36  41 

30  14 

25  21 

21  36 

18  31 

15  28 

24 

28 

4109 

34  29 

29  24 

25  13 

21  02 

28 

32 

45  03 

38  24 

32  57 

27  28 

32 

36 

48  36 

41  41 

34  47 

36 

40 

5128 

42  56 

40 

44 

5157 

44 

48 

48 

52 

52 

56 

56 

60 

60 

t 

If 

r 

1 

t 

n 

» 

n 

H 

H 

II 

It 

Ajh 

4.76 

3.82 

3.15 

2.64 

2.25 

1.93 

1.61 

A,h 

Log. 

0.677 
61 

0.582 
06 

0.498 
31 

0.421 
60 

0.352 

18 

0.285 
56 

0.206 

83 

Log. 

Limit 

0 

3 

6 

9 

12 

16 

19 

22 

25 

28 

32 

36 

Min- 
utes 

Merid- 
ian 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

81° 

80° 

79° 

Alti- 
tudes 

Latitude  60°  Declination  ConitAtj  Name 

Declinations. 


361 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/      // 

0  18 

112 

2  42 

4  50 

7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 

1.13 

/     // 

0  18 

1  11 

2  41 
4  47 
7  28 

10  46 
14  38 
19  06 
24  12 
29  52 
36  09 
43  00 
50  28 
58  33 
67  12 

n 

1.12 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 

14  30 

18  56 

23  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 
It 

1.11 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 
66  00 

n 

1.10 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
41  51 
49  07 
56  58 

65  24 

It 

1.09 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 
It 

1.08 

/      // 

0  17 

108 

2  34 

4  34 

7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 

It 

1.07 

0  17 

108 

2  33 

4  31 

7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
It 

1.06 

/     // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 
It 

1.05 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 
It 

1.04 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

6148 
It 

1.03 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

n 

1.02 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.053 
08 

0.049 
22 

0.045 
32 

0.041 
39 

0.037 
43 

0.033 
42 

0.029 
39 

0.025 
31 

0.021 
19 

0.017 
03 

0.012 

84 

0.008 
60 

Log. 

Limit 

66 

66 

67 

67 

68 

68 

68 

69 

69 

70 

70 

70 

Min- 
utes 

Merid- 
ian 

30° 

29" 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/       // 

/      // 

/      // 

/      // 

/      // 

/      // 

/     // 

1     II 

/      // 

1      II 

1     II 

/      // 

Min. 

4 

0  16 

0  16 

0  15 

0  15 

0  15 

0  15 

0  15 

0  15 

0  15 

0  14 

0  14 

0  14 

4 

8 

1  04 

2  25 

104 
2  24 

103 

102 

102 
2  20 

101 
2  19 

101 
2  17 

100 

IGO 

0  59 

0  58 

0  58 

8 

12 

2  33 

2  22 

2  16 

2  16 

2  14 

2  13 

2  11 

12 

16 

4  19 

4  16 

4  13 

4  10 

4  08 

4  05 

4  03 

4  01 

4  00 

3  58 

3  55 

3  53 

16 

20 

6  44 

6  40 

6  36 

6  32 

6  28 

6  24 

6  20 

6  18 

6  16 

6  12 

6  08 

6  04 

20 

24 

9  42 

9  36 

9  30 

9  24 

9  18 

9  13 

9  07 

9  04 

9  01 

8  55 

8  50 

8  44 

24 

28 

13  12 

13  04 

12  57 

12  49 

12  41 

12  33 

12  25 

12  21 

12  17 

12  10 

12  02 

1154 

28 

32 

17  14 

17  04 

16  54 

16  44 

16  34 

16  23 

16  13 

16  08 

16  03 

15  53 

15  42 

15  32 

32 

36 

21  49 

2136 

21  23 

21  10 

20  57 

20  44 

20  31 

20  24 

20  18 

20  05 

19  52 

19  39 

36 

40 

26  56 

26  40 

26  24 

26  08 

25  52 

25  36 

25  20 

25  12 

25  04 

24  48 

24  32 

24  16 

40 

44 

32  35 

32  16 

31  56 

3137 

31  18 

30  58 

30  39 

30  29 

30  19 

30  00 

29  41 

29  21 

44 

48 

38  47 

38  24 

38  01 

37  38 

37  15 

36  52 

36  29 

36  18 

36  06 

35  43 

35  20 

34  57 

48 

52 

45  31 

45  04 

44  37 

44  10 

43  43 

43  16 

42  49 

42  35 

42  22 

41  55 

41  28 

4101 

52 

66 

52  47 

52  16 

5144 

51  13 

50  42 

50  10 

49  39 

49  22 

49  07 

48  36 

48  05 

47  33 

56 

60 

60  36 

60  00 

59  24 

58  48 

58  12 

57  36 

57  00 

56  42 

56  24 

55  48 

55  12 

54  36 

60 

" 

It 

It 

It 

n 

It 

It 

It 

It 

It 

It 

* 

Ajh 

1.01 

1.00 

0.99 

0.98 

0.97 

0.96 

0.95 

0.945 

0.94 

0.93 

0.92 

0.91 

Aih 

Log. 

0.004 

0.00 

9.995 

9.991 

9.986 

9.982 

9.977 

9.975 

9.973 

9.968 

9.963 

9.959 

Log. 

32 

64 

23 

77 

27 

72 

43 

13 

48 

79 
78 

04 

Limit 

71 

72 

73 

73 

73 

73 

74 

75 

76 

77 

79 

Min- 
utes 

Merid- 
ian 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

Alti- 
tudes 

362 


Latitude  60"  Declination  Contrary  Name. 

Declinations. — Inferior  Meridian. 


Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/  // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

0.90 
9.954 
24 

/  // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

11  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 

n 

0.89 

1 

1 

1 

II 

/ 

// 

n 

/ 

It 

// 

/ 

n 

II 

/ 

n 

// 

/ 

r 

/ 

T 

/   // 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 

n 

0.80 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.949 
39 

9.903 
09 

Log. 

Limit 

80 

80 

95 

Min-- 
utes 

Merid- 
ian 

6° 

5° 

4 

1° 

' 

1° 

2« 

> 

1° 

0= 

Y 

2' 

3 

° 

4° 

5° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/   // 

/  // 

/  // 

Min. 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

4 

8 

0  51 

0  50 

0  50 

0  50 

0  49 

0  49 

0  48 

0  48 

0  47 

0  46 

0  46 

0  45 

8 

12 

1  54 

1  53 

153 

151 

1  50 

150 

148 

147 

145 

144 

142 

1  41 

12 

16 

3  22 

3  21 

3  19 

3  17 

3  15 

3  14 

3  12 

3  09 

3  07 

3  04 

3  02 

2  59 

16 

20 

5  16 

5  14 

5  12 

5  08 

5  06 

5  04 

5  00 

4  56 

4  52 

4  48 

4  44 

4  40 

20 

24 

7  35 

7  32 

7  29 

7  23 

7  20 

7  18 

7  12 

7  06 

7  00 

6  55 

6  49 

6  43 

24 

28 

10  20 

10  16 

10  12 

10  04 

10  00 

9  56 

9  48 

9  40 

9  33 

9  25 

9  17 

9  09 

28 

32 

13  29 

13  24 

13  19 

13  09 

13  03 

12  58 

12  48 

12  38 

12  28 

12  17 

12  07 

11  57 

32 

36 

17  04 

16  57 

16  51 

16  38 

16  32 

16  25 

16  12 

15  59 

15  46 

15  33 

15  20 

15  07 

36 

40 

21  04 

20  56 

20  48 

20  32 

20  24 

20  16 

20  00 

19  44 

19  28 

19  12 

18  56 

18  40 

40 

44 

25  29 

25  20 

25  10 

24  51 

24  41 

24  31 

24  12 

23  52 

23  33 

23  14 

22  54 

22  35 

44 

48 

30  18 

30  07 

29  55 

29  32 

29  20 

29  09 

28  46 

28  23 

28  00 

27  37 

27  14 

26  51 

48 

52 

35  36 

35  23 

35  09 

34  42 

34  28 

34  15 

33  48 

33  21 

32  54 

32  27 

32  00 

31  33 

52 

56 

41  17 

41  02 

40  46 

40  15 

40  00 

39  44 

39  12 

38  41 

38  09 

37  38 

37  06 

36  35 

56 

60 

47  24 

47  06 

46  48 

46  12 

44  54 

45  36 

45  00 

44  24 

43  48 

43  12 

42  36 

42  00 

60 

n 

n 

n 

II 

n 

» 

n 

It 

n 

It 

It 

It 

A,h 

0.79 

0.785 

0.78 

0.77 

0.765 

0.76 

0.75 

0.74 

0.73 

0.72 

0.71 

0.70 

A,h 

Log. 

9.897 

9.894 

9.892 

9.886 

9.883 

9.880 

9.875 

9.869 

9.863 

9.857 

9.851 

9.845 

Log. 

63 

87 

09 

49 

66 

81 

06 

23 

32 

33 

26 

10 

Limit 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

Min- 
utes 

Merid- 
ian 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

Alti- 
tudes 

Latitude  60°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


363 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Mill. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1     II 

Oil 

0  44 

140 

2  58 

4  38 

6  40 

9  05 

1151 

15  01 

18  32 

22  25 

26  40 

31  19 

36  19 

41  42 

0.695 

/      // 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

1146 

14  55 

18  24 

22  16 

26  29 

3105 

36  04 

41  24 

n 

0.69 

/     // 

Oil 

0  44 

1  38 

2  54 
4  32 
6  32 
8  53 

1136 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 
n 

0.68 

/     /' 

Oil 
0  44 
136 
2  52 

4  28 
6  26 
8  45 
11  26 
14  29 
17  52 
21  38 
25  43 
30  11 
35  02 
40  12 

n 

0.67 

/     // 

Oil 

0  42 

1  35 

2  49 
4  24 
6  21 
8  37 

11  15 
14  16 
17  36 
21  18 
25  20 
29  44 
34  30 
39  36 

0.66 

/      // 

Oil 

0  41 

132 

2  44 

4  16 

6  09 

8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
It 

0.64 

/     // 

Oil 

0  41 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 

0.63 

1     II 

0  10 

0  39 

1  29 

2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

n 

0.62 

/     // 

0  10 
0  40 
127 
2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
3153 
36  36 

n 

0.61 

/      // 

0  10 
0  38 
126 
2  34 

4  00 

5  46 
7  50 

10  14 
12  58 
16  00 
19  22 
23  02 
27  02 
31  22 
36  00 

H 

0.60 

1     II 

0  09 
0  38 
125 

2  31 

3  56 
5  40 
7  43 

10  04 

12  45 

15  44 

19  02 

22  39 

26  35 

30  50 

35  24 
II 

0.59 

/     // 

0  09 
0  38 
124 

2  28 

3  52 
5  34 
7  35 
9  54 

12  32 
15  28 
18  43 
22  16 
26  08 
30  19 
34  48 

0.58 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.841 
98 

9.838 
85 

9.832 
51 

9.826 
07 

9.819 
54 

9.806 
18 

9.799 
34 

9.792 
39 

9.785 
33 

9.778 
15 

9.770 
85 

9.763 
43 

Log. 

Limit 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

Min- 
utes 

Merid- 
ian 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28°      29° 

Alti- 
tudes 

Declinations 

.  —  Inferior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/     // 

/     // 

/     // 

/     // 

/     // 

1     II 

/      '/ 

1     II 

1     II 

/      // 

/      // 

/      // 

Min. 

4 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

0  08 

0  07 

0  07 

0  07 

0  07 

0  06 

4 

8 

0  37 

0  37 

0  36 

0  35 

0  33 

0  32 

0  31 

0  31 

0  30 

0  29 

0  28 

0  28 

8 

12 

122 

121 

1  19 

1  16 

1  15 

1  12 

1  11 

108 

107 

1  05 

104 

1  02 

12 

16 

2  26 

2  23 

2  21 

2  16 

2  13 

2  08 

2  05 

2  00 

157 

155 

1  52 

1  50 

16 

20 

3  48 

3  44 

3  40 

3  32 

3  28 

3  20 

3  16 

3  08 

3  04 

3  00 

2  56 

2  52 

20 

24 

5  28 

5  23 

5  17 

5  05 

5  00 

4  48 

4  42 

4  30 

4  25 

4  19 

4  13 

4  07 

24 

28 

7  27 

7  19 

7  11 

6  56 

6  48 

6  32 

6  25 

6  09 

6  01 

5  53 

5  45 

5  38 

28 

32 

9  44 

9  33 

9  23 

9  03 

8  52 

8  32 

8  22 

8  02 

7  51 

7  41 

7  31 

7  21 

32 

36 

12  19 

12  06 

11  53 

11  27 

11  14 

10  48 

10  35 

10  09 

9  56 

9  43 

9  30 

9  17 

36 

40 

15  12 

14  56 

14  40 

14  08 

13  52 

13  20 

13  04 

12  32 

12  16 

12  00 

11  44 

11  28 

40 

44 

18  24 

18  04 

17  45 

17  06 

16  47 

16  08 

15  48 

15  10 

14  50 

14  31 

14  12 

13  52 

44 

48 

21  53 

21  30 

2107 

20  21 

19  58 

19  12 

18  49 

18  03 

17  40 

17  17 

16  54 

16  31 

48 

52 

25  41 

25  14 

24  47 

23  53 

23  26 

22  32 

22  05 

21  11 

20  46 

20  17 

19  50 

19  23 

52 

56 

29  48 

29  16 

28  45 

27  42 

27  11 

26  08 

25  36 

24  34 

24  02 

23  31 

23  00 

22  28 

56 

60 

34  12 

33  36 

33  00 

3148 

31  12 

30  00 

29  24 

28  12 

27  36 

27  00 

26  24 

25  48 

60 

It 

It 

H 

n 

n 

* 

H 

n 

n 

It 

II 

II 

A,h 

0.57 

0.56 

0.55 

0.53 

0.52 

0.50 

0.49 

0.47 

0.46 

0.45 

0.44 

0.43 

A,h 

Log. 

9.755 

9.748 

9.740 

9.724 

9.716 

9.698 

9.690 

9.672 

9.662 

9.653 

9.643 

9.633 

Log. 

87 

19 

36 

28 

00 

97 

20 

10 

76 

21 

45 

47 

Limit 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

95 

Min- 
utes 

Merid- 
ian 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

Alti- 
tudes 

364 


Latitude  6i'*  Declination  Same  Name. 


Declinations. 


Hour 
Angk'H 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Min. 

/  If 

/  // 

1      " 

1        n 

/  // 

/  // 

/  // 

/  // 

/  // 

/  // 

/  II 

/  // 

Min. 

4 

0  17 

0  18 

0  18 

0  18 

0  18 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

4 

8 

1  10 

1  10 

1  11 

1  11 

1  12 

1  13 

1  14 

1  15 

1  15 

1  16 

1  17 

1  18 

8 

12 

2  37 

2  38 

2  39 

2  41 

2  42 

2  44 

2  47 

2  48 

2  50 

2  51 

2  54 

2  56 

12 

16 

4  39 

4  42 

4  45 

4  47 

4  50 

4  52 

4  57 

5  00 

5  02 

5  05 

5  10 

5  12 

16 

20 

7  16 

7  20 

7  24 

7  28 

7  32 

7  36 

7  44 

7  48 

7  52 

7  56 

8  04 

8  08 

20 

24 

10  28 

10  34 

10  40 

10  46 

10  51 

10  57 

1109 

11  14 

11  20 

1126 

1137 

11  43 

24 

28 

14  15 

14  22 

14  30 

14  38 

14  46 

14  53 

15  09 

15  17 

15  25 

15  33 

15  49 

15  57 

28 

32 

18  36 

18  46 

18  56 

19  06 

19  17 

19  27 

19  47 

19  58 

20  08 

20  18 

20  39 

20  49 

32 

36 

23  33 

23  46 

23  59 

24  12 

24  25 

24  38 

25  04 

25  17 

25  30 

25  43 

26  08 

26  21 

36 

40 

29  04 

29  20 

29  36 

29  52 

30  08 

30  24 

30  56 

31  12 

31  28 

31  44 

32  16 

32  32 

40 

44 

35  10 

35  30 

35  49 

36  09 

36  28 

36  47 

37  26 

37  46 

38  05 

38  24 

39  02 

39  22 

44 

48 

41  51 

42  14 

42  37 

43  00 

43  23 

43  46 

44  32 

44  55 

45  18 

45  41 

46  28 

46  51 

48 

52 

49  07 

49  34 

50  01 

50  28 

50  55 

51  22 

52  16 

52  43 

53  10 

53  37 

54  32 

54  59 

52 

56 

56  58 

57  30 

58  01 

58  33 

59  04 

59  35 

60  38 

61  10 

61  41 

62  12 

63  14 

63  46 

56 

60 

65  24 

66  00 

66  36 

67  12 

67  48 

68  24 

69  36 

70  12 

70  48 

71  24 

72  36 

73  12 

60 

n 

It 

If 

n 

n 

n 

n 

If 

n 

n 

n 

n 

A,h 

1.09 

1.10 

1.11 

1.12 

1.13 

1.14 

1.16 

1.17 

1.18 

1.19 

1.21 

1.22 

A,h 

Log. 

0.037 

0.041 

0.045 

0.049 

0.053 

0.056 

0.064 

0.068 

0.071 

0.075 

0.082 

0.086 

Log 

43 

39 

32 

22 

08 

90 

46 

19 

88 

55 

79 

36 

Limit 

67 

66 

65 

64 

63 

63 

63 

62 

61 

61 

61 

60 

Min- 
utes 

Merid- 
ian 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/  II 

0  19 

1  19 

2  57 
5  15 
8  12 

11  48 

16  05 

21  00 

26  34 

32  48 

39  41 

47  14 

55  26 

64  17 

73  48 
n 

1.23 

r       " 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
21  20 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 
75  00 

1.25 

1     II 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 
16  28 
21  30 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 
75  36 

n 

1.26 

/  // 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 
16  44 
21  51 
27  39 
34  08 
41  18 
49  09 
57  41 
66  54 
76  48 

1.28 

/  // 

0  20 

123 

3  06 

5  30 

8  36 

12  23 

16  52 

22  01 

27  52 

34  24 

4137 

49  32 

58  08 

67  25 

77  24 

n 

1.29 

1     II 

0  21 

123 

3  08 

5  36 

8  44 

12  35 

17  07 

22  21 

28  18 

34  56 

42  16 

50  18 

59  02 

68  28 

78  36 

n 

1.31 

/  // 

0  21 

1  25 
3  11 
5  41 
8  52 

12  46 
17  23 
22  42 
28  44 
35  28 
42  55 
51  04 
59  56 
69  31 
79  48 

n 

1.33 

/  // 

0  22 

126 

3  14 

5  46 

9  00 

12  58 

17  38 

23  02 

29  10 

36  00 

43  34 

51  50 

60  50 

70  34 

8100 

1.35 

0  22 
127 
3  16 

5  48 
9  04 
13  04 
17  46 
23  12 
29  23 
36  16 
43  53 
52  13 
61  17 
7105 
8136 

n 

1.36 

1     II 

0  22 

128 

3  19 

5  53 

9  12 

13  15 

18  02 

23  33 

29  49 

36  48 

44  32 

52  59 

62  11 

72  08 

82  48 

n 

1.38 

/  // 

0  22 

1  30 
3  22 
5  58 
9  20 

13  26 
18  18 
23  54 
30  14 
37  20 
45  10 
53  46 
63  06 
73  10 
84  00 

n 

1.40 

/  // 

0  22 

131 

3  25 

6  03 

9  28 

13  38 

18  34 

24  14 

30  40 

37  52 

45  49 

54  32 

64  00 

74  13 

85  12 

n 

1.42 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.089 
91 

0.096 
91 

0.100 
37 

0.107 
21 

0.110 
59 

0.117 

27 

0.123 

85 

0.130 
33 

0.133 
54 

0.139 

88 

0.146 
13 

0.152 
29 

Log. 

Limit 

59 

59 

58 

58 

57 

56 

56 

55 

55 

54 

53 

52 

Min- 
utes 

Merid- 
ian 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

Alti- 
tudes 

Latitude  6t°  Declination  Same  Name. 

Declinations. 


365 


Hour  j  nAo     i   nco 

Angles;  ■^^    ^3 

26° 

27° 

28° 

29° 

30° 

31°   32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/  » 

0  23 

133 

3  28 

6  08 

9  36 

13  49 

18  49 

24  35 

3106 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 

ir 

1.44 

0  23 

1  35 
3  32 
6  16 
9  48 

14  06 
19  13 
25  06 
31  45 
39  12 
47  26 
56  27 
66  15 
76  50 
88  12 

n 

1.47 

/  // 

0  24 

136 

3  36 

6  24 

10  00 

14  24 

19  36 

25  36 

32  24 

40  00 

48  24 

57  36 

67  36 

78  24 

90  00 

H 

1.50 

0  24 

137 

3  39 

6  29 

10  08 

14  36 

19  52 

25  56 

32  50 

40  32 

49  03 

58  22 

68  30 

79  27 

91  12 

n 

1.52 

/  // 

025 

139 

3  43 

6  37 

10  20 

14  53 

20  15 

26  27 

33  29 

41  20 

50  01 

59  31 

69  51 

8101 

It 
1.55 

/  // 

0  25 

1  41 
3  46 
6  42 

10  28 
15  04 
20  31 
26  48 
33  55 
41  52 
50  40 
60  17 
70  45 
82  04 

n 

1.57 

/  // 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
51  38 
61  26 
72  06 
83  38 

It 
1.60 

0  27 
145 
3  56 

7  00 
10  56 
15  45 
21  25 
27  59 
35  26 
43  44 
52  55 
62  58 
73  54 
85  43 

It 
1.64 

I  II 

0  27 
147 
4  00 
7  08 

II  08 
16  02 
2149 
28  30 
36  05 
44  32 
53  54 
64  07 
75  15 
87  18 

It 
1.67 

t     II 

0  27 

1  50 
4  06 
7  18 

1124 
16  25 
22  21 
29  11 
36  56 
45  36 
55  10 
65  38 
77  04 

1.71 

0  28 

1  52 
4  11 
7  25 

11  36 
16  42 
22  44 
29  42 
37  35 
46  24 
56  08 
66  47 
78  25 

It 
1.74 

/   // 

0  29 

154 

4  17 

7  35 

11  52 

17  05 

23  16 

30  23 

38  27 

47  28 

57  26 

68  19 

It 
1.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

liOg. 

0.158 
36 

0.167 
32 

0.176 
09 

0.181 

84 

0.190 
33 

0.195 
90 

0.204 
12 

0.214 

84 

0.222 

72 

0.233 
00 

0.240 
55 

0.250 
42 

Log. 

Limit 

51 

51 

50 

49 

48 

47 

47 

46 

45 

44 

43 

42 

Min- 
utes 

Merid- 
ian 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45°  _ 

46° 

47° 

Hour 
Angles 

/  // 

/  // 

/  It 

t       n 

/  // 

/  // 

/  // 

1     II 

/  // 

/  // 

/  // 

Min. 

Min. 

4 

0  30 

0  30 

0  31 

0  31 

0  33 

0  34 

0  35 

0  37 

0  38 

0  39 

0  42 

0  44 

4 

8 

157 

2  00 

2  03 

2  07 

2  11 

2  15 

2  21 

2  25 

2  31 

2  37 

2  47 

2  58 

8 

12 

4  23 

4  31 

4  39 

4  47 

4  54 

5  06 

5  17 

5  28 

5  40 

5  52 

6  16 

6  37 

12 

16 

7  49 

8  01 

8  14 

8  29 

■  8  42 

9  02 

9  23 

9  43 

10  04 

10  24 

11  06 

11  43 

16 

20 

12  12 

12  32 

12  52 

13  16 

13  36 

14  08 

14  40 

15  12 

15  44 

16  16 

17  20 

18  20 

20 

24 

17  34 

18  03 

18  31 

19  06 

19  35 

20  21 

21  07 

21  54 

22  40 

23  25 

24  58 

26  24 

24 

28 

23  55 

24  34 

25  13 

26  01 

26  39 

27  41 

28  45 

29  47 

30  50 

3153 

33  59 

35  57 

28 

32 

31  14 

32  05 

32  57 

33  58 

34  49 

36  11 

37  33 

38  55 

40  16 

4139 

44  22 

46  56 

32 

36 

39  32 

40  37 

4141 

42  59 

44  04 

45  48 

47  31 

49  15 

50  59 

52  42 

56  10 

59  24 

36 

40 

48  48 

50  08 

51  18 

53  04 

54  24 

56  32 

58  40 

60  48 

62  56 

65  04 

69  20 

40 

44 

59  03 

60  40 

62  16 

64  12 

65  49 

68  25 

70  59 

44 

48 

70  16 

72  11 

74  07 

48 

52 

52 

56 

56 

60 

60 

It 

n 

It 

It 

It 

It 

It 

It 

It 

It 

n 

n 

Ajh 

1.83 

1.88 

1.93 

1.99 

2.04 

2.12 

2.20 

2.28 

2.36 

2.44 

2.60 

2.75 

A,h 

Log. 

0.262 

0.274 

0.285 

0.298 

0.309 

0.326 

0.342 

0.357 

0.372 

0.387 

0.414 

0.439 

Log. 

45 

16 

56 

85 

63 

34 

42 

93 

91 

39 

97 

33 

Limit 

41 

40 

39 

38 

38 

37 

36 

35 

34 

33 

32 

31 

Min- 
utes 

Merid- 
ian 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

Alti- 
tudes 

366 


Latitude  6i°  Decimation  Same  Name. 

Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/      // 

/      // 

1     It 

/      // 

/      // 

/     // 

/     // 

Min. 

Min. 

4 

0  47 

0  49 

0  51 

0  55 

100 

106 

1  13 

1  23 

1  38 

4 

8 

3  07 

3  15 

3  26 

3  41 

4  00 

4  23 

4  54 

5  34 

6  31 

8 

12 

7  00 

7  19 

7  42 

8  17 

9  00 

9  53 

1101 

12  32 

14  39 

12 

16 

12  20 

13  01 

13  42 

14  43 

16  00 

17  35 

19  35 

22  16 

26  05 

16 

20 

19  20 

20  20 

21  24 

23  00 

25  00 

27  28 

30  36 

34  48 

40  44 

20 

24 

27  50 

29  17 

30  49 

33  07 

36  00 

39  34 

44  04 

24 

28 

37  54 

39  51 

4157 

45  05 

49  00 

53  50 

28 

32 

49  30 

52  03 

54  47 

58  53 

32 

36 

36 

40 

40 

44 

44 

48 

48 

62 

52 

56 

56 

60 

60 

It 

n 

n 

H 

It 

n 

It 

It 

It 

H 

It 

n 

Ajh 

2.90 

3.05 

3.21 

3.45 

3.75 

4.12 

4.59 

5.22 

6.11 

A,h 

Log. 

0.462 

0.484 

0.506 

0.537 

0.574 

0.614 

0.661 

0.717 

0.786 

Log. 

40 

30 

51 

82 

03 

90 

81 

67 

04 

Limit 

28 

27 

26 

25 

24 

22 

20 

17 

15 

12 

9 

6 

Min- 
utes 

Merid- 
ian 

77° 

78° 

79 

0 

BO 

0 

81° 

82 

o 

83 

0 

84° 

85° 

86° 

87° 

88° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63°      64° 

B5°      66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 
4 

1       i> 

/      // 

1 

// 

/ 

//    /      // 

1 

1  11 

1     II    1 
0  59 

II 
0  46 

/      // 
0  39 

/      II 
0  33 

/      // 
0  27 

Min. 
4 

8 

4  45 

3  53 

3  07 

2  37 

2  12 

1  47 

8 

12 

i 

10  40 

8  44 

7  02 

5  53 

4  57 

4  00 

12 

16 

. .       18  56 

15  32    \ 

2  30 

10  27 

8  47 

7  08 

16 

20 

29  36 

24  16    ] 

9  32 

16  20 

13  44 

11  08 

20 

24 

34  57    2 

8  07 

23  31 

19  47 

16  02 

24 

28 

8  18 

32  01 

26  55 

21  49 

28 

32 

4149 

35  09 

28  30 

32 

36 

44  30 

36  05 

36 

40 

44  32 

40 

44 
48 
52 
56 
60 

It 

h 

1 

1 

It 

It          It 

It 

It 

It 

It 

44 
48 
52 
56 
60 

A,h 

4.44 

3.64     S 

.93 

2.45 

2.06 

1.67 

A,h 

Log. 

0.647 

38 

0.561    C 
10 

.466 

87 

0.389 
17 

0.313 

87 

0.222 

72 

Log. 

Limit 

3 

0 

3 

6 

9 

14        17 

20 

23 

27 

31 

35 

Min- 
utes 

Merid- 
ian 

89° 

90° 

8 

9° 

8 

8° 

87° 

86°      85 

o 

84° 

83° 

82 

o 

81° 

80° 

Alti. 
tudes 

Latitude  61°  Declination  Contrary  Name. 

Declinations. 


367 


Hour 

Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 

Angles 

/      // 

/      // 

/      // 

/      // 

/      // 

/           IT 

/      // 

/      // 

/      // 

/      // 

Min. 

Min. 

4 

0  17 

0  17 

0  17 

0  17 

0  17 

0  17 

0  16 

0  16 

0  16 

0  16 

0  15 

0  15 

4 

8 

1  10 

109 

108 

1  08 

107 

107 

106 

1  05 

104 

104 

103 

102 

8 

12 

2  37 

2  36 

2  34 

2  33 

2  31 

2  30 

2  28 

2  27 

2  25 

2  24 

2  23 

2  22 

12 

16 

4  39 

4  36 

4  34 

4  31 

4  29 

4  26 

4  24 

4  21 

4  19 

4  16 

4  13 

4  10 

16 

20 

7  16 

7  12 

7  08 

7  04 

7  00 

6  56 

6  52 

6  48 

6  44 

6  40 

6  36 

6  32 

20 

24 

10  28 

10  22 

10  16 

10  11 

10  05 

9  59 

9  53 

9  48 

9  42 

9  36 

9  30 

9  24 

24 

28 

14  15 

14  07 

13  59 

13  51 

13  43 

13  35 

13  28 

13  20 

13  12 

13  04 

12  57 

12  49 

28 

32 

18  36 

18  26 

18  16 

18  05 

17  55 

17  45 

17  35 

17  24 

17  14 

17  04 

16  54 

16  44 

32 

36 

23  33 

23  20 

23  07 

22  54 

22  41 

22  28 

22  15 

22  02 

21  49 

21  36 

2123 

21  10 

36 

40 

29  04 

28  48 

28  32 

28  16 

28  00 

27  44 

27  28 

27  12 

26  56 

26  40 

26  24 

26  08 

40 

44 

35  10 

34  51 

34  22 

34  12 

33  53 

33  33 

33  14 

32  55 

32  35 

32  16 

3156 

31  37 

44 

48 

4151 

41  28 

4105 

40  42 

40  19 

39  56 

39  33 

39  10 

38  47 

38  24 

38  01 

37  38 

48 

52 

49  07 

48  40 

48  13 

47  46 

47  19 

46  52 

46  25 

45  58 

45  31 

45  04 

44  37 

44  10 

52 

56 

56  58 

56  27 

55  56 

55  24 

54  53 

54  21 

53  50 

53  19 

52  47 

52  16 

5144 

51  13 

56 

60 

65  24 

64  48 

64  12 

63  36 

63  00 

62  24 

6148 

61  12 

60  36 

60  00 

59  24 

58  48 

60 

It 

n 

" 

n 

n 

If 

IT 

n 

n 

n 

n 

n 

A,h 

1.09 

1.08 

1.07 

1.06 

1.05 

1.04 

1.03 

1.02 

1.01 

1.00 

0.99 

0.98 

A,h 

Log. 

0.037 

0.033 

0.029 

0.025 

0.021 

0.017 

0.012 

0.008 

0.004 

0.00 

9.995 

9.991 

Log. 

43 

42 

38 

31 

19 

03 
70 

84 

60 

32 

64 

23 

Limit 

68 

68 

69 

69 

70 

70 

71 

71 

72 

72 

72 

Min- 
utes 

Merid- 
ian 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

1       II 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 

0.97 

/      // 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

n 

0.96 

0  15 

101 

2  18 

4  04 

6  22 

9  10 

12  29 

16  18 

20  37 

25  28 

30  49 

36  40 

43  03 

49  54 

57  18 

n 

0.955 

1     II 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

n 

0.95 

1     II 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

n 

0.94 

/      // 
0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 

55  48 

It 

0.93 

1     II 
0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 
15  42 
19  52 
24  32 
29  41 
35  20 
41  28 
48  05 

55  12 

n 

0.92 

/      II 
0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 
54  36 

n 

0.91 

1     II 
0  14 
0  57 

2  10 

3  51 
6  02 
8  41 

1150 
15  27 
19  32 
24  08 
29  12 
34  45 
40  48 
47  18 
54  18 

H 

0.905 

I  II 
0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

II  46 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

It 

0.90 

I  II 
0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

II  38 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

It 

0.89 

/      // 
0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 
15  01 
19  01 
23  28 
28  24 
33  47 
39  39 
46  00 
52  48 

n 

0.88 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.986 
77 

9.982 
27 

9.980 
00 

9.977 
72 

9.973 
13 

9.968 
48 

9.963 
79 

9.959 
04 

9.956 
65 

9.954 
24 

9.949 
39 

9.944 
48 

Log. 

Limit 

72 

73 

74 

74 

74 

74 

75 

76 

77 

78 

79 

80 

Min- 
utes 

Merid- 
ian 

17° 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

Alti- 
tudes 

368 


Latitude  6i°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

1122 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

/r 

0.87 

/ 

/ 

/ 

// 

It 

H 

n 

H 

f 

1 

/ 

T 

/ 

r 

/     // 

0  13 

0  51 

1  55 
3  25 
5  20 
7  41 

10  27 
13  39 
17  17 
21  20 
25  49 
30  43 
36  03 
4149 
48  00 

n 

0.80 

/      // 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

2104 

25  29 

30  18 

35  36 

41  17 

47  24 
It 

0.79 

/     It 

0  12 

0  50 

153 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 
It 

0.78 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.939 
52 

9.903 
09 

9.897 
63 

9.892 
09 

Log. 

Limit 

80 

99 

99 

99 

Min- 
utes 

Merid- 
ian 

5° 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

1     II 

1     II 

/      // 

1     II 

/      // 

/      // 

/      // 

/      // 

Min. 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

4 

8 

0  50 

0  50 

0  49 

0  48 

0  47 

0  47 

0  46 

0  46 

0  46 

0  45]     0  44 

0  43 

8 

12 

152 

151 

150 

148 

147 

145 

1  45 

144 

1  42 

141 

139 

137 

12 

16 

3  18 

3  17 

3  14 

3  12 

3  09 

3  07 

3  06 

3  04 

3  02 

2  59 

2  57 

2  54 

16 

20 

5  10 

5  08 

5  04 

5  00 

4  56 

4  52 

4  50 

4  48 

4  44 

4  40 

4  36 

4  32 

20 

24 

7  26 

7  23 

7  18 

7  12 

7  06 

7  00 

6  57 

6  55 

6  49 

6  43 

6  38 

6  32 

24 

28 

10  08 

10  04 

9  56 

9  48 

9  40 

9  33 

9  29 

9  25 

9  17 

9  09 

9  01 

8  53 

28 

32 

13  14 

13  09 

12  58 

12  48 

12  38 

12  28 

12  22 

12  17 

12  07 

11  57 

11  46 

11  36 

32 

36 

16  44 

16  38 

16  25 

16  12 

15  59 

15  46 

15  40 

15  33 

15  20 

15  07 

14  55 

14  42 

36 

40 

20  40 

20  32 

20  16 

20  00 

19  44 

19  28 

19  20 

19  12 

18  56 

18  40 

18  24 

18  08 

40 

44 

25  00 

24  51 

24  31 

24  12 

23  52 

23  33 

23  23 

23  14 

22  54 

22  35 

22  16 

2157 

44 

48 

29  44 

29  32 

29  09 

28  46 

28  23 

28  00 

27  49 

27  37 

27  14 

26  51 

26  29 

26  06 

48 

52 

34  55 

34  42 

34  15 

33  48 

33  21 

32  54 

32  40 

32  27 

32  00 

31  33 

31  05 

30  38 

52 

56 

40  30 

40  15 

39  44 

39  12 

38  40 

38  09 

37  53 

37  38 

37  07 

36  35 

36  04 

35  33 

56 

60 

46  30 

46  12 

45  36 

45  00 

44  24 

43  48 

43  30 

43  12 

42  36 

42  00 

4124 

40  48 

60 

1 

It 

It 

It 

It 

It 

It 

It 

n 

II 

It 

It 

A,h 

0.775 

0.77 

0.76 

0.75 

0.74 

0.73 

0.725 

0.72 

0.71 

0.70 

0.69 

0.68 

A,h 

Log. 

9.889 

9.886 

9.880 

9.875 

9.869 

9.863 

9.860 

9.857 

9.851 

9.845 

9.838 

9.832 

Log. 

30 

49 

81 

06 

23 

32 

34 

33 

26 

10 

85 

51 

Limit 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

Min- 
utes 

Merid- 
ian 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

Alti- 
tudes 

Latitude  6J°  Decimation  Contrary  Name. 

Declinatioxs.  —  Inferior  Meridian. 


369 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

'      " 

/      // 

1     II 

/      " 

/      // 

/     II 

/     '/ 

'      II 

/     // 

1     II 

/     // 

/      II 

Min. 

4 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  10 

0  09 

0  09 

0  09 

4 

8 

0  43 

0  43 

0  43 

0  42 

0  41 

0  41 

0  39 

0  40 

0  39 

0  38 

0  38 

0  37 

8 

12 

136 

135 

133 

132 

1  32 

130 

129 

1  27 

1  26 

1  25 

1  24 

1  22 

12 

16 

2  52 

2  49 

2  47 

2  45 

2  44 

2  42 

2  39 

2  37 

2  34 

2  31 

2  28 

2  26 

16 

20 

4  28 

4  24 

4  20 

4  18 

4  16 

4  12 

4  08 

4  04 

4  00 

3  56 

3  52 

3  48 

20 

24 

6  26 

6  21 

6  18 

6  12 

6  09 

6  03 

5  58 

5  52 

5  46 

5  40 

5  34 

5  28 

24 

28 

8  45 

8  37 

8  33 

8  25 

8  21 

8  14 

8  06 

7  58 

7  50 

7  43 

7  35 

7  27 

28 

32 

1126 

11  15 

11  10 

1100 

10  55 

10  45 

10  34 

10  24 

10  14 

10  04 

9  54 

9  44 

32 

36 

14  29 

14  16 

14  09 

13  56 

13  50 

13  37 

13  24 

13  11 

12  58 

12  45 

12  32 

12  19 

36 

40 

17  52 

17  36 

17  28 

17  12 

17  04 

16  48 

16  32 

16  16 

16  00 

15  44 

15  28 

15  12 

40 

44 

2138 

21  18 

2109 

20  49 

20  39 

20  20 

20  01 

19  41 

19  22 

19  02 

18  43 

18  24 

44 

48 

25  43 

25  20 

25  07 

24  45 

24  34 

24  11 

23  48 

23  25 

23  02 

22  39 

22  16 

2153 

48 

52 

30  11 

29  44 

29  30 

29  03 

28  50 

28  23 

27  56 

27  29 

27  02 

26  25 

26  08 

25  14 

52 

56 

35  02 

34  40 

34  14 

33  43 

33  27 

32  56 

32  25 

3153 

3122 

30  50 

30  19 

29  48 

56 

60 

40  12 

39  36 

39  18 

38  42 

38  24 

37  48 

37  12 

36  36 

36  00 

35  24 

34  48 

34  12 

60 

ir 

It 

n 

" 

n 

If 

If 

n 

n 

H 

n 

n 

A,h 

0.67 

0.66 

0.655 

0.645 

0.64 

0.63 

0.62 

0.61 

0.60 

9.778 

0.59 

0.58 

0.57 

A,h 

Log. 

9.826 

9.819 

9.816 

9.809 

9.806 

9.799 

9.792 

9.785 

9.770 

9.763 

9.755 

Log. 

07 

54 

24 

56 

18 

34 

39 

33 

15 

85 

43 

87 

Limit 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

99 

Min- 
utes 

Merid- 
ian 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28°      29° 

30° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


60°      61°      62°      63° 


0  09 
0  36 
121 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
21  30 
25  14 
29  16 
33  36 

n 

0.56 


9.748 
19 

99 
31° 


0  09 

0  36 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

11  53 
14  40 
17  45 
21  07 
24  47 
28  45 
33  00 

n 

0.55 


9.740 
36 

99 
32° 


0  09 

0  35 

1  16 

2  16 

3  32 

5  05 

6  56 
9  03 

11  27 
14  08 
17  06 
20  21 
23  53 
27  42 
31  48 

n 

0.53 


9.724 
28 

99 
33° 


0  09 

0  33 

1  15 

2  13 

3  28 

5  00 

6  48 
8  52 

11  14 
13  52 
16  47 
19  58 
23  26 
27  11 
31  12 

n 

0.52 


9.716 
00 

99 
34° 


64° 


0  08 

0  32 

1  13 

2  11 

3  24 

4  54 
6  40 
8  42 

11  01 
13  36 
16  27 
19  35 
22  59 
26  39 

30  36 

It 

0.51 


9.707 
57 

99 
35° 


65= 


0  08 

0  32 

1  12 

2  08 

3  20 

4  48 
6  32 
8  32 

10  48 
13  20 
16  08 
19  12 
22  32 
26  08 
30  00 

n 

0.50 


9.698 
97 

99 
36° 


66° 


0  08 

0  31 

1  11 

2  05 

3  16 

4  42 
6  25 
8  22 

10  35 
13  04 
15  48 
18  49 
22  05 
25  36 
29  24 

n 

0.49 


9.690 
20 

99 
37° 


67° 


0  07 

0  31 

1  08 

2  00 

3  08 

4  30 
6  09 
8  02 

10  09 
12  32 
15  10 
18  03 
21  11 
24  34 
28  12 

n 

0.47 


9.672 
10 

99 
38° 


68° 


0  07 

0  30 

1  07 
157 

3  04 

4  25 

6  01 

7  51 
9  56 

12  16 
14  50 
17  40 
20  46 
24  02 

27  36 

It 

0.46 


9.662 
76 

99 

39° 


69°      70° 


0  07 

0  29 
105 

1  55 

3  00 

4  19 

5  53 
7  41 
9  43 

12  00 

14  31 

17  17 

20  17 

23  31 

27  00 
It 

0.45 


9.653 
21 

99 
40° 


0  07 

0  28 
102 

1  50 

2  52 

4  07 

5  38 
7  21 
9  17 

11  28 

13  52 

16  31 

19  23 

22  28 

25  48 
If 

0.43 


9.633 
47 

99 
41° 


71° 


0  06 
0  27 
101 
147 
2  48 

4  02 

5  30 
7  10 
9  04 

11  12 
13  33 
16  08 
18  56 
21  57 
25  12 

0.42 


9.623 
25 

99 
42° 


Hour 

Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 


Log. 

Min- 

utes 

Alti- 

tudes 


370 


Latitude  62°  Declination  Same  Name* 

Declinations. 


Hour 

Annies 

0» 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

/       // 

/     /' 

/      // 

/      // 

1     ti 

/      // 

/     // 

/     // 

/     // 

/     // 

Min. 

Min. 

4 

0  17 

0  17 

0  17 

0  17 

0  17 

0  17 

0  18 

0  18 

0  18 

0  19 

0  19 

0  19 

4 

8 

107 

107 

108 

108 

109 

1  10 

1  11 

1  11 

1  12 

1  13 

1  13 

1  14 

8 

12 

2  30 

2  31 

2  33 

2  34 

2  36 

2  37 

2  39 

2  41 

2  42 

2  44 

2  45 

2  47 

12 

16 

4  26 

4  29 

4  31 

4  34 

4  36 

4  39 

4  45 

4  47 

4  50 

4  52 

4  55 

4  57 

16 

20 

6  56 

7  00 

7  04 

7  08 

7  12 

7  16 

7  24 

7  28 

7  32 

7  36 

7  40 

7  44 

20 

24 

9  59 

10  05 

10  11 

10  16 

10  22 

10  28 

10  40 

10  46 

10  51 

10  57 

1103 

1109 

24 

28 

13  35 

13  43 

13  51 

13  59 

14  07 

14  15 

14  30 

14  38 

14  46 

14  53 

15  01 

15  09 

28 

32 

17  45 

17  55 

18  05 

18  16 

18  26 

18  36 

18  56 

19  06 

19  17 

19  27 

19  37 

19  47 

32 

36 

22  28 

22  41 

22  54 

23  07 

23  20 

23  33 

23  59 

24  12 

24  25 

24  38 

24  51 

25  04 

36 

40 

27  44 

28  00 

28  16 

28  32 

28  48 

29  04 

29  36 

29  52 

30  08 

30  24 

30  40 

30  56 

40 

44 

33  33 

33  53 

34  12 

34  32 

34  51 

35  10 

35  49 

36  09 

36  28 

36  47 

37  07 

37  26 

44 

48 

39  56 

40  19 

40  42 

4105 

41  28 

4151 

42  37 

43  00 

43  23 

43  46 

44  09 

44  32 

48 

52 

46  52 

47  19 

47  46 

48  13 

48  40 

49  07 

50  01 

50  28 

50  55 

51  22 

51  49 

52  16 

52 

56 

54  21 

54  53 

55  24 

55  56 

56  27 

56  58 

58  01 

58  33 

59  04 

59  35 

60  07 

60  38 

56 

60 

62  24 

63  00 

63  36 

64  12 

64  48 

65  24 

66  36 

67  12 

67  48 

68  24 

69  00 

69  36 

60 

n 

n 

It 

ft 

ti 

It 

n 

It 

IT 

IT 

It 

n 

Ajh 

1.04 

1.05 

1.06 

1.07 

1.08 

1.09 

1.11 

1.12 

1.13 

1.14 

1.15 

1.16 

A,h 

Log. 

0.017 

0.021 

0.025 

0.029 

0.033 

0.037 

0.045 

0.049 

0.053 

0.056 

0.060 

0.064 

Log. 

03 

19 

31 

38 

42 

43 

32 

22 

08 

90 

70 

46 

Limit 

69 

68 

67 

66 

65 

65 

64 

63 

63 

62 

62 

62 

Min- 
utes 

Merid- 
ian 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/     // 

/     // 

/     // 

/     // 

/          // 

/     // 

/     // 

/      // 

/     // 

/     // 

/      // 

Min. 

4 

0  19 

0  19 

0  19 

0  19 

0  19 

0  20 

0  20 

0  20 

0  20 

0  21 

0  21 

0  22 

4 

8 

1  15 

1  16 

1  17 

1  18 

1  19 

120 

121 

122 

123 

123 

125 

126 

8 

12 

2  50 

2  51 

2  53 

2  56 

2  57 

3  00 

3  02 

3  05 

3  06 

3  08 

3  11 

3  14 

12 

16 

5  02 

5  05 

5  07 

5  12 

5  15 

5  20 

5  22 

5  27 

5  30 

5  36 

5  41 

5  46 

16 

20 

7  52 

7  56 

8  00 

8  08 

8  12 

8  20 

8  24 

8  32 

8  36 

8  44 

8  52 

9  00 

20 

24 

11  20 

1126 

11  31 

11  43 

1148 

12  00 

12  06 

12  17 

12  23 

12  35 

12  46 

12  58 

24 

28 

15  25 

15  33 

15  41 

15  57 

16  05 

16  20 

16  28 

16  44 

16  52 

17  07 

17  23 

17  38 

28 

32 

20  08 

20  18 

20  29 

20  49 

21  00 

21  20 

21  30 

2151 

22  01 

22  21 

22  42 

23  02 

32 

36 

25  30 

25  43 

25  55 

26  21 

26  34 

27  00 

27  13 

27  39 

27  52 

28  18 

28  44 

29  10 

36 

40 

3128 

3144 

32  00 

32  32 

32  48 

33  20 

33  36 

34  08 

34  24 

34  56 

35  28 

36  00 

40 

44 

38  05 

38  24 

38  43 

39  22 

39  41 

40  20 

40  39 

41  18 

41  37 

42  16 

42  55 

43  34 

44 

48 

45  18 

45  41 

46  05 

46  51 

47  14 

48  00 

48  23 

49  09 

49  32 

50  18 

5104 

51  50 

48 

52 

53  10 

53  37 

54  05 

54  59 

55  26 

56  20 

56  47 

57  41 

58  08 

59  02 

59  56 

60  50 

52 

56 

6141 

62  12 

62  43 

63  46 

64  17 

65  20 

65  51 

66  54 

67  25 

68  28 

69  31 

70  34 

56 

60 

70  48 

7124 

72  00 

73  12 

73  48 

75  00 

75  36 

76  48 

77  24 

78  36 

79  48 

8100 

60 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

1.18 

1.19 

1.20 

1.22 

1.23 

1.25 

1.26 

1.28 

1.29 

1.31 

1.33 

1.35 

Ajh 

Log. 

0.071 

0.075 

0.079 

0.086 

0.089 

0.096 

0.100 

0.107 

0.110 

0.117 

0.123 

0.130 

Log. 

88 

55 

18 

36 

91 

91 

37 

21 

59 

27 

85 

33 

Limit 

61 

61 

60 

60 

59 

58 

57 

56 

56 

55 

54 

53 

Min- 
utea 

Merid- 
ian 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

Alti- 
tudes 

Latitude  62°  Declination  Same  Name. 
Declinationb. 


371 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  22 

1  28 
3  17 
5  51 
9  08 

13  09 

17  54 

23  23 

29  36 

36  32 

44  13 

52  36 

61  44 

7137 

82  12 
It 

1.37 

0  22 

1  29 
3  20 
5  56 
9  16 

13  21 

18  10 

23  43 

30  02 

37  04 

44  51 

53  22 

62  38 

72  39 

83  24 
It 

1.39 

0  22 

1  31 
3  23 
6  01 
9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 
It 

1.41 

/      // 

0  23 

133 

3  28 

6  08 

9  36 

13  49 

18  49 

24  35 

31  06 

38  24 

46  27 

55  18 

64  54 

75  15 

86  24 
It 

1.44 

/      // 

0  23 

134 

3  31 

6  13 

9  44 

14  01 

19  05 

24  55 

31  32 

38  56 

47  06 

56  04 

65  48 

76  18 

87  36 
It 

1.46 

/      // 

0  23 

1  35 
3  33 
6  18 
9  52 

14  12 

19  21 

25  16 

3158 

39  28 

47  45 

56  50 

66  42 

77  21 

88  48 
It 

1.48 

/      // 

0  24 
137 
3  37 

6  27 

10  04 

14  30 

19  44 

25  46 

32  37 

40  16 

48  43 

57  59 

68  03 

78  55 

90  36 
It 

1.51 

/      // 

0  25 

139 

3  42 

6  34 

10  16 

14  47 

20  07 

26  17 

33  16 

4104 

49  41 

59  08 

69  24 

80  29 

92  24 
It 

1.54 

/     II 

0  25 

141 

3  46 

6  42 

10  28 

15  04 

20  31 

26  48 

33  55 

41  52 

50  40 

60  17 

70  45 

82  04 

It 
1.57 

/      // 

0  26 

1  42 
3  50 
6  50 

10  40 
15  22 
20  54 
27  18 
34  34 
42  40 
51  38 
61  26 
72  06 
83  38 

It 
1.60 

/     // 

0  26 
144 
3  54 

6  58 
10  52 
15  39 
21  18 
27  49 
35  13 
43  28 
52  36 
62  35 
73  27 
85  12 

It 
1.63 

/      // 

0  27 

146 

3  59 

7  05 

11  04 

15  57 

21  41 

28  19 

35  52 

44  16 

53  34 

63  44 

74  48 

1.66 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.136 
72 

0.143 
01 

0.149 
22 

0.158 
36 

0.164 
35 

0.170 
26 

0.178 
98 

0.187 
52 

0.195 
90 

0.204 
12 

0.212 
19 

0.220 
11 

Log. 

Limit 

53 

52 

52 

51 

50 

49 

48 

47 

46 

45 

44 

44 

Min- 
utes 

Merid- 
ian 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

t     II 

/      // 

/     // 

/     // 

/      // 

/      // 

/      // 

/      // 

/      // 

/     // 

/      II 

Min. 

4 

0  27 

0  28 

0  29 

0  30 

0  30 

0  31 

0  31 

0  33 

0  35 

0  36 

0  38 

0  40 

4 

8 

150 

1  52 

155 

158 

2  01 

2  04 

2  09 

2  14 

2  18 

2  23 

2  31 

2  39 

8 

12 

4  06 

4  12 

4  19 

4  25 

4  32 

4  41 

4  51 

5  01 

5  10 

5  22 

5  40 

5  58 

12 

16 

7  18 

7  28 

7  41 

7  51 

8  04 

8  19 

8  37 

8  55 

9  14 

9  31 

10  04 

10  34 

16 

20 

11  24 

1140 

12  00 

12  14 

12  36 

13  00 

13  28 

13  56 

14  24 

14  52 

15  44 

16  32 

20 

24 

16  25 

16  48 

17  17 

17  40 

18  09 

18  43 

19  23 

20  04 

20  45 

21  24 

22  40 

23  48 

24 

28 

22  21 

22  52 

23  31 

24  02 

24  42 

25  29 

26  25 

27  19 

28  13 

29  08 

30  50 

32  25 

28 

32 

29  11 

29  52 

30  43 

31  24 

32  15 

33  17 

34  29 

35  40 

36  51 

38  04 

40  16 

42  20 

32 

36 

36  56 

37  48 

38  53 

39  45 

40  50 

42  07 

43  38 

45  09 

46  40 

48  10 

50  59 

53  34 

36 

40 

45  36 

46  40 

48  00 

49  04 

50  24 

52  00 

53  52 

55  44 

57  36 

59  28 

62  56 

66  08 

40 

44 

55  10 

56  28 

58  05 

59  22 

60  59 

62  55 

65  11 

67  26 

44 

48 

65  38 

67  10 

69  07 

70  39 

72  34 

48 

52 

77  04 

78  52 

52 

56 

56 
60 

It 

It 

It 

It 

It 

" 

It 

It 

It 

It 

It 

It 

A,h 

1.71 

1.75 

1.80 

1.84 

1,89 

1.95 

2.02 

2.09 

2.16 

2.23 

2.36 

2.48 

Ajh 

0.233 

0.243 

0.255 

0.264 

0.276 

0.290 

0.305 

0.320 

0.334 

0.348 

0.372 

0.394 

Log. 

Log. 

00 

04 

27 

82 

46 

03 

35 

15 

45 

30 

91 

45 

Limit 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

Min- 
utes 

Merid- 
ian 

64° 

65° 

66° 

67° 

68° 

69^ 

70° 

7P 

72° 

73° 

74° 

75° 

Alti- 
tudes 

Latitude  62°  Decimation  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/       n 

/       n 

'          H 

/     " 

/     // 

/     // 

/       n 

/      '/ 

/      » 

1       n 

/     It 

f     It 

Min. 

4 

0  43 

0  43 

0  46 

0  49 

0  52 

0  57 

102 

1  10 

1  18 

1  28 

4 

8 

2  47 

2  54 

3  02 

3  15 

3  30 

3  47 

4  09 

4  38 

5  15 

5  52 

8 

12 

6  16 

6  31 

6  50 

7  18 

7  51 

8  31 

9  20 

10  25 

11  50 

13  12 

12 

16 

1104 

11  36 

12  10 

12  58 

13  57 

15  09 

16  36 

18  31 

21  02 

23  28 

16 

20 

17  20 

18  07 

19  00 

20  16 

21  48 

23  40 

25  56 

28  56 

32  52 

36  40 

20 

24 

24  58 

26  05 

27  22 

29  11 

31  23 

34  05 

37  21 

4140 

47  19 

24 

28 

33  59 

35  33 

37  14 

39  43 

42  44 

46  23 

50  50 

28 

32 

44  22 

46  25 

48  38 

5153 

55  49 

32 

36 

56  10 

58  45 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

H 

It 

n 

IT 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

2.60 

2.72 

2.85 

3.04 

3.27 

3.55 

3.89 

4.34 

4.93 

5.50 

A,h 

Log . 

0.414 

0.434 

0.454 

0.482 

0.514 

0.550 

0.589 

0.637 

0.692 

0.740 

Log. 

97 

57 

84 

87 

55 

23 

95 

49 

85 

36 

Limit 

30 

29 

28 

27 

26 

24 

22 

20 

18 

15 

12 

9 

Min- 
utes 

Merid- 
ian 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85°  1    86° 

87° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66 

o        570 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

/      // 

/     // 

1     II 

/     // 

/     // 

1     II 

/ 

//     /       II 

/     // 

/     // 

/      // 

/     // 

Min. 

4 

106 

0  53 

0  43 

0  36 

0  29 

4 

8 

4  24 

3  31 

2  54 

2  26 

156 

8 

12 

9  54 

7  55 

6  32 

5  27 

4  22 

12 

16 

17  38 

14  05 

11  36 

9  41 

7  46 

16 

20 

27  32 

22  00 

18  08 

15  08 

12  08 

20 

24 

39  39 

31  41 

26  07 

2147 

17  29 

24 

28 

43  07 

35  33 

29  40 

23  47 

28 

32 

46  25 

38  45 

3103 

32 

36 

49  02 

39  19 

36 

40 

48  32 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

r 

1 

1 

1 

1 

1 

r 

It 

n 

It 

It 

n 

K 

A,h 

4.13 

3.30 

i.n 

2.27 

1.82 

A,h 

Log. 

0.615 
95 

0.518 
51 

0.434 
57 

0.356 
03 

0.260 
07 

Log. 

Limit 

6 

3 

0 

4 

8 

12 

16 

20 

24 

26 

29 

32 

Min- 
utes 

Merid- 
ian 

88° 

89° 

90° 

89° 

88° 

87° 

86 

°      85° 

84° 

83° 

82° 

81° 

Alti- 
tudes 

Latitude  62°  Decimation  Contrary  Name. 


373 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angles 

Hin. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       // 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 

1.04 

/     // 

0  16 

.   1  06 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

49  25 

53  50 

61  48 
It 

1.03 

/     // 

0  16 

105 

2  27 

4  21 

6  48 

9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 

n 

1.02 

/      // 

0  16 

104 

2  26 

4  20 

6  46 

9  45 

13  16 

17  19 

2155 

27  04 

32  45 

38  59 

45  45 

53  03 

60  54 

1.015 

1     II 

0  16 

104 

2  25 

4  19 

6  44 

9  42 

13  12 

17  14 

21  49 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 

n 

1.01 

0  16 

104 

2  24 

4  16 

6  40 

9  36 

13  04 

17  04 

21  36 

26  40 

32  16 

38  24 

45  04 

52  16 

60  00 

n 

1.00 

1     II 

0  15 

103 

2  23 

4  13 

6  36 

9  30 

12  57 

16  54 

21  23 

26  24 

3156 

38  01 

44  37 

5144 

59  24 

n 

0.99 

/     // 

0  15 

102 

2  22 

4  10 

6  32 

9  24 

12  49 

16  44 

21  10 

26  08 

31  37 

37  38 

44  10 

51  13 

58  48 
It 

0.98 

/      // 

0  15 

102 

2  20 

4  08 

6  28 

9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
It 

0.97 

/     // 

0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 

It 

0.96 

0  15 

1  01 

2  17 
4  03 
6  20 
9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
It 

0.95 

/     // 

0  15 

100 

2  16 

4  01 

6  18 

9  04 

12  21 

16  08 

20  24 

25  12 

30  2C 

36  18 

42  35 

49  23 

56  42 

It 

0.945 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.017 
03 

0.012 
84 

0.008 
60 

0.006 
47 

0.004 
32 

0.00 

9.995 
64 

9.991 
23 

9.986 

77 

9.982 
27 

9.977 

72 

9.975 
43 

Log. 

Limit 

70 

70 

70 

71 

71 

71 

71 

71 

72 

73 

73 

73 

Min- 
utes 

Merid- 
ian 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23" 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/      // 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

It 

0.94 

/     // 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
It 

0.93 

0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 
15  42 
19  52 
24  32 
29  41 
35  20 
4128 
48  05 
55  12 

n 

0.92 

/      // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

It 

0.91 

/     // 

0  14 
0  57 

2  10 

3  51 
6  02 
8  41 

11  50 

15  27 

19  32 

24  08 

29  12 

34  45 

40  47 

47  18 

54  18 
It 

0.905 

/     // 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 

54  00 

It 

0.90 

/     // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 

15  11 

19  14 

23  44 

28  43 

34  10 

40  06 

46  31 

53  24 
II 

0.89 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
It 

0.88 

/     // 

0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 
52  12 

n 

0.87 

/     // 

0  14 
0  55 

2  04 

3  42 
5  46 
8  19 

11  18 
14  45 
18  42 
23  04 
27  55 
33  12 
38  59 
45  13 

51  54 

It 

0.865 

/     // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 

14  40 

18  35 

22  56 

27  45 

33  01 

38  45 

44  57 

5136 
It 

0.86 

/      // 

0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

11  06 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 
5100 

0.85 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.973 
13 

9.968 

48 

9.963 
79 

9.959 
04 

9.956 
65 

9.954 
24 

9.949 
39 

9.944 

48 

9.939 
52 

9.937 
02 

9.934 
50 

9.929 
42 

Log. 

Limit 

74 

75 

75 

75 

75 

76 

77 

78 

79 

79 

80 

80 

Min- 
utes 

Merid- 
ian 

16° 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

Alti- 
tudes 

374 


Latitude  62**  Decimation  Contrary  Name 


Declinations.  — 

-Inferior 

Meridian 

Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Miu. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/ 

/ 

// 

n 

// 

t 

r 

/ 

1 

It 

/ 

r 

/ 

r 

/      // 

0  12 

0  50 

152 

3  18 

5  10 

7  26 

10  08 

13  14 

16  44 

20  40 

25  00 

29  44 

34  55 

40  30 

46  30 

n 

/      // 

0  12 

0  50 

151 

3  17 

5  06 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

n 

0.77 

/        n 

0  12 

0  49 

1  50 
3  14 
5  04 
7  18 
9  56 

12  58 
16  25 
20  16 
24  31 
29  09 
34  15 
39  44 
45  36 

0.76 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.889 
30 

9.886 
49 

9.880 
81 

Log. 

Limit 

101 

101 

101 

Min- 
utes 

Merid- 
ian 

4° 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 

Angles 

/      // 

/      // 

/      // 

/      // 

Min. 

Min. 

4 

0  12 

0  12 

0  12 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

4 

8 

0  48 

0  48 

0  48 

0  47 

0  46 

0  46 

0  45 

0  45 

0  44 

0  44 

0  43 

0  42 

8 

12 

148 

148 

147 

145 

144 

142 

141 

141 

139 

1  38 

1  36 

1  35 

12 

16 

3  12 

3  10 

3  09 

3  07 

3  04 

3  02 

3  00 

2  59 

2  57 

2  54 

2  52 

2  49 

16 

20 

5  00 

4  58 

4  56 

4  52 

4  48 

4  44 

4  42 

4  40 

4  36 

4  32 

4  28 

4  24 

20 

24 

7  12 

7  09 

7  06 

7  00 

6  55 

6  49 

6  46 

6  43 

6  38 

6  32 

6  26 

6  21 

24 

28 

9  48 

9  44 

9  40 

9  33 

9  25 

9  17 

9  13 

9  09 

9  01 

8  53 

8  45 

8  37 

28 

32 

12  48 

12  43 

12  38 

12  28 

12  17 

12  07 

12  02 

1157 

11  46 

1136 

11  26 

11  15 

32 

36 

16  12 

16  06 

15  59 

15  46 

15  33 

15  20 

15  14 

15  07 

14  55 

14  42 

14  29 

14  16 

36 

40 

20  00 

19  52 

19  44 

19  28 

19  12 

18  56 

18  48 

18  40 

18  24 

18  08 

17  52 

17  36 

40 

44 

24  12 

24  02 

23  52 

23  33 

23  14 

22  54 

22  44 

22  35 

22  16 

2157 

2138 

21  18 

44 

48 

28  46 

28  34 

28  23 

28  00 

27  37 

27  14 

27  02 

26  51 

26  29 

26  08 

25  43 

25  20 

48 

52 

33  48 

33  34 

33  21 

32  54 

32  27 

32  00 

31  46 

31  33 

3105 

30  38 

30  11 

29  44 

52 

56 

39  12 

38  56 

38  40 

38  09 

37  38 

37  07 

36  51 

36  35 

36  04 

35  33 

35  02 

34  30 

56 

60 

45  00 

44  42 

44  24 

43  48 

43  12 

42  36 

42  18 

42  00 

41  24 

40  48 

40  12 

39  36 

60 

n 

n 

It 

It 

i> 

It 

It 

It 

" 

It 

It 

It 

A,h 

0.75 

0.745 

0.74 

0.73 

0.72 

0.71 

0.705 

0.70 

0.69 

0.68 

0.67 

0.66 

A,h 

Log. 

9.875 

9.872 

9.869 

9.863 

9.857 

9.851 

9.848 

9.845 

9.838 

9.832 

9.826 

9.819 

Log. 

06 

16 

23 

32 

33 

26 

19 

10 

85 

51 

07 

54 

Limit 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

Min- 
utes 

Merid- 
ian 

8° 

9° 

10° 

IP 

12= 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

Alti- 
tudes 

Latitude  62°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


375 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/     '/ 

/       n 

/     ti 

/     // 

1      II 

/     It 

/     II 

/     // 

/     // 

/     // 

/     // 

/      // 

Min. 

4 

Oil 

Oil 

Oil 

Oil 

0  10 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

4 

8 

0  43 

042 

0  41 

0  41 

0  40 

0  39 

0  38 

0  38 

0  38 

0  37 

0  36 

0  36 

8 

12 

134 

132 

132 

130 

1  29 

127 

126 

1  25 

124 

122 

121 

1  19 

12 

16 

2  48 

2  45 

2  44 

2  42 

2  39 

2  37 

2  34 

2  31 

2  28 

2  26 

2  23 

221 

16 

20 

4  22 

4  18 

4  16 

4  12 

4  08 

4  04 

4  00 

3  56 

3  52 

3  48 

3  44 

3  40 

20 

24 

6  18 

6  12 

6  09 

6  03 

5  58 

5  32 

5  46 

5  40 

5  32 

5  28 

5  23 

5  17 

24 

28 

8  33 

8  25 

8  21 

8  14 

8  06 

7  38 

7  50 

7  43 

7  35 

7  27 

7  19 

7  11 

28 

32 

11  10 

1100 

10  55 

10  45 

10  34 

10  24 

10  14 

10  04 

9  54 

9  44 

9  33 

9  23 

32 

36 

14  10 

13  56 

13  50 

13  37 

13  24 

13  11 

12  58 

12  45 

12  32 

12  18 

12  06 

11  53 

36 

40 

17  28 

17  12 

17  04 

16  48 

16  32 

16  16 

16  00 

15  44 

15  28 

15  12 

14  56 

14  40 

40 

44 

2109 

20  49 

20  39 

20  20 

20  01 

19  41 

19  22 

19  02 

18  43 

18  24 

18  04 

17  45 

44 

48 

25  08 

25  45 

24  34 

24  11 

23  48 

23  25 

23  02 

22  39 

22  16 

21  53 

21  30 

21  07 

48 

52 

29  30 

29  03 

28  50 

28  23 

27  56 

27  29 

27  02 

26  35 

26  08 

25  41 

25  14 

24  47 

52 

56 

34  15 

33  43 

33  27 

32  56 

32  25 

3153 

3122 

30  50 

30  19 

29  48 

29  16 

28  45 

56 

60 

39  18 

38  42 

38  24 

37  48 

37  12 

36  36 

36  00 

35  24 

34  48 

34  12 

33  36 

33  00 

60 

ir 

n 

H 

n 

H 

It 

It 

It 

" 

It 

It 

II 

Ajh 

0.655 

0.645 

0.64 

0.63 

0.62 

0.61 

0.60 

0.59 

0.58 

0.57 

0.56 

0.55 

A,h 

Log. 

9.816 

9.809 

9.806 

9.799 

9.792 

9.785 

9.778 

9.770 

9.763 

9.755 

9.748 

9.740 

Log. 

24 

56 

18 

34 

39 

33 

15 

85 

43 

87 

19 

36 

Limit 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

Min- 
utes 

Merid- 
ian 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

Alti- 
tudes 

Declinations 

.  —  Inferior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64°      65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Augles 

Min. 

1     II 

/      // 

/     // 

/      // 

/     // 

1     II 

/      // 

1     II 

/      // 

/      // 

/      // 

/     // 

Min. 

4 

0  09 

0  09 

0  09 

0  08 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

0  06 

0  06 

4 

8 

0  35 

0  35 

0  33 

0  32 

0  32 

0  31 

0  31 

0  30 

0  29 

0  28 

0  27 

0  27 

8 

12 

1  18 

1  16 

1  15 

1  13 

1  12 

1  11 

109 

107 

105 

1  04 

102 

0  59 

12 

16 

2  18 

2  16 

2  13 

2  11 

2  08 

2  05 

2  02 

157 

1  55 

1  52 

148 

1  45 

16 

20 

3  36 

3  32 

3  28 

3  24 

3  20 

3  16 

3  10 

3  04 

3  00 

2  56 

2  50 

2  44 

20 

24 

5  11 

5  05 

5  00 

4  54 

4  48 

4  42 

4  33 

4  25 

4  19 

4  13 

4  05 

3  56 

24 

28 

7  03 

6  56 

6  48 

6  40 

6  32      6  25 

6  12 

6  01 

5  53 

5  45 

5  34 

5  22 

28 

32 

9  13 

9  03 

8  52 

8  42 

8  32      8  22 

8  07 

7  51 

7  41 

7  31 

7  15 

7  00 

32 

36 

11  40 

1127 

11  14 

1101 

10  48|  10  35 

10  15 

9  56 

9  43 

9  30 

9  10 

8  51 

36 

40 

14  24 

14  08 

13  52 

13  36 

13  20l  13  04 

12  40 

12  16 

12  00 

11  44 

1120 

10  56 

40 

44 

17  25 

17  06 

16  47 

16  27 

16  08    15  48 

15  20 

14  50 

14  31 

14  12 

13  43 

13  13 

44 

48 

20  44 

20  21 

19  58 

19  35 

19  12j  18  49 

18  14 

17  40 

17  17 

16  54 

16  19 

15  45 

48 

52 

24  20 

23  53 

23  26 

22  59 

22  32*  22  05 

21  24 

20  44 

20  17 

19  50 

19  10 

18  29 

52 

56 

28  13 

27  42 

27  11 

26  39 

26  081  25  36 

24  49 

24  04 

23  31 

23  00 

22  12 

21  25 

56 

60 

32  24 

3148 

31  12 

30  36 

30  00    29  24 

28  30 

27  36 

27  00 

26  24 

25  30 

24  36 

60 

It 

It 

It 

n 

It 

It 

It 

n 

n 

It 

It 

H 

Ajh 

0.54 

0.53 

0.52 

0.51 

0.50 

0.49 

0.475 

0.46 

0.45 

0.44 

0.425 

0.41 

A,h 

Log. 

9.732 

9.724 

9.716 

9.707 

9.698 

9.690 

9.676 

9.662 

9.653 

9.643 

9.628 

9.612 

Log. 

39 

28 

00 

57 

97 

20 

69 

76 

21 

45 

39 

78 

Limit 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

101 

Min- 
utes 

Merid- 
ian 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

Alti- 
tudes 

376 


Latitude  63°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Angle::; 

/  // 

/  n 

/  // 

/  // 

/  // 

/  // 

/    K 

/  II 

Min. 

Min. 

4 

0  16 

0  16 

0  16 

0  16 

0  17 

0  17 

0  17 

0  17 

0  17 

0  17 

0  18 

0  18 

4 

8 

1  04 

1  04 

105 

106 

107 

107 

108 

108 

1  09 

1  10 

1  10 

1  11 

8 

12 

2  24 

2  25 

2  27 

2  28 

2  30 

2  31 

2  33 

2  34 

2  36 

2  37 

2  38 

2  39 

12 

16 

*16 

4  19 

4  21 

4  24 

4  26 

4  29 

4  31 

4  34 

4  36 

4  39 

4  42 

4  45 

16 

20 

6  40 

6  44 

6  48 

6  52 

6  56 

7  00 

7  04 

7  08 

7  12 

7  16 

7  20 

7  24 

20 

24 

9  36 

9  42 

9  48 

9  53 

9  59 

10  05 

10  11 

10  16 

10  22 

10  28 

10  34 

10  40 

24 

28 

13  04 

13  12 

13  20 

13  28 

13  35 

13  43 

13  51 

13  59 

14  07 

14  15 

14  22 

14  30 

28 

32 

17  04 

17  14 

17  24 

17  35 

17  45 

17  55 

18  05 

18  16 

18  26 

18  36 

18  46 

18  56 

32 

36 

2136 

21  49 

22  02 

22  15 

22  28 

22  41 

22  54 

23  07 

23  20 

23  33 

23  46 

23  59 

36 

40 

26  40 

26  56 

27  12 

27  28 

27  44 

28  00 

28  16 

28  32 

28  48 

29  04 

29  20 

29  36 

40 

44 

32  16 

32  35 

32  55 

33  14 

33  33 

33  53 

34  12 

34  32 

34  51 

35  10 

35  30 

35  49 

44 

48 

38  24 

38  47 

39  10 

39  33 

39  56 

40  19 

40  42 

41  05 

41  28 

4151 

42  14 

42  37 

48 

52 

45  04 

45  31 

45  58 

46  25 

46  52 

47  19 

47  46 

48  13 

48  40 

49  07 

49  34 

50  01 

52 

56 

52  16 

52  47 

53  19 

53  50 

54  21 

54  53 

55  24 

55  56 

56  27 

56  58 

57  30 

58  01 

56 

60 

60  00 

60  36 

61  12 

61  48 

62  24 

63  00 

63  36 

64  12 

64  48 

65  24 

66  00 

66  36 

60 

n 

It 

II 

n 

It 

n 

" 

" 

n 

IT 

It 

n 

A,h 

1.00 

1.01 

1.02 

1.03 

1.04 

1.05 

1.06 

1.07 

1.08 

1.09 

1.10 

1.11 

A,h 

Log. 

0.00 

0.004 

0.008 

0.012 

0.017 

0.021 

0.025 

0.029 

0.033 

0.037 

0.041 

0.045 

Log. 

32 

60 

84 

03 

19 

31 

38 

42 

43 

39 
64 

32 

Limit 

71 

70 

69 

68 

67 

66 

66 

65 

65 

64 

63 

Min- 
utes 

Merid- 
ian 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/   // 

1     " 

/   '/ 

/  // 

/  // 

1        n 

t     II 

/  // 

1     11 

/  // 

1     II 

/  // 

Min. 

4 

0  18 

0  18 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  19 

0  20 

0  20 

0  20 

4 

8 

1  11 

1  12 

1  13 

1  14 

1  15 

1  16 

1  17 

1  17 

1  19 

1  20 

1  21 

122 

8 

12 

2  41 

2  42 

2  45 

2  47 

2  48 

2  51 

2  53 

2  54 

2  57 

2  59 

3  02 

3  05 

12 

16 

4  47 

4  50 

4  55 

4  57 

5  00 

5  05 

5  07 

5  10 

5  15 

5  17 

5  22 

5  27 

16 

20 

7  28 

7  32 

7  40 

7  44 

7  48 

7  56 

8  00 

8  04 

8  12 

8  16 

8  24 

8  32 

20 

24 

10  46 

10  51 

1103 

11  09 

11  14 

11  26 

11  31 

11  37 

11  48 

11  54 

12  06 

12  17 

24 

28 

14  38 

14  46 

15  01 

15  09 

15  17 

15  33 

15  41 

15  49 

16  05 

16  12 

16  28 

16  44 

28 

32 

19  06 

19  17 

19  37 

19  47 

19  58 

20  18 

20  29 

20  39 

2100 

21  10 

2130 

2151 

32 

36 

24  12 

24  25 

24  51 

25  04 

25  17 

25  43 

25  55 

26  08 

26  34 

26  47 

27  13 

27  39 

36 

40 

29  52 

30  08 

30  40 

30  56 

31  12 

31  44 

32  00 

32  16 

32  48 

33  04 

33  36 

34  08 

40 

44 

36  09 

36  28 

37  07 

37  26 

37  46 

38  24 

38  43 

39  02 

39  41 

40  00 

40  39 

41  18 

44 

48 

43  00 

43  23 

44  09 

44  32 

44  55 

45  41 

46  05 

46  28 

47  14 

47  37 

48  23 

49  09 

48 

52 

50  28 

50  55 

5149 

52  16 

52  43 

53  37 

54  05 

54  32 

55  26 

55  53 

56  47 

57  41 

52 

56 

58  33 

59  04 

60  07 

60  38 

61  10 

62  12 

62  43 

63  14 

64  17 

64  48 

65  51 

66  54 

56 

60 

67  12 

67  48 

69  00 

69  36 

70  12 

71  24 

72  00 

72  36 

73  48 

74  24 

75  36 

76  48 

60 

n 

n 

It 

n 

n 

" 

II 

It 

It 

It 

It 

" 

A,h 

1.12 

1.13 

1.15 

1.16 

1.17 

1.19 

1.20 

1.21 

1.23 

1.24 

1.26 

1.28 

Ajh 

Log. 

0.049 

0.053 

0.060 

0.064 

0.068 

0.075 

0.079 

0.082 

0.089 

0.093 

0.100 

0.107 

Log. 

22 

08 

70 

46 

19 

55 

18 

79 

91 

42 

37 

21 

Limit 

62 

62 

61 

61 

60 

59 

59 

58 

58 

57 

56 

55 

Min- 
utes 

Merid- 
ian 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

Alti- 
tudes 

Latitude  63°  Declination  Same  Name. 

Declinations. 


377 


Hour 
Angles 

24° 

25° 

26° 

27° 

28°      29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 

Angles 

Min. 

/      "  1  '      " 

/      // 

/     // 

1        n 

/     // 

/      // 

/     // 

/      11 

>     11 

/     // 

'      " 

Min. 

4 

0  20 

0  21 

0  22 

0  22 

0  22 

0  23 

0  23 

0  23 

0  24      0  24 

0  25 

0  25 

4 

8 

1  23 

1  24      1  25]     1  26 

128 

130 

1  31 

1  33 

1  34      1  36 

138 

140;      8 

12 

3  06 

3  08     3  11 

3  14 

3  17 

3  23 

3  25 

3  28 

3  32 

3  36 

3  40 

3  45 

12 

16 

5  30 

5  36i     5  41 

5  46 

5  51'     5  59 

6  03 

6  08 

6  17 

6  24 

6  32 

6  39 

16 

20 

8  36     8  44     8  52 

9  00 

9  08     9  20 

9  28 

9  36 

9  49 

10  00 

10  12 

10  24 

20 

24 

12  23    12  35    12  46 

12  58 

13  09 

13  27 

13  38 

13  49 

14  08 

14  23 

14  41 

14  59 

24 

28 

16  52    17  07    17  23 

17  38 

17  54 

18  19 

18  34 

18  49 

19  14 

19  36 

20  00 

20  23 

28 

32 

22  01    22  21    22  42 

23  02 

23  23 

23  55 

24  14 

24  35 

25  06 

25  36 

26  07 

26  37 

32 

36 

27  52,  28  18    28  44 

29  10 

29  36 

30  15 

30  40 

3106 

31  46 

32  24 

33  03 

33  42 

36 

40 

34  24'  34  561  35  28 

36  00 

36  32 

37  19 

37  52 

38  24 

39  12    40  00 

40  48 

41  36     40 

44 

41  37    42  16    42  55    43  34 

44  13    45  08 

45  49 

46  27 

47  26 

48  24 

49  22 

50  18     44 

48 

49  32    50  18    51  04    51  50 

52  36,  53  42!  54  32 

55  18 

56  27 

57  36 

58  45 

59  54 

48 

52 

58  08    59  02 

59  56:  60  50 

61  44    63  06 

64  00 

64  54 

66  15 

67  36 

68  57 

70  18 

52 

56 

67  25    68  28 

69  31    70  34 

71  37    73  10 

74  13 

75  15 

76  50 

78  24 

79  58 

81  32 

56 

60 

77  24    78  36 

79  48    81  00 

82  12'  84  00 

85  12 

86  24 

60 

It          It 

n 

1 

" 

n 

n 

n 

n 

It 

It 

1 

Ajh 

1.29     1.31 

1.33 

1.35 

1.37 

1.40 

1.42 

1.44 

1.47 

1.50 

1.53 

1.56 

A,h 

Log. 

0.110   0.117 

0.123 

0.130 

0.136 

0.146 

0.152 

0.158 

0.167 

0.176 

0.184 

0.193 

Log. 

59        27 

85 

33 

72 

13 

29 

36 

32 

09 

69 

12 

Limit 

54 

54 

53 

52 

51 

50 

50 

49 

48 

47 

46 

46 

Min- 
utes 

Merid- 
ian 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

/      // 

/      II 

Min. 

Min. 

4 

0  25 

0  26 

0  27 

0  27 

0  28 

0  29 

0  30 

0  31 

0  31 

0  33 

0  35 

0  36 

4 

8 

142 

144 

147 

149 

152 

156 

159 

2  02 

2  06 

2  11 

2  17 

2  24 

8 

12 

3  49 

3  54 

4  00 

4  06 

4  12 

4  20 

4  28 

4  37 

4  46 

4  54 

5  08 

5  23 

12 

16 

6  47 

6  58 

7  08 

7  18 

7  28 

7  43 

7  56 

8  11 

8  26 

8  42 

9  08 

9  33 

16 

20 

10  36 

10  52 

1108 

11  24 

11  40 

12  03 

12  24 

12  48 

13  12 

13  36 

14  16 

14  56 

20 

24 

15  16 

15  39 

16  02 

16  25 

16  48 

17  23 

17  52 

18  26 

19  OO!  19  35 

20  33 

2130 

24 

28 

20  47 

21  18 

2149 

22  21 

22  52 

23  39 

24  18 

25  06 

25  53    26  39 

27  57 

29  16 

28 

32 

27  08 

27  49 

28  30 

29  11 

29  52 

30  53 

31  44 

32  46 

33  48    34  49 

36  31 

38  14 

32 

36 

34  21 

35  13 

36  05 

36  56 

37  48 

39  06 

40  11 

4128 

42  46    44  04 

46  14 

48  23 

36 

40 

42  24 

43  28 

44  32 

45  36 

46  40 

48  16 

49  36 

51  12 

52  48    54  24 

57  04 

59  44 

40 

44 

51  18 

52  36 

53  54 

55  10 

56  28 

58  24 

60  01 

6157 

63  53 

65  49 

-  44 

48 

61  03 

62  35 

64  07 

65  38 

67  10 

69  30 

7125 

48 

52 

7139 

73  27 

75  15 

77  04 

52 

56 

83  06 

56 

60 

60 

n 

It 

n 

It 

* 

It 

It 

n 

n 

It 

It 

n 

A,h 

1.59 

1.63 

1.67 

1.71 

1.75 

1.81 

1.86 

1.92 

1.98 

2.04 

2.14 

2.24 

A,h 

Log. 

0.201 

0.212 

0.222 

0.233 

0.243 

0.257 

0.269 

0.283 

0.296 

0.309 

0.330 

0.350 

Log. 

40 

19 

72 

00 

04 

68 

51 

30 

67 

63 

41 

25 

Limit 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

Min- 
utes 

Merid- 
ian 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72» 

73° 

74° 

Alti- 
tudes 

378 


Latitude  6Z°  Declination  Same  Name. 

Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/        n 

/     // 

/      // 

/      // 

/      // 

/      // 

/        n 

/      // 

/      // 

Min. 

Min. 

4 

0  38 

0  39 

0  41 

0  43 

0  46 

0  49 

0  54 

0  59 

105 

1  15 

1  26 

4 

8 

2  30 

2  37 

2  43 

2  53 

3  04 

3  18 

3  34 

3  55 

4  22 

4  57 

5  47 

8 

12 

5  37 

5  53 

6  07 

6  29 

6  55 

7  25 

8  02 

8  48 

9  49 

1108 

13  01 

12 

16 

9  59 

10  27 

10  53 

11  31 

12  17 

13  11 

14  18 

15  40 

17  27 

19  48 

23  07 

16 

20 

15  36 

16  20 

17  00 

18  00 

19  12 

20  36 

22  20 

24  28 

27  16 

30  56 

36  08 

20 

24 

22  28 

23  31 

24  29 

25  55 

27  39 

29  40 

32  10 

35  14 

39  16 

44  33 

24 

28 

30  34 

32  01 

33  19 

35  17 

37  38 

40  23 

43  46 

47  57 

28 

32 

39  56 

4149 

43  31 

46  05 

49  09 

52  44 

32 

36 

50  33 

52  55 

55  05 

58  19 

36 

40 

62  24 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

i> 

n 

* 

1 

n 

n 

H 

If 

n 

n 

r 

Ajh 

2.34 

2.45 

2.55 

2.70 

2.88 

3.09 

3.35 

3.67 

4.09 

4.64 

5.42 

. 

A,h 

Log. 

0.369 

0.389 

0.406 

0.431 

0.459 

0.489 

0.525 

0.564 

0.611 

0.666 

0.734 

Log. 

22 

17 

54 

36 

39 

96 

04 

67 

72 

52 

00 

Limit 

32 

31 

30 

29 

28 

26 

24 

22 

20 

18 

15 

12 

Min- 
utes 

Merid- 
ian 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

t 

r 

f 

/ 

1 

n 

// 

/ 

II 

1 

/ 

r 

/ 

• 

r 

1 

4 

9 

16 

25 

36 

II 
3.8 

// 

01 
05 
11 
21 
32 
46 

3 

1 

( 

'i 

K 
2C 
2£ 
3£ 

3. 

// 

)49 
\  16 
'21 
103 
)24 
23 
59 

06 

/ 

( 

( 
1( 

le 

32 
42 

2. 

)40 
2  40 
)00 
)40 
40 

too 

40 
40 

r 

50 

1 

] 
] 

1 

0 
2 
4 
8 
2 
8 
>5 
3 
1 

n 

.9 

31 
04 
40 
16 
56 
37 
21 
07 
54 

4 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.583 
20 

0.485 
72 

0.397 
94 

0.287 
80 

Log. 

Limit 

10 

6 

3 

0 

5 

10 

14 

18 

21 

24 

27 

30 

Min- 
utes 

Merid- 
ian 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82° 

Alti. 
tudes 

Latitude  63"  Declination  0>ntfafy  Name. 


379 


Declinations 


0  16 

1  04 

2  24 
4  16 
6  40 
9  36 

13  04 
17  04 
21  36 
26  40 
32  16 
38  24 
45  04 
52  16 
60  00 

n 

1.00 


0  15 

1  03 

2  23 
4  13 
6  36 
9  30 

12  57 

16  54 

21  23 

26  24 

31  56 

38  01 

44  37 

5144 

59  24 
It 

0.99 


0  15 

1  02 

2  22 
4  10 
6  32 
9  24 

12  49 
16  44 
21  10 
26  08 
31  37 
37  38 
44  10 
51  13 
58  48 

H 

0.98 


0  15 

1  02 

2  20 
4  08 
6  28 
9  18 

12  41 

16  34 

20  57 

25  52 

31  18 

37  15 

43  43 

50  42 

58  12 
* 

0.97 


0  15 

101 

2  20 

4  06 

6  26 

9  16 

12  37 

16  28 

20  50 

25  44 

3108 

37  04 

43  30 

50  25 

57  54 
It 

0.965 


0  15 

101 

2  19 

4  05 

6  24 

9  13 

12  33 

16  23 

20  44 

25  36 

30  58 

36  52 

43  16 

50  10 

57  36 
It 

0.96 


6" 


0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 
It 

0.95 


0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 
It 

0.94 


0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 

15  53 

20  05 

24  48 

30  00 

35  43 

4155 

48  36 

55  48 
It 

0.93 


0  14 
0  58 

2  13 

3  56 
6  10 
8  53 

12  06 

15  48 

19  59 

24  40 

29  50 

35  31 

41  42 

48  20 

55  30 
It 

0.925 


10° 


0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 

15  42 

19  52 

24  32 

29  41 

35  20 

41  28 

48  05 

55  12 
It 

0.92 


11° 


0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

11  54 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

It 

0.91 


Hour 
Angles 


Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 


0.00 


9.995 
64 


9.991 
23 


9.986 

77 


9.984 
53 


9.982 
27 


9.977 

72 


9.973 
13 


9.968 
48 


9.966 
14 


9.963 
79 


9.959 
04 


Log. 


72 


72 


72 


73 


73 


73 


73 


73 


74 


74 


74 


74 


Min- 
utes 


27° 


26° 


28= 


24° 


23= 


22= 


21° 


20° 


19° 


18° 


17° 


16° 


Alti- 
tudes 


Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18°      19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

1       n 
0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

n 

0.90 

/      // 

0  14 
0  57 

2  09 

3  49 
5  58 
8  36 

1142 

15  16 

19  20 

23  52 

28  53 

34  22 

40  20 

46  46 

53  42 
It 

0.895 

1     II 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 
53  24 

n 

0.89 

/       n 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

1130 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
It 

0.88 

t       n 

0  14 
0  55 

2  06 

3  44 
5  50 
8  24 

11  26 

14  56 

18  54 

23  20 

28  15 

33  36 

39  25 

45  45 

52  30 
It 

0.875 

/      // 
0  14 
0  55 

2  05 

3  43 
5  48 
8  21 

11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

It 

0.87 

/      // 

0  14 
0  55 

2  04 

3  40 
5  44 
8  16 

11  14 
14  40 
18  35 
22  56 
27  45 
33  01 
38  45 
44  57 

5136 

It 

0.86 

/     II 
0  14 
0  54 

2  02 

3  38 
5  40 
8  10 

1106 
14  30 
18  22 
22  40 
27  26 
32  38 
38  18 
44  26 
5100 

n 

0.85 

1      II 

0  13 
0  54 

2  01 

3  36 
5  38 
8  07 

1102 
14  25 
18  15 
22  32 
27  16 
32  27 
38  04 
44  09 

50  42 

It 

0.845 

t     II 

0  13 
0  54 

2  01 

3  35 
5  36 
8  04 

10  58 
14  20 
18  09 
22  24 
27  06 
32  15 
37  51 
43  54 

50  24 

It 

0.84 

/      It 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 
14  10 
17  56 
22  08 
26  47 
31  52 
37  24 
43  23 

49  48 

It 

0.83 

1     II 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

2152 

26  28 

31  29 

36  57 

42  52 

49  12 

It 

0.82 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.954 
24 

9.951 
82 

9.949 
39 

9.944 
48 

9.942 
01 

9.939 
52 

9.934 
50 

9.929 
42 

9.926 
86 

9.924 

28 

9.919 
08 

9.913 
81 

Log. 

Limit 

75 

75 

76 

76 

76 

77 

78 

79 

80 

80 

81 

81 

Min- 
utes 

Merid- 
ian 

15° 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

70 

6° 

5° 

4° 

Alti- 
tudes 

380 


Latitude  63°  Decimation  Owitrary  Name. 
Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/ 

1 

/ 

r 

/ 

r 

/ 

// 

/ 

n 

r 

r 

// 

/ 

// 

/      // 

0  12 

0  49 

150 

3  14 

5  04 

7  18 

9  56 

12  58 

16  25 

20  16 

24  31 

29  09 

34  15 

39  44 

45  36 
It 

0.76 

0  12 

0  48 

148 

3  12 

5  00 

7  12 

9  48 

12  48 

16  12 

20  00 

24  12 

28  46 

33  48 

39  12 

45  00 
It 

0.75 

0  12 

0  48 
148 

3  10 

4  58 
7  09 
9  44 

12  43 
16  06 
19  52 
24  02 
28  34 
33  34 
38  56 
44  42 

n 

0.745 

/      // 

0  12 
0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 

15  59 

19  44 

23  52 

28  23 

33  21 

38  40 

44  24 
It 

0.74 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.880 
81 

9.875 
06 

9.872 
16 

9.869 
23 

Log. 

Limit 

103 

103 

103 

103 

Min- 
utes 

Merid- 
ian 

3° 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      // 

/      // 

/      // 

1     /' 

/      // 

/      II 

/      // 

/      // 

/      // 

/      // 

Min. 

4 

0  12 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

Oil 

4 

8 

0  47 

0  46 

0  46 

0  46 

0  45 

0  44 

0  44 

0  43 

0  43 

0  42 

0  42 

0  42 

8 

12 

145 

144 

143 

142 

141 

139 

139 

138 

136 

135 

134 

1  33 

12 

16 

3  07 

3  04 

3  03 

3  02 

2  59 

2  57 

2  56 

2  54 

2  52 

2  49 

2  48 

2  47 

16 

20 

4  52 

4  48 

4  46 

4  44 

4  40 

4  36 

4  34 

4  32 

4  28 

4  24 

4  22 

4  20 

20 

24 

7  00 

6  55 

6  52 

6  49 

6  43 

6  38 

6  36 

6  32 

6  26 

6  21 

6  18 

6  15 

24 

28 

9  33 

9  25 

9  21 

9  17 

9  09 

9  01 

8  57 

8  53 

8  45 

8  37 

8  33 

8  29 

28 

32 

12  28 

12  17 

12  12 

12  07 

1157 

1146 

1141 

1136 

11  26 

11  15 

11  10 

11  05 

32 

36 

15  46 

15  33 

15  26 

15  20 

15  07 

14  55 

14  48 

14  42 

14  29 

14  16 

14  10 

14  03 

36 

40 

19  28 

19  12 

19  04 

18  56 

18  40 

18  24 

18  16 

18  08 

17  52 

17  36 

17  28 

17  20 

40 

44 

23  33 

23  14 

23  04 

22  54 

22  35 

22  16 

22  07 

21  57 

21  38 

21  18 

21  09 

20  59 

44 

48 

28  00 

27  37 

27  26 

27  14 

26  51 

26  29 

26  18 

26  08 

25  43 

25  20 

25  08 

24  57 

48 

52 

32  54 

32  27 

32  13 

32  00 

31  33 

31  05 

30  51 

30  38 

30  11 

29  44 

29  30 

29  17 

52 

56 

38  09 

37  38 

37  22 

37  06 

36  35 

36  04 

35  48 

35  33 

35  02 

34  30 

34  15 

33  59 

56 

60 

43  48 

43  12 

42  54 

42  36 

42  00 

41  24 

4106 

40  48 

40  12 

39  36 

39  18 

39  00 

60 

It 

It 

If 

It 

It 

It 

It 

ff 

It 

It 

It 

It 

A,h 

0.73 

0.72 

0.715 

0.71 

0.70 

0.69 

0.685 

0.68 

0.67 

0.66 

0.655 

0.65 

A,h 

Log. 

9.863 

9.857 

9.854 

9.851 

9.845 

9.838 

9.835 

9.832 

9.826 

9.819 

9.816 

9.812 

Log. 

32 

33 

31 

26 

10 

85 

69 

51 

07 

54 

24 

91 

Limit 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

Min- 
utes 

Merid- 
ian 

9° 

10° 

IP 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

Alti- 
tudes 

Latitude  63°  Declination  Contrary  Name. 

Declinations.  —  Inferior  Meridian. 


381 


Hour  j  ^oo 
Angles!  **> 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angle 

Min. 
4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Oil 

0  40 

1  32 
244 
4  16 
6  09 
8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
It 

0.64 

/  // 

Oil 

0  40 

1  30 

2  42 
4  12 
6  03 
8  14 

10  45 
13  37 
16  48 
20  20 
24  11 
28  23 
32  56 
37  48 

n 

0.63 

1     II 

0  10 
0  40 
129 
2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

n 

0.62 

1     II 

0  10 
0  39 
127 

2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
31  53 

36  36 

It 

0.61 

/  // 

0  10 
0  39 
127 
2  36 

4  02 

5  49 
7  54 

10  19 

13  05 

16  08 

19  31 

23  14 

27  15 

3137 

36  18 
It 

0.605 

/   n 

0  10 

0  39 

1  26 

2  34 

4  00 

5  46 
7  50 

10  14 
12  58 
16  00 
19  22 
23  02 
27  02 
31  22 
36  00 

0.60 

/  // 

0  09 

0  38 

1  26 

2  31 

3  56 
5  40 
7  43 

10  04 
12  45 
15  44 
19  02 
22  39 
26  35 
30  50 
35  24 

0.59 

1      It 

0  09 

0  38 

1  25 

2  28 

3  52 
5  34 
7  35 
9  54 

12  32 

15  28 

18  43 

22  16 

26  08 

30  19 

34  48 
It 

0.58 

1     II 

0  09 

0  37 

1  22 

2  26 

3  48 
5  28 
7  27 
9  44 

12  19 
15  12 
18  24 
2153 
25  41 
29  48 
34  12 

0.57 

0  09 

0  36 

1  21 

2  23 

3  44 
5  23 
7  19 
9  33 

12  06 
14  56 
18  04 
2130 
25  14 
29  16 
33  36 

0.56 

/  // 

0  09 

0  36 

1  19 

2  21 

3  40 
5  17 
7  11 
9  23 

1153 

14  40 

17  45 

2107 

24  47 

28  45 

33  00 
It 

0.55 

'  n 

0  09 

0  35 

1  18 

2  18 

3  36 
5  11 
7  03 
9  13 

1140 

14  24 

17  25 

20  44 

24  20 

28  13 

32  24 
It 

0.54 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

9.806 
18 

9.799 
34 

9.792 
39 

9.785 
33 

9.781 
76 

9.778 
15 

9.770 
85 

9.763 
43 

9.755 
87 

9.748 
19 

9.740 
36 

9.732 
39 

Log. 

Limit 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

1C3 

Min- 
utes 

Merid- 
ian 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32= 

Alti- 
tudes 

Declinations. — Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

/  '/ 

/  // 

t      II 

1     II 

/  // 

/  // 

t     II 

/   // 

1     II 

/  II 

/  II 

/   // 

Min. 

4 

0  09 

0  09 

0  08 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

0  07 

0  06 

0  06 

4 

8 

0  35 

0  33 

0  32 

0  32 

0  31 

0  31 

0  30 

0  29 

0  28 

0  28 

0  27 

0  27 

8 

12 

1  16 

1  15 

113 

1  12 

1  11 

109 

108 

1  05 

104 

102 

101 

0  59 

12 

16 

2  16 

2  13 

2  11 

2  08 

2  05 

2  03 

1  58 

155 

152 

150 

147 

145 

16 

20 

3  32 

3  28 

3  24 

3  20 

3  16 

3  12 

3  06 

3  00 

2  56 

2  52 

2  48 

2  44 

20 

24 

5  05 

5  00 

4  54 

4  48 

4  42 

4  36 

4  28 

4  19 

4  13 

4  07 

4  02 

3  56 

24 

28 

6  56 

6  48 

6  40 

6  32 

6  25 

6  16 

6  05 

5  53 

5  45 

5  38 

5  30 

5  22 

28 

32 

9  03 

8  52 

8  42 

8  32 

8  22 

8  12 

7  56 

7  41 

7  31 

7  21 

7  10 

7  00 

32 

36 

11  27 

11  14 

1101 

10  48 

10  35 

10  22 

10  02 

9  43 

9  30 

9  17 

9  04 

8  51 

36 

40 

14  08 

13  52 

13  36 

13  20 

13  04 

12  48 

12  24 

12  00 

11  44 

11  28 

11  12 

10  56 

40 

44 

17  06 

16  47 

16  27 

16  08 

15  48 

15  29 

15  00 

14  31 

14  12 

13  52 

13  33 

13  13 

44 

48 

20  21 

19  58 

19  35 

19  12 

18  49 

18  26 

17  52 

17  17 

16  54 

16  31 

16  08 

15  45 

48 

52 

23  53 

23  26 

22  59 

22  32 

22  05 

2138 

20  57 

20  17 

19  50 

19  23 

18  56 

18  29 

52 

56 

27  42 

27  11 

26  39 

26  08 

25  36 

25  05 

24  18 

23  31 

23  00 

22  28 

2157 

2125 

56 

60 

3148 

31  12 

30  36 

30  00 

29  24 

28  48 

27  54 

27  00 

26  24 

25  48 

25  12 

24  36 

60 

It 

It 

If 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

0.53 

0.52 

0.51 

0.50 

0.49 

0.48 

0.465 

0.45 

0.44 

0.43 

0.42 

0.41 

A,li 

Log. 

9.724 

9.716 

9.707 

9.698 

9.690 

9.681 

9.667 

9.653 

9.643 

9.633 

9.623 

9.612 

Log. 

28 

00 

57 

97 

20 

24 

45 

21 

45 

47 

25 

78 

Limit 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

103 

Min- 
utes 

Merid- 
ian 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43= 

44= 

Alti- 
tudes 

382 


Latitude  64°  Decimation  Same  Name* 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Honr 
Angles 

Min. 

/       // 

/     // 

/     // 

1     II 

/     // 

/     // 

/      // 

/      // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  15 

0  15 

0  15 

0  15 

0  15 

0  16 

0  16 

0  16 

0  16 

0  17 

0  17 

0  17 

4 

8 

101 

102 

102 

1  02 

1  03 

104 

104 

1  05 

106 

107 

1  07 

108 

8 

12 

2  19 

2  20 

2  21 

2  22 

2  23 

2  24 

2  25 

2  27 

2  28 

2  30 

2  31 

2  33 

12 

16 

4  05 

4  08 

4  09 

4  10 

4  13 

4  16 

4  19 

4  21 

4  24 

4  26 

4  29 

4  31 

16 

20 

6  24 

6  28 

6  30 

6  32 

6  36 

6  40 

6  44 

6  48 

6  52 

6  56 

7  00 

7  04 

20 

24 

9  13 

9  18 

9  21 

9  24 

9  30 

9  36 

9  42 

9  48 

9  53 

9  59 

10  05 

10  11 

24 

28 

12  33 

12  41 

12  45 

12  49 

12  57 

13  04 

13  12 

13  20 

13  28 

13  35 

13  43 

13  51 

28 

32 

16  23 

16  34 

16  39 

16  44 

16  54 

17  04 

17  14 

17  24 

17  35 

17  45 

17  55 

18  05 

32 

36 

20  44 

20  57 

21  03 

21  10 

21  23 

21  36 

21  49 

22  02 

22  15 

22  28 

22  41 

22  54 

36 

40 

25  36 

25  52 

26  00 

26  08 

26  24 

26  40 

26  56 

27  12 

27  28 

27  44 

28  00 

28  16 

40 

44 

30  58 

31  18 

31  28 

31  37 

3156 

32  16 

32  35 

32  55 

33  14 

33  33 

33  53 

34  12 

44 

48 

36  52 

37  15 

37  27 

37  38 

38  01 

38  24 

38  47 

39  10 

39  33 

39  56 

40  19 

40  42 

48 

52 

43  16 

43  43 

43  56 

44  10 

44  37 

45  04 

45  31 

45  58 

46  25 

46  52 

47  19 

47  46 

52 

56 

50  10 

50  42 

50  57 

51  13 

51  44 

52  16 

52  47 

53  19 

53  50 

54  21 

54  53 

55  24 

56 

60 

57  36 

58  12 

58  30 

58  48 

59  24 

60  00 

60  36 

61  12 

6148 

62  24 

63  00 

63  36 

60 

H 

It 

H 

H 

n 

n 

n 

It 

It 

It 

It 

It 

A,h 

0.96 

0.97 

0.975 

0.98 

0.99 

1.00 

1.01 

1.02 

1.03 

1.04 

1.05 

1.06 

A,h 

Log. 

9.982 

9.986 

9.989 

9.991 

9.995 

0.00 

0.004 

0.008 

0.012 

0.017 

0.021 

0.025 

Log. 

27 

77 

00 

23 

64 

32 

60 

84 

03 

19 

31 

Limit 

72 

71 

70 

69 

68 

68 

67 

67 

66 

66 

65 

65 

Min- 
utes 

Merid- 
ian 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

0  17 

1  08 

2  34 
4  34 
7  08 

10  16 

13  59 

18  16 

23  07 

28  32 

34  32 

4105 

48  13 

55  56 

64  12 
It 

1.07 

/     // 

0  17 

1  09 

2  36 
4  36 
7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 
It 

1.08 

/     // 

0  17 

1  10 

2  37 
4  39 

7  16 

10  28 

14  15 

18  36 

23  33 

29  04 

35  10 

41  51 

49  07 

56  58 

65  24 
It 

1.09 

/      // 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 
14  22 
18  46 
23  46 
29  20 
35  30 
42  14 
49  34 
57  30 

66  00 

It 

1.10 

/     // 

0  18 

111 

2  39 

4  45 

7  24 

10  40 

14  30 

18  56 

23  59 

29  36 

35  49 

42  37 

50  01 

58  01 

66  36 

It 

1.11 

0  18 

1  11 

2  41 

4  47 

7  28 

10  46 

14  38 

19  06 

24  12 

29  52 

36  09 

43  00 

50  28 

58  33 

67  12 
It 

1.12 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

51  22 

59  35 

68  24 
It 

1.14 

/     // 

0  19 

113 

2  45 

4  55 

7  40 

1103 

15  01 

19  37 

24  51 

30  40 

37  07 

44  09 

51  49 

60  07 

69  00 
It 

1.15 

/      // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 

69  36 

It 

1.16 

1      II 

0  19 

1  15 

2  50 
5  02 
7  52 

1120 

15  25 

20  08 

25  30 

3128 

38  05 

45  18 

53  10 

61  41 

70  48 
It 

1.18 

/     // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 

15  33 

20  18 

25  43 

31  44 

38  24 

45  41 

53  37 

62  12 

7124 
It 

1.19 

/     // 

0  19 

1  17 

2  54 
5  10 
8  04 

11  37 
15  49 
20  39 
26  08 
32  16 
39  02 
46  28 
54  32 
63  14 

72  36 

It 

1.21 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.029 
38 

0.033 
42 

0.037 
43 

0.041 
39 

0.045 
32 

0.049 
22 

0.056 
90 

0.060 
70 

0.064 
46 

0.071 
88 

0.075 
55 

0.082 
79 

Log. 

Limit 

64 

64 

63 

63 

62 

61 

61 

60 

60 

59 

58 

57 

Min- 
utes 

Merid- 
ian 

38°  i   39°  1  40° 

41° 

42°      43° 

44° 

45° 

46° 

47° 

48° 

49° 

Alti- 
tudes 

Latitude  64°  Declination  Same  Name* 


383 


Declinations. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/     // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 
73  12 

IT 

1.22 

/     // 

0  20 

1  20 

2  59 

5  17 
8  16 
11  54 
16  12 
21  10 
26  47 
33  04 
40  00 
47  37 
55  53 
64  48 

74  24 

If 

1.24 

/     // 

0  20 

1  21 
3  02 
5  22 
8  24 

12  06 
16  28 
21  30 
27  13 
33  36 
40  39 
48  23 
56  47 
65  51 
75  36 

1.26 

/     // 

0  20 

1  22 
3  05 
5  27 
8  32 

12  17 
16  44 
2151 
27  39 
34  08 
41  18 
49  09 
57  41 
66  54 
76  48 

1.28 

/     // 

0  21 

1  23 
3  07 
5  33 
8  40 

12  29 
16  59 
22  11 
28  05 
34  40 
4157 
49  55 
58  35 
67  57 
78  00 

n 

1.30 

/     // 

021, 
'^13 

TUs 

5  36 
8  44 
12  35 
17  07 
22  21 
28  18 
34  56 
42  16 
50  18 
59  02 
68  28 
78  36 

n 

1.31 

1     II 

0  21 

1    125 

311 

5  41 

8  52 

12  46 

17  23 

22  42 

28  44 

35  28 

42  55 

5104 

59  56 

69  31 

79  48 

1.33 

1     II 

0  22 

1  27 
3  16 
5  48 
9  04 

13  04 
17  46 
23  12 
29  23 
36  16 
43  53 
52  13 
61  17 
7105 
81  36 

1.36 

/     // 

0  22 

1  28 
3  18 
5  53 
9  12 

13  15 
18  02 
23  33 
29  49 
36  48 
44  32 
52  59 
62  11 
72  08 
82  48 

1.38 

/     // 

0  22 

130 

3  23 

6  01 

9  24 

13  32 

18  26 

24  04 

30  27 

37  36 

45  29 

54  09 

63  33 

73  41 

84  36 

n 

1.41 

/     // 

0  22 

1  32 
3  24 
6  06 
9  32 

13  43 
18  42 
24  25 
30  53 
38  08 
46  08 
54  55 
64  27 
74  44 

n 

1.43 

0  23 

1  33 
3  29 
6  11 
9  40 

13  55 
18  57 
24  45 
31  19 
38  40 
46  47 
55  41 
65  21 
^5  37 

H 

1.45 

Min. 

4 

8 
12 
16 
20 

24    . 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

Log. 

0.086 
36 

0.093 
42 

0.100 
37 

0.107 
21 

0.113 
94 

0.117 

27 

0.123 
85 

0.133 
54 

0.139 

88 

0.149 
22 

0.155 
34 

0.161 
37 

Log. 

Limit 

56 

56 

55 

54 

53 

52 

52 

51 

50 

49 

48 

48 

Min- 
utes 

Merid- 
ian 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      // 

/     II 

/      // 

1      II 

/      // 

1     II 

1     II 

/      // 

/     // 

'     // 

Min. 

4 

0  23 

0  24 

0  25 

0  25 

0  26 

0  27 

0  27 

0  28 

0  29 

0  30 

0  31 

0  33 

4 

8 

136 

137 

139 

142 

143 

147 

150 

154 

156 

2  00 

2  04 

2  11 

8 

12 

3  35 

3  39 

3  43 

3  49 

3  53 

4  00 

4  08 

4  16 

4  22 

4  29 

4  41 

4  54 

12 

16 

6  21 

6  29 

6  37 

6  47 

6  55 

7  08 

7  20 

7  33 

7  46 

7  59 

8  19 

8  42 

16 

20 

9  56 

10  08 

10  20 

10  36 

10  48 

1108 

11  28 

11  48 

12  08 

12  28 

13  00 

13  36 

20 

24 

14  18 

14  36 

14  53 

15  16 

15  34 

16  02 

16  31 

16  59 

17  29 

17  57 

18  43 

19  35 

24 

28 

19  29 

19  52 

20  15 

20  47 

21  10 

21  49 

22  29 

23  08 

23  47 

24  26 

25  29 

26  39 

28 

32 

25  26 

25  56 

26  27 

27  08 

27  38 

28  30 

29  21 

30  13 

3103 

3155 

33  17 

34  49 

32 

36 

32  11 

32  50 

33  29 

34  21 

35  00 

36  05 

37  09 

38  14 

39  19 

40  24 

42  07 

44  04 

36 

40 

39  44 

40  32 

41  20 

42  24 

43  12 

44  32 

45  52 

47  12 

48  32 

49  52 

52  00 

54  24 

40 

44 

48  04 

49  03 

50  01 

51  18 

52  17 

53  54 

55  30 

57  07 

58  44 

60  21 

62  55 

65  49 

44 

48 

57  13 

58  22 

59  31 

6103 

62  12 

64  07 

66  01 

67  56 

69  53 

48 

52 

67  09 

68  30 

69  51 

7139 

73  00 

52 

56 

77  52 

79  27 

8101 

83  06 

56 

60 

60 

n 

" 

n 

n 

" 

It 

n 

It 

n 

n 

If 

If 

A,h 

1.49 

1.52 

1.55 

1.59 

1.62 

1.67 

1.72 

\ni 

1.82 

1.87 

1.95 

2.04 

A,h 

Log. 

0.173 

0.181 

0.190 

0.201 

0.209 

0.222 

0.235 

0.247 

0.260 

0.271 

0.290 

0.309 

Log. 

19 

84 

,33 

40 

52 

72 

53 

97 

07 

84 

03 

63 

Limit 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

Min- 
utes 

Merid- 
ian 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

Alti- 
tudes 

384 


Latitude  64°  Declination  Same  Name. 


Declinations. 


Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Alleles 

Min. 

/         H 

/       n 

r       IT 

/     » 

/     // 

/     // 

/       n 

1     " 

/       n 

1       u 

/      a 

/     // 

Min. 

4 

0  34 

0  35 

0  36 

0  38 

0  41 

0  43 

0  46 

0  51 

0  55 

102 

1  10 

1  21 

4 

8 

2  15 

2  21 

2  27 

2  35 

2  43 

2  54 

3  06 

3  22 

3  42 

4  06 

4  39 

5  26 

8 

12 

5  05 

5  17 

5  30 

5  47 

6  07 

6  32 

6  59 

7  35 

8  19 

9  14 

10  28 

12  13 

12 

16 

9  03 

9  23 

9  46 

10  17 

10  53 

1136 

12  25 

13  29 

14  45 

16  26 

18  36 

21  43 

16 

20 

14  08 

14  40 

15  16 

16  04 

17  00 

18  08 

19  24 

2104 

23  04 

25  40 

29  04 

33  56 

20 

24 

20  22 

2107 

21  59 

23  08 

24  29 

26  07 

27  56 

30  21 

33  13 

36  58 

24 

28 

27  42 

28  45 

29  56 

31  30 

33  19 

35  33 

38  02 

41  17 

28 

32 

36  10 

37  33 

39  05 

41  08 

43  31 

46  25 

49  40 

32 

36 

45  48 

47  31 

49  28 

52  03 

55  05 

36 

40 

56  32 

58  40 

6104 

40 

44 

68  25 

44 

48 

48 

52 

52 

56 

56 

60 

60 

It 

" 

" 

" 

n 

n 

n 

n 

H 

H 

It 

It 

A,h 

2.12 

2.20 

2.29 

2.41 

2.55 

2.72 

2.91 

3.16 

3.46 

3.85 

4.36 

5.09 

A,li 

Log. 

0.326 

0.342 

0.369 

0.382 

0.406 

0.434 

0.463 

0.499 

0.539 

0.585 

0.639 

0.706 

Log. 

34 

42 

84 

02 

54 

57 

89 

69 

08 

46 

49 

72 

Limit 

35 

33 

32 

31 

30 

28 

26 

24 

22 

20 

18 

15 

Min- 
utes 

Merid- 
ian 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

Alti- 
tudes 

Declinations. 


Hour 

Angles 

60°      61° 

62° 

63° 

64° 

65° 

66 

o      67° 

68°      6 

9° 

70° 

710      Hour 
'^      Angles 

Min.     ' 

//    /     // 

/     // 

/      // 

/      // 

/     // 

/ 

//    /      // 

1     II    t 

// 

/     // 

'       "     Min. 

4 

( 

)57 

0  45 

0  34 

4 

8 

$47 

3  00 

2  14 

8 

12 

{ 

J  30 

6  46 

5  02 

12 

16 

...       \l 

)06 

12  02 

8  58 

16 

20 

...      2: 

136 

18  48 

14  00 

20 

24 

...       3C 

59 

27  05 

20  10 

24 

28 

36  51 

27  26 

28 

32 

35  50 

32 

36 

36 

40 

40 

44 

44 

48 

48 

52 

52 

56 

56 

60 

60 

H                   It 

It 

It 

It 

It 

It 

r 

It 

It 

A,h 

...       3. 

54 

2.82 

2.10 

A,h 

Log. 

...       0. 

549 
00 

0.450 
25 

0.322 
22 

Log. 

Limit 

13        9 

6 

3 

0 

5 

9 

13 

17        2 

1 

25 

29 

Min- 
utes 

Merid- 
ian 

B6°      87° 

88° 

89° 

90° 

89° 

88 

D      87° 

86°      8 

5° 

84 

0 

83° 

Alti- 
tudes 

Latitude  64°  Declination  Contrary  Name. 


386 


Declinations. 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

ironr 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

/       n 

0  15 
101 
2  19 

4  05 
6  24 
9  13 
12  33 
16  23 
20  44 
25  36 
30  58 
36  52 
43  16 
50  10 
57  36 

0.96 

/      // 

0  15 

101 

2  17 

4  03 

6  20 

9  07 

12  25 

16  13 

20  31 

25  20 

30  39 

36  29 

42  49 

49  39 

57  00 

IT 

0.95 

/        n 

0  15 

100 

2  16 

4  00 

6  16 

9  01 

12  17 

16  03 

20  18 

25  04 

30  19 

36  06 

42  22 

49  07 

56  24 

0.94 

/      // 

0  14 
0  59 

2  14 

3  58 
6  12 
8  55 

12  10 
15  53 
20  05 
24  48 
30  00 
35  43 
41  55 
48  36 
55  48 

0.93 

0  14 
0  58 

2  13 

3  56 
6  10 
8  52 

12  06 

15  48 

19  59 

24  40 

29  50 

35  31 

41  42 

48  20 

55  30 
It 

0.925 

/      // 

0  14 
0  58 

2  13 

3  55 
6  08 
8  50 

12  02 

15  42 

19  52 

24  32 

29  41 

35  20 

41  28 

48  05 

55  12 
It 

0.92 

/     // 

0  14 
0  58 

2  11 

3  53 
6  04 
8  44 

1154 
15  32 
19  39 
24  16 
29  21 
34  57 
4101 
47  33 

54  36 

It 

0.91 

/      II 

0  14 
0  57 

2  10 

3  51 
6  02 
8  41 

11  50 

15  27 

19  32 

24  08 

29  12 

34  45 

40  47 

47  18 

54  18 
It 

0.905 

0  14 
0  57 

2  10 

3  50 
6  00 
8  38 

1146 
15  22 
19  26 
24  00 
29  02 
34  34 
40  34 
47  02 
54  00 

0.90 

/      // 

0  14 
0  57 

2  08 

3  48 
5  56 
8  33 

1138 
15  11 
19  14 
23  44 
28  43 
34  10 
40  06 
46  31 

53  24 

It 

0.89 

/      // 

0  14 
0  56 

2  07 

3  45 
5  52 
8  27 

11  30 

15  01 

19  01 

23  28 

28  24 

33  47 

39  39 

46  00 

52  48 
It 

0.88 

/      // 

0  14 
0  55 

2  05 

3  43 

5  48 
8  21 
11  22 
14  51 
18  48 
23  12 
28  05 
33  24 
39  12 
45  29 

52  12 

It 

0.87 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.982    9.977 
27         72 

9.973 
13 

9.968 
48 

9.966 
14 

9.963 
79 

9.959 
04 

9.956 
65 

9.954 
24 

9.949 
39 

9.944 

48 

9.939 
52 

Log. 

Limit 

74        74 

74 

75 

75 

75 

75 

76 

76 

77 

77 

77 

Min- 
utes 

Merid- 
ian 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

Alti- 
tudes 

Declinations 

Hour 

Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

/      // 

/      // 

/      // 

/      /' 

1     II 

1     II 

/      // 

/     // 

1     II 

1     II 

/     // 

/      /' 

Min. 

4 

0  14 

0  14 

0  14 

0  14 

0  14 

0  13 

0  13 

0  13 

0  13 

0  13 

0  13 

0  12 

4 

8 

0  55 

0  55 

0  54 

0  54 

0  54 

0  53 

0  52 

0  52 

0  51 

0  51 

0  51 

0  51 

8 

12 

2  04 

2  04 

2  02 

2  01 

2  01 

159 

158 

158 

156 

155 

155 

154 

12 

16 

3  42 

3  40 

3  38 

3  36 

3  35 

3  33 

3  31 

3  30 

3  28 

3  26 

3  25 

3  22 

16 

20 

5  46 

5  44 

5  40 

5  38 

5  36 

5  32 

5  30 

5  28 

5  24 

5  22 

5  20 

5  16 

20 

24 

8  18 

8  16 

8  10 

8  07 

8  04 

7  58 

7  56 

7  53 

7  47 

7  44 

7  41 

7  35 

24 

28 

11  18 

11  14 

1106 

1102 

10  58 

10  51 

10  47 

10  43 

10  35 

10  31 

10  27 

10  20 

28 

32 

14  45 

14  40 

14  30 

14  25 

14  20 

14  10 

14  05 

13  59 

13  49 

13  44 

13  39 

13  29 

32 

36 

18  42 

18  35 

18  22 

18  16 

18  09 

17  56 

17  50 

17  43 

17  30 

17  24 

17  17 

17  04 

36 

40 

23  04 

22  56 

22  40 

22  32 

22  24 

22  08 

22  00 

21  52 

2136 

21  28 

21  20 

21  04 

40 

44 

27  55 

27  45 

27  26 

27  16 

27  06 

26  47 

26  37 

26  28 

26  08 

25  59 

25  49 

25  29 

44 

.48 

33  12 

33  01 

32  38 

32  27 

32  15 

31  52 

3140 

31  29 

31  06 

30  54 

30  43 

30  18 

48 

52 

38  59 

38  45 

38  18 

38  05 

37  51 

37  24 

37  10 

36  57 

36  30 

36  17 

36  03 

35  36 

52 

56 

45  13 

44  57 

44  26 

44  10 

43  54 

43  23 

43  08 

42  52 

42  20 

42  05 

4149 

41  17 

56 

60 

5154 

5136 

5100 

50  42 

50  24 

49  48 

49  30 

49  12 

48  36 

48  18 

48  00 

47  24 

60 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

0.865 

0.86 

0.85 

0.845 

0.84 

0.83 

0.825 

0.82 

0.81 

0.805 

0.80 

0.79 

Ajh 

Log. 

9.937 

9.934 

^29 

9.926 

9.924 

9.919 

9.916 

9.913 

9.908 

9.905 

9.903 

9.897 

Log. 

02 

50 

42 

86 

28 

08 

45 

81 

49 

80 

09 

63 

Limit 

77 

78 

78 

78 

78 

79 

80 

80 

81 

81 

81 

82 

Min- 
utes 

Merid- 
ian 

14° 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

Alti- 
tudes 

386 


Latitude  64°  Declination  Contrafy  Name. 


Declinations.  — 

-Infekior  Meridian 

r. 

Hour 

Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

H 

48 

52 

56 

60 

A,h 

/ 

// 

/ 

/ 

f 

// 

f 

r 

/ 

// 

/ 

// 

/      // 

0  12 
0  48 
147 

3  09 

4  56 
7  06 
9  40 

12  38 
15  59 
19  44 
23  52 
28  23 
33  21 
38  40 
44  24 

n 

0.74 

/      // 

0  12 
0  47 
145 

3  07 

4  52 
7  00 
9  33 

12  28 
15  46 
19  28 
23  33 
28  00 
32  54 
38  09 
43  48 

n 

0.73 

0  12 
0  47 
145 

3  06 

4  50 
6  57 
9  29 

12  22 
15  40 
19  20 
23  23 
27  49 
32  40 
37  53 
43  30 

n 

0.725 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 
43  12 

n 

0.72 

/      // 

Oil 
0  46 
143 

3  03 

4  46 
6  52 
9  21 

12  12 

15  26 

19  04 

23  04 

27  26 

32  13 

37  22 

42  54 
It 

0.715 

Min. 

4 

8 

12 

16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.869 
23 

9.863 
32 

9.860 
34 

9.857 
33 

9.854 
31 

Log. 

Limit 

107 

107 

107 

107 

107 

Min- 
utes 

Merid- 
ian 

2° 

1° 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Oil 
0  45 
141 

3  00 

4  42 
6  46 
9  13 

12  02 
15  14 
18  48 
22  44 
27  02 
3146 
36  51 
42  18 

n 

0.705 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

1157 
15  07 
18  40 
22  35 
26  51 
3133 
36  35 
42  00 

n 

0.70 

Oil 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

11  46 

14  55 

18  24 

22  16 

26  29 

3105 

36  04 

4124 

n 

0.69 

/      // 

0  11 

0  44 

139 

2  55 

4  34 

6  35 

8  56 

1141 

14  48 

18  16 

22  07 

26  18 

30  51 

35  48 

4106 

n 

0.685 

Oil 

0  43 

138 

2  54 

4  32 

6  32 

8  53 

11  36 

14  42 

18  08 

2157 

26  08 

30  38 

35  33 

40  48 
If 

0.68 

1      II 

Oil 

0  43 

1  36 

3  52 

4  28 
6  26 
8  45 

1126 
14  29 
17  52 
2138 
25  43 
30  11 
35  02 
40  12 

n 

0.67 

/      // 

Oil 

0  42 

135 

2  50 

4  26 

6  24 

8  41 

1120 

14  23 

17  44 

21  28 

25  32 

29  57 

34  46 

39  54 

0.665 

0  42 

135 

2  49 

4  24 

6  21 

8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 

n 

0.66 

/      // 

Oil 

0  42 

1  33 

2  47 
4  20 
6  15 
8 '29 

1105 
14  03 
17  20 
20  59 
24  57 
29  17 
33  59 
39  00 

0.65 

/      // 

Oil 

0  41 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 

13  50 

17  04 

20  39 

24  34 

28  50 

33  27 

38  24 
It 

0.64 

1     II 

0  11 

0  41 

131 

2  43 

4  14 

6  06 

8  17 

10  50 

13  43 

16  56 

20  29 

24  23 

28  37 

33  12 

38  06 
It 

0.635 

/      // 

Oil 

0  41 

130 

2  42 

4  12 

6  03 

8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 

n 

0.63 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.848 
19 

9.845 
10 

9.838 
85 

9.835 
69 

9.832 
51 

9.826 
07 

9.822 
82 

9.819 
54 

9.812 
91 

9.806 
18 

9.802 
77 

9.799 
34 

Log. 

Limit 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

Min- 
utes 

Merid- 
ian 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

Alti- 
tudes 

Latitude  64°  Declination  Contrary  Name. 


387 


Declinations.  —  iNrERiOR  Meridian 

Hour 
Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

Min. 

/     // 

/     ff 

/      // 

/          N 

/     // 

/     // 

/     // 

1     II 

/     // 

/      // 

/     // 

/      // 

Min. 

4 

0  10 

0  10 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

4 

8 

0  40 

0  40 

0  39 

0  38 

0  38 

0  38 

0  37 

0  36 

0  36 

0  35 

0  35 

0  33 

8 

12 

129 

127 

126 

126 

125 

124 

1  23 

1  21 

120 

1  19 

117 

1  16 

12 

16 

2  39 

2  37 

2  36 

2  34 

2  31 

2  28 

2  26 

2  23 

2  22 

2  20 

2  17 

2  15 

16 

20 

4  08 

4  04 

4  02 

4  00 

3  56 

3  52 

3  50 

3  44 

3  42 

3  38 

3  34 

3  30 

20 

24 

5  58 

5  52 

5  49 

5  46 

5  40 

5  34 

5  31 

5  23 

5  20 

5  14 

5  08 

5  03 

24 

28 

8  06 

7  58 

7  54 

7  50 

7  43 

7  35 

7  31 

7  19 

7  15 

7  07 

7  00 

6  52 

28 

32 

10  34 

10  24 

10  19 

10  14 

10  04 

9  54 

9  49 

9  33 

9  28 

9  18 

9  08 

8  57 

32 

36 

13  24 

13  11 

13  05 

12  58 

12  45 

12  32 

12  26 

12  06 

12  00 

11  46 

1134 

11  20 

36 

40 

16  32 

16  16 

16  08 

16  00 

15  44 

15  28 

15  20 

14  56 

14  48 

14  32 

14  16 

14  00 

40 

44 

20  01 

19  41 

19  31 

19  22 

19  02 

18  43 

18  34 

18  04 

17  54 

17  35 

17  15 

16  56 

44 

48 

23  48 

23  25 

23  14 

23  02 

22  39 

22  16 

22  05 

2130 

21  18 

20  56 

20  33 

20  10 

48 

52 

27  56 

27  29 

27  15 

27  02 

26  35 

26  08 

25  55 

25  14 

25  00 

24  34 

24  06 

23  40 

52 

56 

32  25 

31  53 

3137 

3122 

30  50 

30  19 

30  03 

29  16 

29  00 

28  28 

27  58 

27  27 

56 

60 

37  12 

36  36 

36  18 

36  00 

35  24 

34  48 

34  30 

33  36 

33  18 

32  42 

32  06 

31  30 

60 

ir 

It 

n 

n 

n 

n 

n 

If 

It 

It 

It 

It 

A,h 

0.62 

0.61 

0.605 

0.60 

0.59 

0.58 

0.575 

0.56 

0.555 

0.545 

0.535 

0.525 

Ajh 

Log. 

9.792 

9.785 

9.781 

9.778 

9.770 

9.763 

9.759 

9.748 

9.744 

9.736 

9.728 

9.720 

Log. 

39 

33 

76 

15 

85 

43 

67 

19 

29 

40 

35 

16 

Limit 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

Min- 
utes 

Merid- 
ian 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

Alti- 
tudes 

Declinations 

.  —  Inferior  Meridian 

Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

1     II 

/     /' 

/      // 

/      '/ 

/      // 

Min. 

Min. 

4 

0  09 

0  09 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

0  07 

0  06 

0  06 

0  06 

4 

8 

0  33 

0  32 

0  32 

0  31 

0  31 

0  31 

0  29 

0  29 

0  28 

0  27 

0  26 

0  26 

8 

12 

1  15 

1  13 

1  12 

1  11 

109 

108 

1^6 

104 

102 

101 

0  59 

0  58 

12 

16 

2  13 

2  11 

2  08 

2  05 

2  03 

2  00 

156 

154 

150 

147 

145 

142 

16 

20 

3  28 

3  24 

3  20 

3  16 

3  12 

3  08 

3  02 

2  58 

2  52 

2  48 

2  44 

2  40 

20 

24 

5  00 

4  54 

4  48 

4  42 

4  36 

4  30 

4  22 

4  16 

4  07 

4  02 

3  56 

3  50 

24 

28 

6  48 

6  40 

6  32 

6  25 

6  16 

6  09 

5  57 

5  49 

5  38 

5  30 

5  22 

5  14 

28 

32 

8  52 

8  42 

8  32 

8  22 

8  12 

8  02 

7  46 

7  36 

7  21 

7  10 

7  00 

6  50 

32 

36 

11  14 

11  01 

10  48 

10  35 

10  22 

10  09 

9  49 

9  36 

9  17 

9  04 

8  51 

8  38 

36 

40 

13  52 

13  36 

13  20 

13  04 

12  48 

12  32 

12  08 

1152 

1128 

11  12 

10  56 

10  40 

40 

44 

16  47 

16  27 

16  08 

15  48 

15  29 

15  10 

14  41 

14  21 

13  52 

13  33 

13  13 

12  54 

44 

48 

19  58 

19  35 

19  12 

18  49 

18  26 

18  03 

17  29 

17  05 

16  31 

16  08 

15  45 

15  22 

48 

52 

23  26 

22  59 

22  32 

22  05 

21  35 

21  11 

20  31 

20  04 

19  23 

18  56 

18  29 

18  02 

52 

56 

27  11 

26  39 

26  08 

25  36 

25  05 

24  34 

23  46 

23  15 

22  28 

21  57 

21  25 

20  54 

56 

60 

31  12 

30  36 

30  00 

29  24 

28  18 

28  12 

27  18 

26  42 

25  48 

25  12 

24  36 

24  00 

60 

It 

It 

It 

It 

It 

It 

It 

It 

It 

It 

n 

It 

Ajh 

0.52 

0.51 

0.50 

0.49 

0.48 

0.47 

0.455 

0.445 

0.43 

0.42 

0.41 

0.40 

A,h 

Log. 

9.716 

9.707 

9.698 

9.690 

9.681 

9.672 

9.658 

9.648 

9.633 

9.623 

9.612 

9.602 

Log. 

00 

57 

97 

20 

24 

10 

01 

36 

47 

25 

78 

06 

Limit 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

107 

Min- 
utes 

Merid- 
ian 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

440 

45° 

Alti- 
tudes 

388 


Latitude  65°  Declination  Same  Name. 

Declinations. 


Hotir 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Hour 
Anglei 

/           H 

/       n 

/      " 

/      It 

/      // 

Min. 

Min. 

4 

0  14 

0  14 

0  14 

0  14 

0  15 

0  15 

0  15 

0  15 

0  15 

0  15 

0  16 

0  16 

4 

8 

0  58 

0  58 

0  58 

0  59 

100 

1  01 

101 

1  02 

1  02 

103 

104 

104 

8 

12 

2  11 

2  13 

2  13 

2  14 

2  16 

2  17 

2  19 

2  20 

2  22 

2  23 

2  24 

2  25 

12 

16 

3  53 

3  55 

3  56 

3  58 

4  00 

4  03 

4  05 

4  08 

4  10 

4  13 

4  16 

4  19 

16 

20 

6  04 

6  08 

6  10 

6  12 

6  16 

6  20 

6  24 

6  28 

6  32 

6  36 

6  40 

6  44 

20 

24 

8  44 

8  50 

8  53 

8  55 

9  01 

9  07 

9  13 

9  18 

9  24 

9  30 

9  36 

9  42 

24 

28 

1154 

12  02 

12  06 

12  10 

12  17 

12  25 

12  33 

12  41 

12  49 

12  57 

13  04 

13  12 

28 

32 

15  32 

15  42 

15  48 

15  53 

16  03 

16  13 

16  23 

16  34 

16  44 

16  54 

17  04 

17  14 

32 

36 

19  39 

19  52 

19  59 

20  05 

20  18 

20  31 

20  44 

20  57 

21  10 

2123 

21  36 

21  49 

36 

40 

24  16 

24  32 

24  40 

24  48 

25  04 

25  20 

25  36 

25  52 

26  08 

26  24 

26  40 

26  56 

40 

44 

29  21 

29  41 

29  50 

30  00 

30  19 

30  39 

30  58 

31  18 

31  37 

31  56 

32  16 

32  35 

44 

48 

34  57 

35  20 

35  31 

35  43 

36  06 

36  29 

36  52 

37  15 

37  38 

38  01 

38  24 

38  47 

48 

52 

41  01 

41  28 

41  42 

4155 

42  22 

42  49 

43  16 

43  43 

44  10 

44  37 

45  04 

45  31 

52 

56 

47  33 

48  05 

48  20 

48  36 

49  07 

49  39 

50  10 

50  42 

51  13 

51  44 

52  16 

52  47 

56 

60 

54  36 

55  12 

55  30 

55  48 

56  24 

57  00 

57  36 

58  12 

58  48 

59  24 

60  00 

60  36 

60 

It 

It 

11 

It 

It 

It 

It 

It 

It 

It 

It 

It 

A,h 

0.91 

0.92 

0.925 

0.93 

0.94 

0.95 

0.96 

0.97 

0.98 

0.99 

1.00 

1.01 

A,h 

Log. 

9.959 

9.963 

9.966 

9.968 

9.973 

9.977 

9.982 

9.986 

9.991 

9.995 

0.00 

0.004 

Log. 

04 

79 

14 

48 

13 

72 

27 

77 

23 

64 

■  •  • 

32 

Limit 

73 

72 

71 

70 

69 

69 

69 

68 

68 

67 

67 

66 

Min- 
utes 

Merid- 
ian 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
CO 

A,h 

/        n 

0  16 

1  04 

2  25 
4  19 
6  44 
9  42 

13  12 

17  14 

2149 

26  56 

32  35 

38  47 

45  31 

52  47 

60  36 
It 

1.015 

1     II 

0  16 

1  05 

2  27 
4  21 
6  48 
9  48 

13  20 

17  24 

22  02 

27  12 

32  55 

39  10 

45  58 

53  19 

61  12 
It 

1.02 

1      II 

0  16 

106 

2  28 

4  24 

6  52 

9  53 

13  28 

17  35 

22  15 

27  28 

33  14 

39  33 

46  25 

53  50 

61  48 

1.03 

/      // 

0  17 

107 

2  30 

4  26 

6  56 

9  59 

13  35 

17  45 

22  28 

27  44 

33  33 

39  56 

46  52 

54  21 

62  24 
It 

1.04 

/      // 

0  17 

107 

2  31 

4  29 

7  00 

10  05 

13  43 

17  55 

22  41 

28  00 

33  53 

40  19 

47  19 

54  53 

63  00 

1.05 

/      // 

0  17 

1  08 

2  33 
4  31 
7  04 

10  11 

13  51 

18  05 

22  54 

28  16 

34  12 

40  42 

47  46 

55  24 

63  36 
It 

1.06 

/      // 

0  17 

109 

2  36 

4  36 

7  12 

10  22 

14  07 

18  26 

23  20 

28  48 

34  51 

41  28 

48  40 

56  27 

64  48 

n 

1.08 

/      // 

0  17 

1  10 

2  37 
4  39 
7  16 

10  28 
14  15 
18  36 
23  33 
29  04 
35  10 
4151 
49  07 
56  58 

65  24 

It 

1.09 

1     II 

0  18 

1  10 

2  38 
4  42 
7  20 

10  34 

14  22 

18  46 

23  46 

29  20 

35  30 

42  14 

49  34 

57  30 

66  00 
It 

1.10 

/      // 

0  18 

1  11 

2  39 
4  45 
7  24 

10  40 
14  30 
18  56 
23  59 
29  36 
35  49 
42  37 
50  01 
58  01 

66  36 

It 

1.11 

1     II 

0  18 

1  12 

2  42 
4  50 
7  32 

10  51 

14  46 

19  17 

24  25 

30  08 

36  28 

43  23 

50  55 

59  04 

67  48 
It 

1.13 

/      // 

0  19 

1  13 

2  44 
4  52 
7  36 

10  57 

14  53 

19  27 

24  38 

30  24 

36  47 

43  46 

5122 

59  35 

68  24 
It 

1.14 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.006 
47 

0.008 
60 

0.012 
84 

0.017 
03 

0.021 
19 

0.025 
31 

0.033 
42 

0.037 
43 

0.041 
39 

0.045 
32 

0.053 
08 

0.056 
90 

Log. 

Limit 

65 

65 

64 

64 

63 

63 

62 

62 

61 

61 

60 

59 

Min- 
utes 

Merid- 
ian 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

Alti- 
tudes 

Latitude  65°  Declination  Same  Name, 
Declinations. 


389 


Hour 
Angles 

24» 

25» 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 

8 

12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
GO 

A,h 

/     // 

0  19 

1  14 

2  47 
4  57 
7  44 

1109 
15  09 
19  47 
25  04 
30  56 
37  26 
44  32 
52  16 
60  38 
69  36 

n 

1.16 

0  19 

1  15 

2  48 
5  00 
7  48 

11  14 
15  17 
19  58 
25  17 
31  12 
37  46 
44  55 
52  43 
61  10 

70  12 

It 

1.17 

/     // 

0  19 

1  16 

2  51 
5  05 
7  56 

11  26 
15  33 
20  18 
25  43 
3144 
38  24 
45  41 
53  37 
62  12 
7124 

n 

1.19 

1     II 

0  19 
117 
2  53 
5  07 

8  00 
1131 
15  41 
20  29 
25  55 
32  00 
38  43 
46  05 
54  05 
62  43 
72  00 

n 

1.20 

/     // 

0  19 

1  18 

2  56 
5  12 
8  08 

11  43 
15  57 
20  49 
26  21 
32  32 
39  22 
46  51 
54  59 
63  46 

73  12 

If 

1.22 

/     II 

0  20 

120 

2  59 

5  17 

8  16 

1154 

16  12 

21  10 

26  47 

33  04 

40  00 

47  37 

55  53 

64  48 

74  24 

n 

1.24 

/     // 

0  20 

1  20 
3  00 
5  20 
8  20 

12  00 
16  20 
21  20 
27  00 
33  20 
40  20 
48  00 
56  20 
65  20 

75  00 

It 

1.25 

/     // 

0  20 

1  21 
3  03 
5  25 
8  28 

12  11 

16  36 

21  41 

27  26 

33  52 

40  59 

48  46 

57  14 

66  23 

76  12 
It 

1.27 

/      // 

0  21 

1  23 
3  07 
5  33 
8  40 

12  29 
16  59 
22  11 
28  05 
34  40 
4157 
49  55 
58  35 
67  57 

78  00 

It 

1.30 

/     // 

0  21 

1  24 
3  10 
5  38 
8  48 

12  41 
17  15 
22  31 
28  31 
35  12 
42  36 
50  41 
59  29 
69  00 

79  12 

It 

1.32 

/      // 

0  22 

1  26 
3  13 
5  43 
8  56 

12  52 
17  30 
22  52 
28  57 
35  44 
43  14 
51  27 
60  23 
70  02 
80  24 

1.34 

0  22 

127 

3  16 

5  48 

9  04 

13  04 

17  46 

23  12 

29  23 

36  16 

43  53 

52  13 

61  17 

7105 

8136 
It 

1.36 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

Log. 

0.064 
46 

0.068 
19 

0.075 
55 

0.079 

18 

0.086 
36 

0.093 
42 

0.096 
91 

0.103 
80 

0.113 
94 

0.120 
57 

0.127 
10 

0.133 
54 

Log 

Limit 

57 

57 

56 

55 

54 

53 

53 

52 

51 

50 

49 

49 

Min- 
utes 

Merid- 
ian 

49° 

50°      51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

/     // 

/     // 

/      II 

'      // 

/      // 

/      // 

1     II 

/      // 

/     // 

/     // 

/     // 

1     11 

Min. 

4 

0  22 

0  22 

0  23 

0  23 

0  24 

0  25 

0  25 

0  26 

0  27 

0  27 

0  28 

0  30 

4 

8 

1  29 

131 

133 

135 

1  36 

1  39 

1  42 

1  44 

147 

150 

1  54 

1  58 

8 

12 

3  20 

3  25 

3  29 

3  34 

3  36 

3  43 

3  49 

3  54 

4  00 

4  08 

4  17 

4  26 

12 

16 

5  56 

6  03 

6  11 

6  18 

6  24 

6  37 

6  47 

6  58 

7  08 

7  20 

7  35 

7  54 

16 

20 

9  16 

9  28 

9  40 

9  52 

10  00 

10  20 

10  36 

10  52 

1108 

11  28 

1152 

12  20 

20 

24 

13  21 

13  38 

13  55 

14  12 

14  24 

14  53 

15  16 

15  39 

16  02 

16  31 

17  05 

17  46 

24 

28 

18  10 

18  34 

18  57 

19  21 

19  36 

20  15 

20  47 

21  18 

2149 

22  29 

23  16 

24  10 

28 

32 

23  43 

24  14 

24  45 

25  16 

25  36 

26  27 

27  08 

27  49 

28  30 

29  21 

30  23 

3134 

32 

36 

30  02 

30  40 

31  19 

3158 

32  24 

33  29 

34  21 

35  13 

36  05 

37  09 

38  27 

39  58 

36 

40 

37  04 

37  52 

38  40 

39  28 

40  00 

4120 

42  24 

43  28 

44  32 

45  52 

47  28 

49  20 

40 

44 

44  51 

45  49 

46  47 

47  45 

48  24 

50  01 

51  18 

52  36 

53  54 

55  30 

57  26 

59  42 

44 

48 

53  22 

54  32 

55  41 

56  50 

57  36 

59  31 

6103 

62  35 

64  07 

66  01 

48 

52 

62  38 

64  00 

65  21 

66  42 

67  36 

69  51 

52 

56 

72  39 

74  13 

75  37 

56 

60 

60 

II 

It 

It 

» 

n 

It 

i> 

» 

If 

ff 

It 

It 

A,h 

1.39 

1.42 

1.45 

1.48 

1.50 

1.55 

1.59 

1.63 

1.67 

1.72 

1.78 

1.85 

A,h 

Log. 

0.143 

0.152 

0.161 

0.170 

0.176 

0.190 

0.201 

0.212 

0.222 

0.235 

0.250 

0.267 

Log. 

01 

29 

37 

26 

09 

33 

40 

19 

72 

53 

42 

17 

Limit 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

Min- 
utes 

Merid- 
ian 

61° 

62° 

63° 

64° 

65^ 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

Alti- 
tudes 

390 


Latitude  65°  Decimation  Same  Name. 

Declinations. 


Hour 

Angles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
Angles 

/      /' 

/      // 

/     // 

/     // 

/      // 

/     // 

/      // 

/     // 

/     // 

/     // 

/     // 

Mln, 

Min. 

4 

0  30 

0  31 

0  33 

0  35 

0  36 

0  38 

0  41 

0  44 

0  47 

0  52 

0  58 

105 

4 

8 

2  02 

2  07 

2  12 

2  17 

2  26 

2  34 

2  44 

2  56 

3  10 

3  28 

3  51 

4  22 

8 

12 

4  37 

4  47 

4  57 

5  09 

5  27 

5  46 

6  09 

6  35 

7  08 

7  48 

8  39 

9  49 

12 

16 

8  11 

8  29 

8  47 

9  11 

9  41 

10  14 

10  55 

11  41 

12  40 

13  52 

15  25 

17  27 

16 

20 

12  48 

13  16 

13  44 

14  20 

15  08 

16  00 

17  04 

18  16 

19  48 

21  40 

24  04 

27  16 

20 

24 

18  26 

19  06 

19  47 

20  39 

2147 

23  02 

24  35 

26  18 

28  30 

31  12 

34  40 

24 

28 

25  06 

26  01 

26  55 

28  05 

29  40 

31  22 

33  27 

35  48 

38  49 

42  28 

28 

32 

32  46 

33  58 

35  09 

36  41 

38  45 

40  58 

43  41 

46  46 

32 

36 

4128 

42  59 

44  30 

46  27 

49  02 

51  50 

36 

40 

51  12 

53  04 

54  56 

57  20 

60  32 

40 

44 

6157 

64  12 

44 

48 

48 

52 

52 

56 

56 

60 

60 

n 

" 

It 

n 

n 

n 

n 

n 

n 

n 

H 

n 

A,h 

1.92 

1.99 

2.06 

2.15 

2.27 

2.40 

2.56 

2.74 

2.97 

3.25 

3.61 

4.09 

A,h 

Log. 

0.283 

0.298 

0.313 

0.332 

0.356 

0.380 

0.408 

0.437 

0.472 

0.511 

0.557 

0.611 

Log. 

30 

85 

87 

44 

03 

21 

24 

75 

76 

88 

51 

72 

Limit 

36 

35 

34 

33 

32 

30 

28 

26 

24 

22 

20 

18 

Min- 
utes 

Merid- 
ian 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

Alti- 
tudes 

Declinatiox.s. 


Hour 

Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

r 
1 

5 
11 
20 

n 

4.7 

// 

16 
05 
26 
18 

6 

r 

// 

t 

T 

/ 

// 

/ 

T 

/ 

• 

r 

1 

1 

r 

/ 

0 
3 

7 
13 
21 

3.2 

// 

52 

28 
48 
52 
40 

5 

/ 

1 

1 
2 

0 
2 
6 

1 
7 
4 

H 

!.5 

// 

41 
46 
13 
03 
16 
52 

9 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

0.677 
61 

0.511 

88 

0.413 
30 

Log. 

Limit 

16 

12 

9 

6 

3 

0 

5 

8 

10 

12 

14 

16 

Min- 
utes 

Merid- 
ian 

85° 

86° 

87° 

88° 

89° 

90° 

89° 

88° 

87° 

86° 

85° 

84° 

Alti- 
tudes 

Latitude  65**  Declination  Contrary  Name. 


391 


Declinations 


Hour 
Angles 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

IP 

Hour 

Angles 

Mill. 

/        n 

'       n 

/     II 

/     // 

/      // 

/     // 

/          H 

/     // 

/     // 

/     // 

/     // 

/     // 

Min. 

4 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

0  14 

4 

8 

0  58 

0  57 

0  57 

0  57 

0  56 

0  56 

0  55 

0  55 

0  54 

0  54 

0  54 

0  54 

8 

12 

2  11 

2  10 

2  10 

2  08 

2  07 

2  07 

2  05 

2  04 

2  03 

2  02 

2  01 

2  00 

12 

16 

3  53 

3  51 

3  50 

3  48 

3  46 

3  45 

3  43 

3  40 

3  39 

3  38 

3  35 

3  33 

16 

20 

6  04 

6  02 

6  00 

5  56 

5  54 

5  52 

5  48 

5  44 

5  42 

5  40 

5  36 

5  34 

20 

24 

8  44 

8  41 

8  38 

8  33 

8  30 

8  27 

8  21 

8  16 

8  13 

8  10 

8  04 

8  01 

24 

28 

1154 

11  50 

1146 

1138 

11  34 

1130 

11  22 

11  14 

11  10 

1106 

10  58 

10  54 

28 

32 

15  32 

15  27 

15  22 

15  11 

15  06 

15  01 

14  51 

14  40 

14  35 

14  30 

14  20 

14  15 

32 

36 

19  39 

19  31 

19  26 

19  14 

19  07 

19  01 

18  48 

18  35 

18  28 

18  22 

18  09 

18  03 

36 

40 

24  16 

24  08 

24  00 

23  44 

23  36 

23  28 

23  12 

22  56 

22  48 

22  40 

22  24 

22  16 

40 

44 

29  21 

29  12 

29  02 

28  43 

28  34 

28  24 

28  05 

27  45 

27  36 

27  26 

27  06 

26  56 

44 

48 

34  57 

34  45 

34  34 

34  10 

33  59 

33  47 

33  24 

33  01 

32  50 

32  38 

32  15 

32  03 

48 

52 

4101 

40  47 

40  34 

40  06 

39  52 

39  39 

39  12 

38  45 

38  31 

38  18 

37  51 

37  38 

52 

56 

47  33 

47  18 

47  02 

46  31 

46  15 

46  00 

45  29 

44  57 

44  42 

44  26 

43  54 

43  39 

56 

60 

54  36 

54  18 

54  00 

53  24 

53  06 

52  48 

52  12 

5136 

51  18 

5100 

50  24 

50  06 

60 

It 

n 

n 

n 

n 

n 

n 

n 

n 

If 

n 

It 

Ajh 

0.91 

0.905 

0.90 

0.89 

0.885 

0.88 

0.87 

0.86 

0.855 

0.85 

0.84 

0.835 

A,h 

Log. 

9.959 

9.956 

9.954 

9.949 

9.946 

9.944 

9.939 

9.934 

9.931 

9.929 

9.924 

9.921 

Log. 

04 

65 

24 

39 

94 

48 

52 

50 

97 

42 

28 

69 

Limit 

76 

76 

76 

77 

77 

77 

77 

77 

78 

78 

78 

78 

Min- 
utes 

Merid- 
ian 

25° 

24° 

23° 

22° 

21° 

20° 

19° 

18° 

17° 

16° 

15° 

14° 

Alti- 
tudes 

Declinations. 


Hour 
Angles 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

Hour 

Angles 

Min. 
4 
8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

A,h 

/       // 

0  13 

0  53 

1  59 
3  33 
5  32 
7  58 

10  51 

14  10 

17  56 

22  08 

26  47 

31  52 

37  24 

43  23 

49  48 
It 

0.83 

0  13 

0  52 

158 

3  31 

5  30 

7  55 

10  47 

14  05 

17  50 

22  00 

26  37 

31  40 

37  10 

43  08 

49  30 

0.825 

/      // 

0  13 

0  52 

158 

3  30 

5  28 

7  53 

10  43 

13  59 

17  43 

21  52 

26  28 

31  29 

36  57 

42  52 

49  12 

0.82 

t     II 

0  13 

0  51 

156 

3  28 

5  24 

7  47 

10  35 

13  49 

17  30 

2136 

26  08 

3106 

36  30 

42  20 

48  36 
II 

0.81 

/     // 

0  13 

0  51 

155 

3  26 

5  22 

7  44 

10  31 

13  44 

17  24 

21  28 

25  59 

30  54 

36  17 

42  05 

48  18 

0.805 

1     II 

0  13 

0  51 

155 

3  25 

5  20 

7  41 

10  27 

13  39 

17  17 

21  20 

25  49 

30  43 

36  03 

41  49 

48  00 
It 

0.80 

t     II 

0  12 

0  51 

154 

3  22 

5  16 

7  35 

10  20 

13  29 

17  04 

21  04 

25  29 

30  18 

35  36 

41  17 

47  24 
It 

0.79 

/      // 

0  12 

0  50 

153 

3  21 

5  14 

7  32 

10  16 

13  24 

16  57 

20  56 

25  20 

30  07 

35  23 

4102 

47  06 
It 

0.785 

/      // 

0  12 

0  50 

152 

3  19 

5  12 

7  29 

10  12 

13  19 

16  51 

20  48 

25  10 

29  55 

35  09 

40  46 

46  48 

If 

0.78 

/      // 

0  12 

0  50 

151 

3  18 

5  10 

7  26 

10  08 

13  14 

16  44 

20  40 

25  00 

29  44 

34  55 

40  30 

46  30 

n 

0.775 

/      II 

0  12 

0  50 

151 

3  17 

5  08 

7  23 

10  04 

13  09 

16  38 

20  32 

24  51 

29  32 

34  42 

40  15 

46  12 

It 

0.77 

t     II 

0  12 

0  50 

150 

3  16 

5  06 

7  20 

10  00 

13  04 

16  32 

20  24 

24  42 

29  20 

34  18 

40  00 

45  54 
It 

0.765 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.919 
08 

9.916 
45 

9.913 
81 

9.908 
49 

9.905 
80 

9.903 
09 

9.897 
63 

9.894 

87 

9.892 
09 

9.889 
30 

9.886 
49 

9.883 
66 

Log. 

Limit 

78 

79 

79 

79 

80 

80 

81 

81 

81 

82 

82 

83 

Min- 
utes 

Merid- 
ian 

13° 

12° 

11° 

10° 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

Alti- 
tudes 

392 


Latitude  65°  Declination  Contrary  Name* 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Hour 
Angles 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

Ajh 

/      // 

It 

ft 

/     // 

/     // 

n 

n 

If 

1     II 

Oil 

0  46 

1  44 

3  04 

4  48 
6  55 
9  25 

12  17 
15  33 
19  12 
23  14 
27  37 
32  27 
37  38 
43  12 

n 

0.72 

/     // 

Oil 
0  46 
143 

3  03 

4  46 
6  52 
9  21 

12  12 
15  26 
19  04 
23  04 
27  25 
32  14 
37  22 
42  54 

n 

0.715 

/     // 

Oil 

0  46 

1  42 

3  02 

4  44 
6  49 
9  17 

12  07 
15  20 
18  56 
22  54 
27  14 
32  00 
37  06 
42  36 

n 

0.71 

/     // 

Oil 

0  45 

1  41 

2  59 
4  40 
6  43 
9  09 

11  57 
15  07 
18  40 
22  35 
26  51 
31  33 
36  35 
42  00 

n 

0.70 

/     // 

Oil 

0  44 

1  40 

2  58 
4  38 
6  40 
9  05 

11  51 

15  01 

18  32 

22  26 

26  40 

31  19 

36  20 

41  42 
It 

0.695 

/     // 

0  11 

0  44 

139 

2  57 

4  36 

6  38 

9  01 

11  46 

14  55 

18  24 

22  16 

26  29 

31  05 

36  04 

41  24 

n 

0.69 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.857 
33 

9.854 
31 

9.851 
26 

9.845 
10 

9.841 
98 

9.838 
85 

Log. 

Limit 

110 

110 

110 

110 

110 

110 

Min- 
utes 

Merid- 
ian 

1° 

0° 

1° 

2° 

3= 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

Alti- 
tudes 

Declinations. — Inferior  Meridian. 


Hour 
Angles 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

Hour 
Angles 

Min. 

4 

8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

/       // 

Oil 

0  44 

1  39 

2  55 
4  34 
6  35 
8  56 

1141 
14  48 
18  16 
22  07 
26  18 
30  51 
35  48 
4106 

n 

0.685 

/     // 

Oil 

0  43 

1  37 

2  53 
4  30 
6  29 
8  49 

11  31 
14  35 
18  00 
21  48 
25  54 
30  24 
35  18 
40  30 

H 

0.675 

/      // 

Oil 

0  43 

136 

2  52 

4  28 

6  26 

8  45 

11  26 

14  29 

17  52 

2138 

25  43 

30  11 

35  02 

40  12 

n 

0.67 

/      // 

Oil 

0  43 

135 

2  50 

4  26 

6  24 

8  41 

11  20 

14  22 

17  44 

2128 

25  31 

29  57 

34  46 

39  54 

n 

0.665 

/     // 

Oil 

0  43 

135 

2  49 

4  24 

6  21 

8  37 

11  15 

14  16 

17  36 

21  18 

25  20 

29  44 

34  30 

39  36 

H 

0.66 

Oil 
0  43 
133 

2  47 

4  20 

6  15 

8  29 

1105 

14  03 

17  20 

20  59 

24  57 

29  17 

33  59 

39  00 

n 

0.65 

/      // 

Oil 

0  40 

1  32 

2  45 
4  18 
6  12 
8  25 

1100 
13  56 
17  12 
20  49 
24  45 
29  03 
33  44 
38  42 

n 

0.645 

/      // 

Oil 

0  40 

1  32 

2  44 
4  16 
6  09 
8  21 

10  55 
13  50 
17  04 
20  39 
24  34 
28  50 
33  27 
38  24 

n 

0.64 

/     // 

0  10 

0  40 

1  30 

2  42 
4  12 
6  03 
8  14 

10  45 

13  37 

16  48 

20  20 

24  11 

28  23 

32  56 

37  48 
If 

0.63 

/      // 

0  10 

0  40 

1  30 

2  41 
4  10 
6  00 
8  10 

10  39 
13  30 
16  40 
20  10 
24  00 
28  10 
32  40 

37  30 

It 

0.625 

/      // 

0  10 

0  40 

1  29 

2  39 

4  08 

5  58 
8  06 

10  34 
13  24 
16  32 
20  01 
23  48 
27  56 
32  25 
37  12 

H 

0.62 

0  10 

0  40 

1  27 

2  37 

4  04 

5  52 
7  58 

10  24 
13  11 
16  16 
19  41 
23  25 
27  29 
31  53 

36  36 

It 

0.61 

Min. 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
60 

A,h 

Log. 

9.835 
69 

9.829 
30 

9.826 
07 

9.822 
82 

9.819 
54 

9.812 
91 

9.809 
56 

9.806 
18 

9.799 
34 

9.795 

88 

9.792 
39 

9.785 
33 

Log. 

Limit 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

Min- 
utes 

Merid- 
ian 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20^ 

21° 

22° 

Alti- 
tudes 

Latitude  65°  Declination  Contrary  Name. 
Declinations.  —  Inferior  Meridian. 


393 


Hour 
Jingles 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

Hour 
AnglM 

Min. 

/      'f 

1     It 

1       n 

1       n 

/     /' 

/          H 

/     * 

/      It 

/     // 

/     * 

/     // 

/       n 

Min. 

4 

0  10 

0  10 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  09 

0  08 

4 

8 

0  39 

0  39 

0  38 

0  38 

0  37 

0  37 

0  37 

0  36 

0  35 

0  34 

0  33 

0  32 

8 

12 

126 

126 

125 

124 

122 

1  22 

121 

1  19 

1  18 

1  16 

1  15 

1  13 

12 

16 

2  34 

2  33 

2  31 

2  28 

2  26 

2  24 

2  23 

2  21 

2  18 

2  16 

2  13 

2  11 

16 

20 

4  00 

3  58 

3  56 

3  52 

3  48 

3  46 

344 

3  40 

3  36 

3  32 

3  28 

3  24 

20 

24 

5  46 

5  43 

5  40 

5  34 

5  28 

5  26 

5  23 

5  17 

5  11 

5  05 

5  00 

4  54 

24 

28 

7  50 

7  46 

7  43 

7  35 

7  27 

7  23 

7  19 

7  11 

7  03 

6  56 

6  48 

6  40 

28 

32 

10  14 

10  09 

10  04 

9  54 

9  44 

9  38 

9  33 

9  23 

9  13 

9  03 

8  52 

8  42 

32 

36 

12  58 

12  52 

12  45 

12  32 

12  19 

12  12 

12  06 

11  53 

11  40 

1127 

11  14 

^1101 

36 

40 

16  00 

15  52 

15  44 

15  28 

15  12 

15  04 

14  56 

14  40 

14  24 

14  08 

13  52 

13  36 

40 

44 

19  22 

19  12 

19  02 

18  43 

18  24 

18  14 

18  04 

17  45 

17  25 

17  06 

16  47 

16  27 

44 

48 

23  02 

22  50 

22  39 

22  16 

2153 

2142 

2130 

2107 

20  44 

20  21 

19  58 

19  35 

48 

52 

27  02 

26  48 

26  35 

26  08 

25  41 

25  27 

25  14 

24  47 

24  20 

23  53 

23  26 

22  59 

52 

56 

31  22 

3106 

30  50 

30  19 

29  48 

29  32 

29  16 

28  45 

28  13 

27  42 

27  11 

26  39 

56 

60 

36  00 

35  42 

35  24 

34  48 

34  12 

33  54 

33  36 

33  00 

32  24 

3148 

31  12 

30  36 

60 

" 

n 

n 

H 

It 

n 

It 

It 

H 

IT 

* 

" 

A,h 

0.60 

0.595 

0.59 

0.58 

0.57 

0.565 

0.56 

0.55 

0.54 

0.53 

0.52 

0.51 

A,h 

Log. 

9.778 

9.774 

9.770 

9.763 

9.755 

9.752 

9.748 

9.740 

9.732 

9.724 

9.716 

9.707 

Log. 

15 

52 

85 

43 

87 

05 

19 

36 

39 

28 

00 

57 

Limit 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

Min- 
utes 

Merid- 
ian 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

Alti- 
tudes 

Declinations.  —  Inferior  Meridian. 


Hour 
Angles 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

Hour 

Angles 

Min. 

1     II 

/     // 

1     II 

/      // 

/      // 

/      // 

1     II 

/     // 

1      II 

/     It 

/     II 

/     // 

Min. 

4 

0  08 

0  08 

0  08 

0  08 

0  07 

0  07 

0  07 

0  07 

0  06 

0  06 

0  06 

0  06 

4 

8 

0  32 

0  32 

0  32 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

0  26 

0  26     0  25 

8 

12 

1  13 

1  12 

1  11 

109 

108 

107 

105 

102 

1  01 

0  59 

0  58      0  57 

12 

16 

2  10 

2  08 

2  05 

2  03 

2  00 

157 

155 

150 

1  47 

1  45 

1  42 

1  39 

16 

20 

3  22 

3  20 

3  16 

3  12 

3  08 

3  04 

3  00 

2  52 

2  48 

2  44 

2  40 

2  36 

20 

24 

4  51 

4  48 

4  42 

4  36 

4  30 

4  25 

4  19 

4  07 

4  02 

3  56 

3  50 

3  44 

24 

28 

6  36 

6  32 

6  25 

6  16 

6  09 

6  01 

5  53 

5  38 

5  30 

5  22 

5  14 

5  06 

28 

32 

8  37 

8  32 

8  22 

8  12 

8  02 

7  51 

7  41 

7  21 

7  la 

7  00 

6  50 

6  40 

32 

36 

10  54 

10  48 

10  35 

10  22 

10  09 

9  56 

9  43 

9  17 

9  04 

8  51 

8  38 

8  25 

36 

40 

13  28 

13  20 

13  04 

12  48 

12  32 

12  16 

12  00 

1128 

11  12 

10  56 

10  40 

10  24 

40 

44 

16  18 

16  08 

15  48 

15  29 

15  10 

14  50 

14  31 

13  52 

13  33 

13  13 

12  54 

12  35 

44 

48 

19  24 

19  12 

18  49 

18  26 

18  03 

17  40 

17  17 

16  31 

16  08 

15  45 

15  22 

15  00 

48 

52 

22  45 

22  32 

22  05 

2138 

21  11 

20  44 

20  17 

19  23 

18  56 

18  29 

18  02 

17  35 

52 

56 

26  24 

26  08 

25  36 

25  05 

24  34 

24  04 

23  31 

22  28 

2157 

2125 

20  54 

20  23 

56 

60 

30  18 

30  00 

19  24 

28  48 

28  12 

27  36 

27  00 

25  48 

25  12 

24  36 

24  00 

23  24 

60 

n 

n 

n 

n 

It 

It 

If 

n 

n 

n 

It 

It 

A,h 

0.505 

0.50 

0.49 

0.48 

0.47 

0.46 

0.45 

0.435 

0.42 

0.41 

0.40 

0.39 

A,h 

Log, 

9.703 

9.698 

9.690 

9.681 

9.672 

9.662 

9.653 

9.638 

9.623 

9.612 

9.602 

9.591 

Log. 

29 

■     97 

20 

24 

10 

76 

21 

49 

25 

78 

06 

06 

Limit 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

110 

Min- 
utes 

Merid- 
ian 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

Alti- 
tudes 

DIAGRAM 

FOR  THE 

SECON 

1 

1 

- 

1 

- 

— 

— 

— 

1 

1 

1 

1 

— 

1 

1 

1 

1 

1    1 

1 

1    ■ 

1 

1 

1 

1     ! 

: 

1 

' 

1 

! 

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/ 

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f— 

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1 

7 

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/ 

1 

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/ 

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i 

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1 

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,^/\ 

1 

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1 

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^ 

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V 

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A  / 

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1  /< 

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1/ 

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k     > 

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4 
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0° 
LRID 

REDUCTION  TO  THE  MERIDIAN 


PLATE  I      , 
17 


48°         52°         56^ 
N  ALTITUDES 


60"         64"         68°         72°         76°        80°         84° 

For  the  lower  ortnferior  Meridian  Passage;  add  the  Second 
Reduction  to  the  First  Reduction 


OF  THE 

UNIVERSITY 

OF 


84°  88°  90*' 


ALTITUDE-AZIMUTH  DIAGRAM 


PLATE  IL   o 


4°  8°  12°  10°  20°  24° 


32°  3C°  40°  44°  48  = 

AZIMUTHS 


50°  60°  64°  68°  72°  76°  80°  84°  88°  90° 


PLATE  111 

55    50    45    40    35    30    25    20    15 

2G    27    28    29 


bonds.  Wben  the  time  is  found  in  tlie  numbers  which  run  from  right  to  left  use  the 
Jnargin;  the  corresponding  Azimuth  will  be  found  on  the  curves  betweenl6'^and2'i 


PLATE  111 

55    50    45    40    35    30    25    20    15 

26    27    28    29 


55    50    45    40    35    30    25'    20    15 


;f60 


^onds.MTien  the  time  is  found  in  tbe  numbers  which  run  from  right  to  left  use  the 
inargln;  the  correspondiug  Azimuth  will  be  found  on  the  curves  between  16'and  2' 


TIME-AZIMUTH  DIAGRAM. 


PLATE  HI 

25  20         15 


TIME  IN  SECONDS  TO  CHANGE  ALTITUDE  ONE  MINUTE. 

Which  run  from  left  to  right  uae  the  There  are  two  scnles  for  seconds.  Wlien  the  time  la  (bund  hi  the  numbers  which  rim  ftom  right  to  left  use  Uia_ 

betwceDOO"  audio!'  Latitude  oa  the  right  hand  margin;  thccorresroudtugArlmuthwUlbe  round  on  thee 


s  between  le'aod  2t 


NGLE  OR   LONGITUDE 


PLATE  IV. 
30" 


,0  3.3  3.4  3.6  3.8 

ITUDES  ON  THE  CURVES 


4.0  4.2 


NGLE  OR   LONGITUDE 


PLATE  IV. 
80' 


,0  3.2  3.4  3.6  3.8 

ITUDES  ON  THE  CURVES 


4.0  4.2 


ERROR  IN  LATITUDE  DUE  TO  AN   ERROR  OF  ONE  MINUTE  OF  TIME  IN  THE  HOUR    ANGLE  OR   LONGITUDE 

0    0  0  00  0  30  140  0 '0  0  10  0  10  0 


PLATE  IV, 


LATITUDES  ON  THE  CURVES 


LATITUDES  ON  THE  CURVES 


ERROR  IN  LATITUDE  DUE  TO  AN  ERROR  OF  ONE  K 


4.0     4.2     4.4     4.G     4.8     5.0 
LATITUDES  ON  THE  CURVES 


Ml 


MUTE  OF  TIME  IN  THE  HOUR  ANGLE  OR    LONGITUDE      PLATE  V. 


5.8 


:s 


6.0  6.2  6.4  6.6  6.8  7.0  7.2  7.4 

LATITUDES  ON  THE  CURVES 


CO 

UJ 

_l 
o 

Z 
< 

D 
O 

I 

Q 

Z 
< 

CO 

I 
h 

N 

< 


90°                 85°                   80° 

STAR-FINE 
75°                 70°               G5° 

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1          r~  '         ~r 

1 

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i  '              i— 

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7r°     _U.     -       -t          ..             -41 

7       /      i T 7  tit  tt 

^*       _.^^     _       ..             .-              -       t    I 

/      /                       1      1 

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J-O-                I 

u 

0)  SinZ  cosh=sint  cosd;    ) 

4G  DIAGRAM. 


PLATE  VI. 
30"      25°    20^15°10°0° 


Si;nZcosL  =  sinM  cosd. 


•   -^^^r^s. 


ll^  . 


fe<^^r) 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


ASTRONOMY  LIB 


...==atft^S=«^?6i 


LD  21-100m-9,'48XB399sl6)476 


RARY 


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